1
Orientation for
Physics Lab for Chemists
2304191
Email physicslabchulaacth
This document is available at Physicslab Homepage
Website httpwwwphysicslabscchulaacth
Facebook PhysicsLab CHULA
A Glimpse of Physics
Experiments
2
3
Why experiment is important Experiment is used to identify a value of unknown quantity from the
known physics formula ie to find a gravitational constant (g) from
a swing of pendulum using an equation
Results from experiments can help formulate the relationship
between two quantities despite precise formula is yet to be
identified
It is well accepted that any new theoryhypothesis must be
physically verified by a real observation (experiment)
Sometimes an advanced experiment can lead to a new physics
phenomenon
2l
Tg
4
Goals of the physics lab courses
Measurement skills that minimize errors -
discrepancy between result and theoretical values
The use of instruments - understand how it works
and basic operation
Data recording with appropriate accuracy and
precision
Error analysis of the results
Data analysis by statistical and graphical methods
Gaining physics concept
Important Accessories
Pen
Pencil
RubberEraser
Transparent Ruler (make sure it is long enough to
draw graph)
Scientific Calculator (use of Calculator Apps on
smartphone is not allowed)
5
List of 2nd Year Physics Experiments
Number Experiment name Post-Test
1 Measurement and UncertaintiesYes
2
Simple Pendulum Linear Graph and Statistical
AnalysisNo
4 Simple Harmonic Motion and Hookersquos Law No
7 Rotational Motion No
8 Speed of sound in air Yes
11 Electrical MeasurementYes
17 Lenses and Spherical Mirrors Yes
19 Interference and Diffraction of Light No
20 Radioactivity No
21 Heat Capacity No
6
Lab Schedule
7
BSAC 191Friday 900 - 1200 AM
Week Date
Orientation 10-Jan-2020
Sport Day 17-Jan-2020
1st 24-Jan-2020
2nd 31-Jan-2020
3rd 7-Feb-2020
4th 14-Feb-2020
5th 21-Feb-2020
6th 28-Feb-2020
Midterm Week (NO LAB) 6-Mar-2020
7th 13-Mar-2020
8th 20-Mar-2020
9th 27-Mar-2020
10th 3-Apr-2020
Review 10-Apr-2020
Make -up lab 17-Apr-2020
Final Exam As announced
8
Grading policy
Experimental part (10 Labs) 70 points
7 points for each lab
2 points for general evaluations
On time for class
Manner in class
Behavior in class
5 points for
Data sheet
Post-Test in class (see course syllabus)
Final exam (written) 30 points
9
General rules Be in class no later than 10 minutes
After 10 minutes is considered being late (1 point reduction)
After 30 minutes student is not allowed to enter the lab
Dress properly according to the university code of uniforms IF NOT
you may be refused to enter the lab or 1-2 points of score will be
deduced
No use of mobile phoneTablet PCPC in class Keep those devices in a
provided plastic box on your table
2 points reduction for 1st warning on use of devices
Additional 5 points reduction for 2nd warning on use of devices
Students are required to bring the laboratory handbook and present to
the staff when signing for attendance One point will be deducted from
your total score if the laboratory handbook is not presented
10
General rules Do not leave the laboratory room at any time without notifying an
instructor
Stay at your table until the experiment is finished unless necessary
Do not make unnecessary loud noise
No food or drink in the laboratory room
11
General procedures 2-3 students per group for each experiment
Check your lab schedule and partners at the front of room 506-507 MHMK
Building or on the Website httpwwwphysicslabscchulaacth
Sign your name before getting into the lab room and obtain the data sheet
Sign up for other person is considered cheating All parties involved will
get a punishment - maximum of 7 points score deduction The issue will
also be reported to your course administrator
In some lab student is required to sign up for checking out an experiment kit
After finishing the lab all checked-out items must be returned
If damage occurs student(s) will be held responsible (charge or replacement)
Submit your data sheet on time (informed at the briefing)
Do not take your data sheet out of the lab room
It is not accepted after the class is already over
A Make-Up Class Policy If you miss more than 2 classes you have no right to take the final
examination (lt80 attendance) You are advised to ldquoWITHDRAWrdquo
before the final exam otherwise an F grade will be given
If you miss any class please contact the laboratory staff within 7 days
with supporting documents ie a medical certificate official letter from
a respected organization etc sufficiently explaining why you could not
attend the class The laboratory instructorstaff retains the right to
acceptreject those documents
Only ONE make-up experiment can be arranged for any student during
the MAKE-UP week Beware that attending a make-up class does not
necessarily reduce the number of your absences in normal class
12
Personnel amp Staff Security Issue
Threatening or injuring instructorsstaffs is a very
serious issue The issue will be reported to your
course administrator and your family If seriously
punishment will be executed to the maximum extend
by university law and criminal law
13
Personnel amp Staff Security IssueEvacuation Procedure
In Case of FireWhen you hear fire alarm or are
instructed to leave the building you should
- Bring valuable items eg money or cellphone
- Follow the staff who carries the ldquoPhysics
Room XXXrdquo sign
- Leave the building quickly and calmly to the
nearest ldquoFire Exitrdquo
- Do not use an elevator during an evacuation
- Do not use the central stairwell as emergency
exit
- Gather for a head count at the ldquoFire Assembly
Pointrdquo behind the Geology-Botany building
- Do not enter the building again until it has
been declared safe to enter by the local Fire Department
14
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 501-503
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 502
Room 503Room 501
15
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
16
Experiment 7 Rotational MotionA wheel and an axle are heavy and they are not fixed with the
clamp Therefore during the experiment do not move the wheel
or the axle and beware of the loaded mass ndash when it moves it
may hit you or your partners
Laboratory Room 503
Personnel amp Staff Security Issue
17
Experiment 11 Electrical Measurement
bull Be careful about electronic devices eg multimeters or
resistors before connecting them to a power supply
Check whether devices work well before doing the
experiment
Laboratory Room 503
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
A Glimpse of Physics
Experiments
2
3
Why experiment is important Experiment is used to identify a value of unknown quantity from the
known physics formula ie to find a gravitational constant (g) from
a swing of pendulum using an equation
Results from experiments can help formulate the relationship
between two quantities despite precise formula is yet to be
identified
It is well accepted that any new theoryhypothesis must be
physically verified by a real observation (experiment)
Sometimes an advanced experiment can lead to a new physics
phenomenon
2l
Tg
4
Goals of the physics lab courses
Measurement skills that minimize errors -
discrepancy between result and theoretical values
The use of instruments - understand how it works
and basic operation
Data recording with appropriate accuracy and
precision
Error analysis of the results
Data analysis by statistical and graphical methods
Gaining physics concept
Important Accessories
Pen
Pencil
RubberEraser
Transparent Ruler (make sure it is long enough to
draw graph)
Scientific Calculator (use of Calculator Apps on
smartphone is not allowed)
5
List of 2nd Year Physics Experiments
Number Experiment name Post-Test
1 Measurement and UncertaintiesYes
2
Simple Pendulum Linear Graph and Statistical
AnalysisNo
4 Simple Harmonic Motion and Hookersquos Law No
7 Rotational Motion No
8 Speed of sound in air Yes
11 Electrical MeasurementYes
17 Lenses and Spherical Mirrors Yes
19 Interference and Diffraction of Light No
20 Radioactivity No
21 Heat Capacity No
6
Lab Schedule
7
BSAC 191Friday 900 - 1200 AM
Week Date
Orientation 10-Jan-2020
Sport Day 17-Jan-2020
1st 24-Jan-2020
2nd 31-Jan-2020
3rd 7-Feb-2020
4th 14-Feb-2020
5th 21-Feb-2020
6th 28-Feb-2020
Midterm Week (NO LAB) 6-Mar-2020
7th 13-Mar-2020
8th 20-Mar-2020
9th 27-Mar-2020
10th 3-Apr-2020
Review 10-Apr-2020
Make -up lab 17-Apr-2020
Final Exam As announced
8
Grading policy
Experimental part (10 Labs) 70 points
7 points for each lab
2 points for general evaluations
On time for class
Manner in class
Behavior in class
5 points for
Data sheet
Post-Test in class (see course syllabus)
Final exam (written) 30 points
9
General rules Be in class no later than 10 minutes
After 10 minutes is considered being late (1 point reduction)
After 30 minutes student is not allowed to enter the lab
Dress properly according to the university code of uniforms IF NOT
you may be refused to enter the lab or 1-2 points of score will be
deduced
No use of mobile phoneTablet PCPC in class Keep those devices in a
provided plastic box on your table
2 points reduction for 1st warning on use of devices
Additional 5 points reduction for 2nd warning on use of devices
Students are required to bring the laboratory handbook and present to
the staff when signing for attendance One point will be deducted from
your total score if the laboratory handbook is not presented
10
General rules Do not leave the laboratory room at any time without notifying an
instructor
Stay at your table until the experiment is finished unless necessary
Do not make unnecessary loud noise
No food or drink in the laboratory room
11
General procedures 2-3 students per group for each experiment
Check your lab schedule and partners at the front of room 506-507 MHMK
Building or on the Website httpwwwphysicslabscchulaacth
Sign your name before getting into the lab room and obtain the data sheet
Sign up for other person is considered cheating All parties involved will
get a punishment - maximum of 7 points score deduction The issue will
also be reported to your course administrator
In some lab student is required to sign up for checking out an experiment kit
After finishing the lab all checked-out items must be returned
If damage occurs student(s) will be held responsible (charge or replacement)
Submit your data sheet on time (informed at the briefing)
Do not take your data sheet out of the lab room
It is not accepted after the class is already over
A Make-Up Class Policy If you miss more than 2 classes you have no right to take the final
examination (lt80 attendance) You are advised to ldquoWITHDRAWrdquo
before the final exam otherwise an F grade will be given
If you miss any class please contact the laboratory staff within 7 days
with supporting documents ie a medical certificate official letter from
a respected organization etc sufficiently explaining why you could not
attend the class The laboratory instructorstaff retains the right to
acceptreject those documents
Only ONE make-up experiment can be arranged for any student during
the MAKE-UP week Beware that attending a make-up class does not
necessarily reduce the number of your absences in normal class
12
Personnel amp Staff Security Issue
Threatening or injuring instructorsstaffs is a very
serious issue The issue will be reported to your
course administrator and your family If seriously
punishment will be executed to the maximum extend
by university law and criminal law
13
Personnel amp Staff Security IssueEvacuation Procedure
In Case of FireWhen you hear fire alarm or are
instructed to leave the building you should
- Bring valuable items eg money or cellphone
- Follow the staff who carries the ldquoPhysics
Room XXXrdquo sign
- Leave the building quickly and calmly to the
nearest ldquoFire Exitrdquo
- Do not use an elevator during an evacuation
- Do not use the central stairwell as emergency
exit
- Gather for a head count at the ldquoFire Assembly
Pointrdquo behind the Geology-Botany building
- Do not enter the building again until it has
been declared safe to enter by the local Fire Department
14
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 501-503
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 502
Room 503Room 501
15
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
16
Experiment 7 Rotational MotionA wheel and an axle are heavy and they are not fixed with the
clamp Therefore during the experiment do not move the wheel
or the axle and beware of the loaded mass ndash when it moves it
may hit you or your partners
Laboratory Room 503
Personnel amp Staff Security Issue
17
Experiment 11 Electrical Measurement
bull Be careful about electronic devices eg multimeters or
resistors before connecting them to a power supply
Check whether devices work well before doing the
experiment
Laboratory Room 503
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
3
Why experiment is important Experiment is used to identify a value of unknown quantity from the
known physics formula ie to find a gravitational constant (g) from
a swing of pendulum using an equation
Results from experiments can help formulate the relationship
between two quantities despite precise formula is yet to be
identified
It is well accepted that any new theoryhypothesis must be
physically verified by a real observation (experiment)
Sometimes an advanced experiment can lead to a new physics
phenomenon
2l
Tg
4
Goals of the physics lab courses
Measurement skills that minimize errors -
discrepancy between result and theoretical values
The use of instruments - understand how it works
and basic operation
Data recording with appropriate accuracy and
precision
Error analysis of the results
Data analysis by statistical and graphical methods
Gaining physics concept
Important Accessories
Pen
Pencil
RubberEraser
Transparent Ruler (make sure it is long enough to
draw graph)
Scientific Calculator (use of Calculator Apps on
smartphone is not allowed)
5
List of 2nd Year Physics Experiments
Number Experiment name Post-Test
1 Measurement and UncertaintiesYes
2
Simple Pendulum Linear Graph and Statistical
AnalysisNo
4 Simple Harmonic Motion and Hookersquos Law No
7 Rotational Motion No
8 Speed of sound in air Yes
11 Electrical MeasurementYes
17 Lenses and Spherical Mirrors Yes
19 Interference and Diffraction of Light No
20 Radioactivity No
21 Heat Capacity No
6
Lab Schedule
7
BSAC 191Friday 900 - 1200 AM
Week Date
Orientation 10-Jan-2020
Sport Day 17-Jan-2020
1st 24-Jan-2020
2nd 31-Jan-2020
3rd 7-Feb-2020
4th 14-Feb-2020
5th 21-Feb-2020
6th 28-Feb-2020
Midterm Week (NO LAB) 6-Mar-2020
7th 13-Mar-2020
8th 20-Mar-2020
9th 27-Mar-2020
10th 3-Apr-2020
Review 10-Apr-2020
Make -up lab 17-Apr-2020
Final Exam As announced
8
Grading policy
Experimental part (10 Labs) 70 points
7 points for each lab
2 points for general evaluations
On time for class
Manner in class
Behavior in class
5 points for
Data sheet
Post-Test in class (see course syllabus)
Final exam (written) 30 points
9
General rules Be in class no later than 10 minutes
After 10 minutes is considered being late (1 point reduction)
After 30 minutes student is not allowed to enter the lab
Dress properly according to the university code of uniforms IF NOT
you may be refused to enter the lab or 1-2 points of score will be
deduced
No use of mobile phoneTablet PCPC in class Keep those devices in a
provided plastic box on your table
2 points reduction for 1st warning on use of devices
Additional 5 points reduction for 2nd warning on use of devices
Students are required to bring the laboratory handbook and present to
the staff when signing for attendance One point will be deducted from
your total score if the laboratory handbook is not presented
10
General rules Do not leave the laboratory room at any time without notifying an
instructor
Stay at your table until the experiment is finished unless necessary
Do not make unnecessary loud noise
No food or drink in the laboratory room
11
General procedures 2-3 students per group for each experiment
Check your lab schedule and partners at the front of room 506-507 MHMK
Building or on the Website httpwwwphysicslabscchulaacth
Sign your name before getting into the lab room and obtain the data sheet
Sign up for other person is considered cheating All parties involved will
get a punishment - maximum of 7 points score deduction The issue will
also be reported to your course administrator
In some lab student is required to sign up for checking out an experiment kit
After finishing the lab all checked-out items must be returned
If damage occurs student(s) will be held responsible (charge or replacement)
Submit your data sheet on time (informed at the briefing)
Do not take your data sheet out of the lab room
It is not accepted after the class is already over
A Make-Up Class Policy If you miss more than 2 classes you have no right to take the final
examination (lt80 attendance) You are advised to ldquoWITHDRAWrdquo
before the final exam otherwise an F grade will be given
If you miss any class please contact the laboratory staff within 7 days
with supporting documents ie a medical certificate official letter from
a respected organization etc sufficiently explaining why you could not
attend the class The laboratory instructorstaff retains the right to
acceptreject those documents
Only ONE make-up experiment can be arranged for any student during
the MAKE-UP week Beware that attending a make-up class does not
necessarily reduce the number of your absences in normal class
12
Personnel amp Staff Security Issue
Threatening or injuring instructorsstaffs is a very
serious issue The issue will be reported to your
course administrator and your family If seriously
punishment will be executed to the maximum extend
by university law and criminal law
13
Personnel amp Staff Security IssueEvacuation Procedure
In Case of FireWhen you hear fire alarm or are
instructed to leave the building you should
- Bring valuable items eg money or cellphone
- Follow the staff who carries the ldquoPhysics
Room XXXrdquo sign
- Leave the building quickly and calmly to the
nearest ldquoFire Exitrdquo
- Do not use an elevator during an evacuation
- Do not use the central stairwell as emergency
exit
- Gather for a head count at the ldquoFire Assembly
Pointrdquo behind the Geology-Botany building
- Do not enter the building again until it has
been declared safe to enter by the local Fire Department
14
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 501-503
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 502
Room 503Room 501
15
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
16
Experiment 7 Rotational MotionA wheel and an axle are heavy and they are not fixed with the
clamp Therefore during the experiment do not move the wheel
or the axle and beware of the loaded mass ndash when it moves it
may hit you or your partners
Laboratory Room 503
Personnel amp Staff Security Issue
17
Experiment 11 Electrical Measurement
bull Be careful about electronic devices eg multimeters or
resistors before connecting them to a power supply
Check whether devices work well before doing the
experiment
Laboratory Room 503
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
4
Goals of the physics lab courses
Measurement skills that minimize errors -
discrepancy between result and theoretical values
The use of instruments - understand how it works
and basic operation
Data recording with appropriate accuracy and
precision
Error analysis of the results
Data analysis by statistical and graphical methods
Gaining physics concept
Important Accessories
Pen
Pencil
RubberEraser
Transparent Ruler (make sure it is long enough to
draw graph)
Scientific Calculator (use of Calculator Apps on
smartphone is not allowed)
5
List of 2nd Year Physics Experiments
Number Experiment name Post-Test
1 Measurement and UncertaintiesYes
2
Simple Pendulum Linear Graph and Statistical
AnalysisNo
4 Simple Harmonic Motion and Hookersquos Law No
7 Rotational Motion No
8 Speed of sound in air Yes
11 Electrical MeasurementYes
17 Lenses and Spherical Mirrors Yes
19 Interference and Diffraction of Light No
20 Radioactivity No
21 Heat Capacity No
6
Lab Schedule
7
BSAC 191Friday 900 - 1200 AM
Week Date
Orientation 10-Jan-2020
Sport Day 17-Jan-2020
1st 24-Jan-2020
2nd 31-Jan-2020
3rd 7-Feb-2020
4th 14-Feb-2020
5th 21-Feb-2020
6th 28-Feb-2020
Midterm Week (NO LAB) 6-Mar-2020
7th 13-Mar-2020
8th 20-Mar-2020
9th 27-Mar-2020
10th 3-Apr-2020
Review 10-Apr-2020
Make -up lab 17-Apr-2020
Final Exam As announced
8
Grading policy
Experimental part (10 Labs) 70 points
7 points for each lab
2 points for general evaluations
On time for class
Manner in class
Behavior in class
5 points for
Data sheet
Post-Test in class (see course syllabus)
Final exam (written) 30 points
9
General rules Be in class no later than 10 minutes
After 10 minutes is considered being late (1 point reduction)
After 30 minutes student is not allowed to enter the lab
Dress properly according to the university code of uniforms IF NOT
you may be refused to enter the lab or 1-2 points of score will be
deduced
No use of mobile phoneTablet PCPC in class Keep those devices in a
provided plastic box on your table
2 points reduction for 1st warning on use of devices
Additional 5 points reduction for 2nd warning on use of devices
Students are required to bring the laboratory handbook and present to
the staff when signing for attendance One point will be deducted from
your total score if the laboratory handbook is not presented
10
General rules Do not leave the laboratory room at any time without notifying an
instructor
Stay at your table until the experiment is finished unless necessary
Do not make unnecessary loud noise
No food or drink in the laboratory room
11
General procedures 2-3 students per group for each experiment
Check your lab schedule and partners at the front of room 506-507 MHMK
Building or on the Website httpwwwphysicslabscchulaacth
Sign your name before getting into the lab room and obtain the data sheet
Sign up for other person is considered cheating All parties involved will
get a punishment - maximum of 7 points score deduction The issue will
also be reported to your course administrator
In some lab student is required to sign up for checking out an experiment kit
After finishing the lab all checked-out items must be returned
If damage occurs student(s) will be held responsible (charge or replacement)
Submit your data sheet on time (informed at the briefing)
Do not take your data sheet out of the lab room
It is not accepted after the class is already over
A Make-Up Class Policy If you miss more than 2 classes you have no right to take the final
examination (lt80 attendance) You are advised to ldquoWITHDRAWrdquo
before the final exam otherwise an F grade will be given
If you miss any class please contact the laboratory staff within 7 days
with supporting documents ie a medical certificate official letter from
a respected organization etc sufficiently explaining why you could not
attend the class The laboratory instructorstaff retains the right to
acceptreject those documents
Only ONE make-up experiment can be arranged for any student during
the MAKE-UP week Beware that attending a make-up class does not
necessarily reduce the number of your absences in normal class
12
Personnel amp Staff Security Issue
Threatening or injuring instructorsstaffs is a very
serious issue The issue will be reported to your
course administrator and your family If seriously
punishment will be executed to the maximum extend
by university law and criminal law
13
Personnel amp Staff Security IssueEvacuation Procedure
In Case of FireWhen you hear fire alarm or are
instructed to leave the building you should
- Bring valuable items eg money or cellphone
- Follow the staff who carries the ldquoPhysics
Room XXXrdquo sign
- Leave the building quickly and calmly to the
nearest ldquoFire Exitrdquo
- Do not use an elevator during an evacuation
- Do not use the central stairwell as emergency
exit
- Gather for a head count at the ldquoFire Assembly
Pointrdquo behind the Geology-Botany building
- Do not enter the building again until it has
been declared safe to enter by the local Fire Department
14
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 501-503
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 502
Room 503Room 501
15
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
16
Experiment 7 Rotational MotionA wheel and an axle are heavy and they are not fixed with the
clamp Therefore during the experiment do not move the wheel
or the axle and beware of the loaded mass ndash when it moves it
may hit you or your partners
Laboratory Room 503
Personnel amp Staff Security Issue
17
Experiment 11 Electrical Measurement
bull Be careful about electronic devices eg multimeters or
resistors before connecting them to a power supply
Check whether devices work well before doing the
experiment
Laboratory Room 503
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
Important Accessories
Pen
Pencil
RubberEraser
Transparent Ruler (make sure it is long enough to
draw graph)
Scientific Calculator (use of Calculator Apps on
smartphone is not allowed)
5
List of 2nd Year Physics Experiments
Number Experiment name Post-Test
1 Measurement and UncertaintiesYes
2
Simple Pendulum Linear Graph and Statistical
AnalysisNo
4 Simple Harmonic Motion and Hookersquos Law No
7 Rotational Motion No
8 Speed of sound in air Yes
11 Electrical MeasurementYes
17 Lenses and Spherical Mirrors Yes
19 Interference and Diffraction of Light No
20 Radioactivity No
21 Heat Capacity No
6
Lab Schedule
7
BSAC 191Friday 900 - 1200 AM
Week Date
Orientation 10-Jan-2020
Sport Day 17-Jan-2020
1st 24-Jan-2020
2nd 31-Jan-2020
3rd 7-Feb-2020
4th 14-Feb-2020
5th 21-Feb-2020
6th 28-Feb-2020
Midterm Week (NO LAB) 6-Mar-2020
7th 13-Mar-2020
8th 20-Mar-2020
9th 27-Mar-2020
10th 3-Apr-2020
Review 10-Apr-2020
Make -up lab 17-Apr-2020
Final Exam As announced
8
Grading policy
Experimental part (10 Labs) 70 points
7 points for each lab
2 points for general evaluations
On time for class
Manner in class
Behavior in class
5 points for
Data sheet
Post-Test in class (see course syllabus)
Final exam (written) 30 points
9
General rules Be in class no later than 10 minutes
After 10 minutes is considered being late (1 point reduction)
After 30 minutes student is not allowed to enter the lab
Dress properly according to the university code of uniforms IF NOT
you may be refused to enter the lab or 1-2 points of score will be
deduced
No use of mobile phoneTablet PCPC in class Keep those devices in a
provided plastic box on your table
2 points reduction for 1st warning on use of devices
Additional 5 points reduction for 2nd warning on use of devices
Students are required to bring the laboratory handbook and present to
the staff when signing for attendance One point will be deducted from
your total score if the laboratory handbook is not presented
10
General rules Do not leave the laboratory room at any time without notifying an
instructor
Stay at your table until the experiment is finished unless necessary
Do not make unnecessary loud noise
No food or drink in the laboratory room
11
General procedures 2-3 students per group for each experiment
Check your lab schedule and partners at the front of room 506-507 MHMK
Building or on the Website httpwwwphysicslabscchulaacth
Sign your name before getting into the lab room and obtain the data sheet
Sign up for other person is considered cheating All parties involved will
get a punishment - maximum of 7 points score deduction The issue will
also be reported to your course administrator
In some lab student is required to sign up for checking out an experiment kit
After finishing the lab all checked-out items must be returned
If damage occurs student(s) will be held responsible (charge or replacement)
Submit your data sheet on time (informed at the briefing)
Do not take your data sheet out of the lab room
It is not accepted after the class is already over
A Make-Up Class Policy If you miss more than 2 classes you have no right to take the final
examination (lt80 attendance) You are advised to ldquoWITHDRAWrdquo
before the final exam otherwise an F grade will be given
If you miss any class please contact the laboratory staff within 7 days
with supporting documents ie a medical certificate official letter from
a respected organization etc sufficiently explaining why you could not
attend the class The laboratory instructorstaff retains the right to
acceptreject those documents
Only ONE make-up experiment can be arranged for any student during
the MAKE-UP week Beware that attending a make-up class does not
necessarily reduce the number of your absences in normal class
12
Personnel amp Staff Security Issue
Threatening or injuring instructorsstaffs is a very
serious issue The issue will be reported to your
course administrator and your family If seriously
punishment will be executed to the maximum extend
by university law and criminal law
13
Personnel amp Staff Security IssueEvacuation Procedure
In Case of FireWhen you hear fire alarm or are
instructed to leave the building you should
- Bring valuable items eg money or cellphone
- Follow the staff who carries the ldquoPhysics
Room XXXrdquo sign
- Leave the building quickly and calmly to the
nearest ldquoFire Exitrdquo
- Do not use an elevator during an evacuation
- Do not use the central stairwell as emergency
exit
- Gather for a head count at the ldquoFire Assembly
Pointrdquo behind the Geology-Botany building
- Do not enter the building again until it has
been declared safe to enter by the local Fire Department
14
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 501-503
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 502
Room 503Room 501
15
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
16
Experiment 7 Rotational MotionA wheel and an axle are heavy and they are not fixed with the
clamp Therefore during the experiment do not move the wheel
or the axle and beware of the loaded mass ndash when it moves it
may hit you or your partners
Laboratory Room 503
Personnel amp Staff Security Issue
17
Experiment 11 Electrical Measurement
bull Be careful about electronic devices eg multimeters or
resistors before connecting them to a power supply
Check whether devices work well before doing the
experiment
Laboratory Room 503
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
List of 2nd Year Physics Experiments
Number Experiment name Post-Test
1 Measurement and UncertaintiesYes
2
Simple Pendulum Linear Graph and Statistical
AnalysisNo
4 Simple Harmonic Motion and Hookersquos Law No
7 Rotational Motion No
8 Speed of sound in air Yes
11 Electrical MeasurementYes
17 Lenses and Spherical Mirrors Yes
19 Interference and Diffraction of Light No
20 Radioactivity No
21 Heat Capacity No
6
Lab Schedule
7
BSAC 191Friday 900 - 1200 AM
Week Date
Orientation 10-Jan-2020
Sport Day 17-Jan-2020
1st 24-Jan-2020
2nd 31-Jan-2020
3rd 7-Feb-2020
4th 14-Feb-2020
5th 21-Feb-2020
6th 28-Feb-2020
Midterm Week (NO LAB) 6-Mar-2020
7th 13-Mar-2020
8th 20-Mar-2020
9th 27-Mar-2020
10th 3-Apr-2020
Review 10-Apr-2020
Make -up lab 17-Apr-2020
Final Exam As announced
8
Grading policy
Experimental part (10 Labs) 70 points
7 points for each lab
2 points for general evaluations
On time for class
Manner in class
Behavior in class
5 points for
Data sheet
Post-Test in class (see course syllabus)
Final exam (written) 30 points
9
General rules Be in class no later than 10 minutes
After 10 minutes is considered being late (1 point reduction)
After 30 minutes student is not allowed to enter the lab
Dress properly according to the university code of uniforms IF NOT
you may be refused to enter the lab or 1-2 points of score will be
deduced
No use of mobile phoneTablet PCPC in class Keep those devices in a
provided plastic box on your table
2 points reduction for 1st warning on use of devices
Additional 5 points reduction for 2nd warning on use of devices
Students are required to bring the laboratory handbook and present to
the staff when signing for attendance One point will be deducted from
your total score if the laboratory handbook is not presented
10
General rules Do not leave the laboratory room at any time without notifying an
instructor
Stay at your table until the experiment is finished unless necessary
Do not make unnecessary loud noise
No food or drink in the laboratory room
11
General procedures 2-3 students per group for each experiment
Check your lab schedule and partners at the front of room 506-507 MHMK
Building or on the Website httpwwwphysicslabscchulaacth
Sign your name before getting into the lab room and obtain the data sheet
Sign up for other person is considered cheating All parties involved will
get a punishment - maximum of 7 points score deduction The issue will
also be reported to your course administrator
In some lab student is required to sign up for checking out an experiment kit
After finishing the lab all checked-out items must be returned
If damage occurs student(s) will be held responsible (charge or replacement)
Submit your data sheet on time (informed at the briefing)
Do not take your data sheet out of the lab room
It is not accepted after the class is already over
A Make-Up Class Policy If you miss more than 2 classes you have no right to take the final
examination (lt80 attendance) You are advised to ldquoWITHDRAWrdquo
before the final exam otherwise an F grade will be given
If you miss any class please contact the laboratory staff within 7 days
with supporting documents ie a medical certificate official letter from
a respected organization etc sufficiently explaining why you could not
attend the class The laboratory instructorstaff retains the right to
acceptreject those documents
Only ONE make-up experiment can be arranged for any student during
the MAKE-UP week Beware that attending a make-up class does not
necessarily reduce the number of your absences in normal class
12
Personnel amp Staff Security Issue
Threatening or injuring instructorsstaffs is a very
serious issue The issue will be reported to your
course administrator and your family If seriously
punishment will be executed to the maximum extend
by university law and criminal law
13
Personnel amp Staff Security IssueEvacuation Procedure
In Case of FireWhen you hear fire alarm or are
instructed to leave the building you should
- Bring valuable items eg money or cellphone
- Follow the staff who carries the ldquoPhysics
Room XXXrdquo sign
- Leave the building quickly and calmly to the
nearest ldquoFire Exitrdquo
- Do not use an elevator during an evacuation
- Do not use the central stairwell as emergency
exit
- Gather for a head count at the ldquoFire Assembly
Pointrdquo behind the Geology-Botany building
- Do not enter the building again until it has
been declared safe to enter by the local Fire Department
14
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 501-503
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 502
Room 503Room 501
15
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
16
Experiment 7 Rotational MotionA wheel and an axle are heavy and they are not fixed with the
clamp Therefore during the experiment do not move the wheel
or the axle and beware of the loaded mass ndash when it moves it
may hit you or your partners
Laboratory Room 503
Personnel amp Staff Security Issue
17
Experiment 11 Electrical Measurement
bull Be careful about electronic devices eg multimeters or
resistors before connecting them to a power supply
Check whether devices work well before doing the
experiment
Laboratory Room 503
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
Lab Schedule
7
BSAC 191Friday 900 - 1200 AM
Week Date
Orientation 10-Jan-2020
Sport Day 17-Jan-2020
1st 24-Jan-2020
2nd 31-Jan-2020
3rd 7-Feb-2020
4th 14-Feb-2020
5th 21-Feb-2020
6th 28-Feb-2020
Midterm Week (NO LAB) 6-Mar-2020
7th 13-Mar-2020
8th 20-Mar-2020
9th 27-Mar-2020
10th 3-Apr-2020
Review 10-Apr-2020
Make -up lab 17-Apr-2020
Final Exam As announced
8
Grading policy
Experimental part (10 Labs) 70 points
7 points for each lab
2 points for general evaluations
On time for class
Manner in class
Behavior in class
5 points for
Data sheet
Post-Test in class (see course syllabus)
Final exam (written) 30 points
9
General rules Be in class no later than 10 minutes
After 10 minutes is considered being late (1 point reduction)
After 30 minutes student is not allowed to enter the lab
Dress properly according to the university code of uniforms IF NOT
you may be refused to enter the lab or 1-2 points of score will be
deduced
No use of mobile phoneTablet PCPC in class Keep those devices in a
provided plastic box on your table
2 points reduction for 1st warning on use of devices
Additional 5 points reduction for 2nd warning on use of devices
Students are required to bring the laboratory handbook and present to
the staff when signing for attendance One point will be deducted from
your total score if the laboratory handbook is not presented
10
General rules Do not leave the laboratory room at any time without notifying an
instructor
Stay at your table until the experiment is finished unless necessary
Do not make unnecessary loud noise
No food or drink in the laboratory room
11
General procedures 2-3 students per group for each experiment
Check your lab schedule and partners at the front of room 506-507 MHMK
Building or on the Website httpwwwphysicslabscchulaacth
Sign your name before getting into the lab room and obtain the data sheet
Sign up for other person is considered cheating All parties involved will
get a punishment - maximum of 7 points score deduction The issue will
also be reported to your course administrator
In some lab student is required to sign up for checking out an experiment kit
After finishing the lab all checked-out items must be returned
If damage occurs student(s) will be held responsible (charge or replacement)
Submit your data sheet on time (informed at the briefing)
Do not take your data sheet out of the lab room
It is not accepted after the class is already over
A Make-Up Class Policy If you miss more than 2 classes you have no right to take the final
examination (lt80 attendance) You are advised to ldquoWITHDRAWrdquo
before the final exam otherwise an F grade will be given
If you miss any class please contact the laboratory staff within 7 days
with supporting documents ie a medical certificate official letter from
a respected organization etc sufficiently explaining why you could not
attend the class The laboratory instructorstaff retains the right to
acceptreject those documents
Only ONE make-up experiment can be arranged for any student during
the MAKE-UP week Beware that attending a make-up class does not
necessarily reduce the number of your absences in normal class
12
Personnel amp Staff Security Issue
Threatening or injuring instructorsstaffs is a very
serious issue The issue will be reported to your
course administrator and your family If seriously
punishment will be executed to the maximum extend
by university law and criminal law
13
Personnel amp Staff Security IssueEvacuation Procedure
In Case of FireWhen you hear fire alarm or are
instructed to leave the building you should
- Bring valuable items eg money or cellphone
- Follow the staff who carries the ldquoPhysics
Room XXXrdquo sign
- Leave the building quickly and calmly to the
nearest ldquoFire Exitrdquo
- Do not use an elevator during an evacuation
- Do not use the central stairwell as emergency
exit
- Gather for a head count at the ldquoFire Assembly
Pointrdquo behind the Geology-Botany building
- Do not enter the building again until it has
been declared safe to enter by the local Fire Department
14
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 501-503
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 502
Room 503Room 501
15
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
16
Experiment 7 Rotational MotionA wheel and an axle are heavy and they are not fixed with the
clamp Therefore during the experiment do not move the wheel
or the axle and beware of the loaded mass ndash when it moves it
may hit you or your partners
Laboratory Room 503
Personnel amp Staff Security Issue
17
Experiment 11 Electrical Measurement
bull Be careful about electronic devices eg multimeters or
resistors before connecting them to a power supply
Check whether devices work well before doing the
experiment
Laboratory Room 503
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
8
Grading policy
Experimental part (10 Labs) 70 points
7 points for each lab
2 points for general evaluations
On time for class
Manner in class
Behavior in class
5 points for
Data sheet
Post-Test in class (see course syllabus)
Final exam (written) 30 points
9
General rules Be in class no later than 10 minutes
After 10 minutes is considered being late (1 point reduction)
After 30 minutes student is not allowed to enter the lab
Dress properly according to the university code of uniforms IF NOT
you may be refused to enter the lab or 1-2 points of score will be
deduced
No use of mobile phoneTablet PCPC in class Keep those devices in a
provided plastic box on your table
2 points reduction for 1st warning on use of devices
Additional 5 points reduction for 2nd warning on use of devices
Students are required to bring the laboratory handbook and present to
the staff when signing for attendance One point will be deducted from
your total score if the laboratory handbook is not presented
10
General rules Do not leave the laboratory room at any time without notifying an
instructor
Stay at your table until the experiment is finished unless necessary
Do not make unnecessary loud noise
No food or drink in the laboratory room
11
General procedures 2-3 students per group for each experiment
Check your lab schedule and partners at the front of room 506-507 MHMK
Building or on the Website httpwwwphysicslabscchulaacth
Sign your name before getting into the lab room and obtain the data sheet
Sign up for other person is considered cheating All parties involved will
get a punishment - maximum of 7 points score deduction The issue will
also be reported to your course administrator
In some lab student is required to sign up for checking out an experiment kit
After finishing the lab all checked-out items must be returned
If damage occurs student(s) will be held responsible (charge or replacement)
Submit your data sheet on time (informed at the briefing)
Do not take your data sheet out of the lab room
It is not accepted after the class is already over
A Make-Up Class Policy If you miss more than 2 classes you have no right to take the final
examination (lt80 attendance) You are advised to ldquoWITHDRAWrdquo
before the final exam otherwise an F grade will be given
If you miss any class please contact the laboratory staff within 7 days
with supporting documents ie a medical certificate official letter from
a respected organization etc sufficiently explaining why you could not
attend the class The laboratory instructorstaff retains the right to
acceptreject those documents
Only ONE make-up experiment can be arranged for any student during
the MAKE-UP week Beware that attending a make-up class does not
necessarily reduce the number of your absences in normal class
12
Personnel amp Staff Security Issue
Threatening or injuring instructorsstaffs is a very
serious issue The issue will be reported to your
course administrator and your family If seriously
punishment will be executed to the maximum extend
by university law and criminal law
13
Personnel amp Staff Security IssueEvacuation Procedure
In Case of FireWhen you hear fire alarm or are
instructed to leave the building you should
- Bring valuable items eg money or cellphone
- Follow the staff who carries the ldquoPhysics
Room XXXrdquo sign
- Leave the building quickly and calmly to the
nearest ldquoFire Exitrdquo
- Do not use an elevator during an evacuation
- Do not use the central stairwell as emergency
exit
- Gather for a head count at the ldquoFire Assembly
Pointrdquo behind the Geology-Botany building
- Do not enter the building again until it has
been declared safe to enter by the local Fire Department
14
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 501-503
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 502
Room 503Room 501
15
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
16
Experiment 7 Rotational MotionA wheel and an axle are heavy and they are not fixed with the
clamp Therefore during the experiment do not move the wheel
or the axle and beware of the loaded mass ndash when it moves it
may hit you or your partners
Laboratory Room 503
Personnel amp Staff Security Issue
17
Experiment 11 Electrical Measurement
bull Be careful about electronic devices eg multimeters or
resistors before connecting them to a power supply
Check whether devices work well before doing the
experiment
Laboratory Room 503
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
9
General rules Be in class no later than 10 minutes
After 10 minutes is considered being late (1 point reduction)
After 30 minutes student is not allowed to enter the lab
Dress properly according to the university code of uniforms IF NOT
you may be refused to enter the lab or 1-2 points of score will be
deduced
No use of mobile phoneTablet PCPC in class Keep those devices in a
provided plastic box on your table
2 points reduction for 1st warning on use of devices
Additional 5 points reduction for 2nd warning on use of devices
Students are required to bring the laboratory handbook and present to
the staff when signing for attendance One point will be deducted from
your total score if the laboratory handbook is not presented
10
General rules Do not leave the laboratory room at any time without notifying an
instructor
Stay at your table until the experiment is finished unless necessary
Do not make unnecessary loud noise
No food or drink in the laboratory room
11
General procedures 2-3 students per group for each experiment
Check your lab schedule and partners at the front of room 506-507 MHMK
Building or on the Website httpwwwphysicslabscchulaacth
Sign your name before getting into the lab room and obtain the data sheet
Sign up for other person is considered cheating All parties involved will
get a punishment - maximum of 7 points score deduction The issue will
also be reported to your course administrator
In some lab student is required to sign up for checking out an experiment kit
After finishing the lab all checked-out items must be returned
If damage occurs student(s) will be held responsible (charge or replacement)
Submit your data sheet on time (informed at the briefing)
Do not take your data sheet out of the lab room
It is not accepted after the class is already over
A Make-Up Class Policy If you miss more than 2 classes you have no right to take the final
examination (lt80 attendance) You are advised to ldquoWITHDRAWrdquo
before the final exam otherwise an F grade will be given
If you miss any class please contact the laboratory staff within 7 days
with supporting documents ie a medical certificate official letter from
a respected organization etc sufficiently explaining why you could not
attend the class The laboratory instructorstaff retains the right to
acceptreject those documents
Only ONE make-up experiment can be arranged for any student during
the MAKE-UP week Beware that attending a make-up class does not
necessarily reduce the number of your absences in normal class
12
Personnel amp Staff Security Issue
Threatening or injuring instructorsstaffs is a very
serious issue The issue will be reported to your
course administrator and your family If seriously
punishment will be executed to the maximum extend
by university law and criminal law
13
Personnel amp Staff Security IssueEvacuation Procedure
In Case of FireWhen you hear fire alarm or are
instructed to leave the building you should
- Bring valuable items eg money or cellphone
- Follow the staff who carries the ldquoPhysics
Room XXXrdquo sign
- Leave the building quickly and calmly to the
nearest ldquoFire Exitrdquo
- Do not use an elevator during an evacuation
- Do not use the central stairwell as emergency
exit
- Gather for a head count at the ldquoFire Assembly
Pointrdquo behind the Geology-Botany building
- Do not enter the building again until it has
been declared safe to enter by the local Fire Department
14
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 501-503
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 502
Room 503Room 501
15
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
16
Experiment 7 Rotational MotionA wheel and an axle are heavy and they are not fixed with the
clamp Therefore during the experiment do not move the wheel
or the axle and beware of the loaded mass ndash when it moves it
may hit you or your partners
Laboratory Room 503
Personnel amp Staff Security Issue
17
Experiment 11 Electrical Measurement
bull Be careful about electronic devices eg multimeters or
resistors before connecting them to a power supply
Check whether devices work well before doing the
experiment
Laboratory Room 503
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
10
General rules Do not leave the laboratory room at any time without notifying an
instructor
Stay at your table until the experiment is finished unless necessary
Do not make unnecessary loud noise
No food or drink in the laboratory room
11
General procedures 2-3 students per group for each experiment
Check your lab schedule and partners at the front of room 506-507 MHMK
Building or on the Website httpwwwphysicslabscchulaacth
Sign your name before getting into the lab room and obtain the data sheet
Sign up for other person is considered cheating All parties involved will
get a punishment - maximum of 7 points score deduction The issue will
also be reported to your course administrator
In some lab student is required to sign up for checking out an experiment kit
After finishing the lab all checked-out items must be returned
If damage occurs student(s) will be held responsible (charge or replacement)
Submit your data sheet on time (informed at the briefing)
Do not take your data sheet out of the lab room
It is not accepted after the class is already over
A Make-Up Class Policy If you miss more than 2 classes you have no right to take the final
examination (lt80 attendance) You are advised to ldquoWITHDRAWrdquo
before the final exam otherwise an F grade will be given
If you miss any class please contact the laboratory staff within 7 days
with supporting documents ie a medical certificate official letter from
a respected organization etc sufficiently explaining why you could not
attend the class The laboratory instructorstaff retains the right to
acceptreject those documents
Only ONE make-up experiment can be arranged for any student during
the MAKE-UP week Beware that attending a make-up class does not
necessarily reduce the number of your absences in normal class
12
Personnel amp Staff Security Issue
Threatening or injuring instructorsstaffs is a very
serious issue The issue will be reported to your
course administrator and your family If seriously
punishment will be executed to the maximum extend
by university law and criminal law
13
Personnel amp Staff Security IssueEvacuation Procedure
In Case of FireWhen you hear fire alarm or are
instructed to leave the building you should
- Bring valuable items eg money or cellphone
- Follow the staff who carries the ldquoPhysics
Room XXXrdquo sign
- Leave the building quickly and calmly to the
nearest ldquoFire Exitrdquo
- Do not use an elevator during an evacuation
- Do not use the central stairwell as emergency
exit
- Gather for a head count at the ldquoFire Assembly
Pointrdquo behind the Geology-Botany building
- Do not enter the building again until it has
been declared safe to enter by the local Fire Department
14
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 501-503
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 502
Room 503Room 501
15
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
16
Experiment 7 Rotational MotionA wheel and an axle are heavy and they are not fixed with the
clamp Therefore during the experiment do not move the wheel
or the axle and beware of the loaded mass ndash when it moves it
may hit you or your partners
Laboratory Room 503
Personnel amp Staff Security Issue
17
Experiment 11 Electrical Measurement
bull Be careful about electronic devices eg multimeters or
resistors before connecting them to a power supply
Check whether devices work well before doing the
experiment
Laboratory Room 503
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
11
General procedures 2-3 students per group for each experiment
Check your lab schedule and partners at the front of room 506-507 MHMK
Building or on the Website httpwwwphysicslabscchulaacth
Sign your name before getting into the lab room and obtain the data sheet
Sign up for other person is considered cheating All parties involved will
get a punishment - maximum of 7 points score deduction The issue will
also be reported to your course administrator
In some lab student is required to sign up for checking out an experiment kit
After finishing the lab all checked-out items must be returned
If damage occurs student(s) will be held responsible (charge or replacement)
Submit your data sheet on time (informed at the briefing)
Do not take your data sheet out of the lab room
It is not accepted after the class is already over
A Make-Up Class Policy If you miss more than 2 classes you have no right to take the final
examination (lt80 attendance) You are advised to ldquoWITHDRAWrdquo
before the final exam otherwise an F grade will be given
If you miss any class please contact the laboratory staff within 7 days
with supporting documents ie a medical certificate official letter from
a respected organization etc sufficiently explaining why you could not
attend the class The laboratory instructorstaff retains the right to
acceptreject those documents
Only ONE make-up experiment can be arranged for any student during
the MAKE-UP week Beware that attending a make-up class does not
necessarily reduce the number of your absences in normal class
12
Personnel amp Staff Security Issue
Threatening or injuring instructorsstaffs is a very
serious issue The issue will be reported to your
course administrator and your family If seriously
punishment will be executed to the maximum extend
by university law and criminal law
13
Personnel amp Staff Security IssueEvacuation Procedure
In Case of FireWhen you hear fire alarm or are
instructed to leave the building you should
- Bring valuable items eg money or cellphone
- Follow the staff who carries the ldquoPhysics
Room XXXrdquo sign
- Leave the building quickly and calmly to the
nearest ldquoFire Exitrdquo
- Do not use an elevator during an evacuation
- Do not use the central stairwell as emergency
exit
- Gather for a head count at the ldquoFire Assembly
Pointrdquo behind the Geology-Botany building
- Do not enter the building again until it has
been declared safe to enter by the local Fire Department
14
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 501-503
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 502
Room 503Room 501
15
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
16
Experiment 7 Rotational MotionA wheel and an axle are heavy and they are not fixed with the
clamp Therefore during the experiment do not move the wheel
or the axle and beware of the loaded mass ndash when it moves it
may hit you or your partners
Laboratory Room 503
Personnel amp Staff Security Issue
17
Experiment 11 Electrical Measurement
bull Be careful about electronic devices eg multimeters or
resistors before connecting them to a power supply
Check whether devices work well before doing the
experiment
Laboratory Room 503
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
A Make-Up Class Policy If you miss more than 2 classes you have no right to take the final
examination (lt80 attendance) You are advised to ldquoWITHDRAWrdquo
before the final exam otherwise an F grade will be given
If you miss any class please contact the laboratory staff within 7 days
with supporting documents ie a medical certificate official letter from
a respected organization etc sufficiently explaining why you could not
attend the class The laboratory instructorstaff retains the right to
acceptreject those documents
Only ONE make-up experiment can be arranged for any student during
the MAKE-UP week Beware that attending a make-up class does not
necessarily reduce the number of your absences in normal class
12
Personnel amp Staff Security Issue
Threatening or injuring instructorsstaffs is a very
serious issue The issue will be reported to your
course administrator and your family If seriously
punishment will be executed to the maximum extend
by university law and criminal law
13
Personnel amp Staff Security IssueEvacuation Procedure
In Case of FireWhen you hear fire alarm or are
instructed to leave the building you should
- Bring valuable items eg money or cellphone
- Follow the staff who carries the ldquoPhysics
Room XXXrdquo sign
- Leave the building quickly and calmly to the
nearest ldquoFire Exitrdquo
- Do not use an elevator during an evacuation
- Do not use the central stairwell as emergency
exit
- Gather for a head count at the ldquoFire Assembly
Pointrdquo behind the Geology-Botany building
- Do not enter the building again until it has
been declared safe to enter by the local Fire Department
14
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 501-503
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 502
Room 503Room 501
15
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
16
Experiment 7 Rotational MotionA wheel and an axle are heavy and they are not fixed with the
clamp Therefore during the experiment do not move the wheel
or the axle and beware of the loaded mass ndash when it moves it
may hit you or your partners
Laboratory Room 503
Personnel amp Staff Security Issue
17
Experiment 11 Electrical Measurement
bull Be careful about electronic devices eg multimeters or
resistors before connecting them to a power supply
Check whether devices work well before doing the
experiment
Laboratory Room 503
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
Personnel amp Staff Security Issue
Threatening or injuring instructorsstaffs is a very
serious issue The issue will be reported to your
course administrator and your family If seriously
punishment will be executed to the maximum extend
by university law and criminal law
13
Personnel amp Staff Security IssueEvacuation Procedure
In Case of FireWhen you hear fire alarm or are
instructed to leave the building you should
- Bring valuable items eg money or cellphone
- Follow the staff who carries the ldquoPhysics
Room XXXrdquo sign
- Leave the building quickly and calmly to the
nearest ldquoFire Exitrdquo
- Do not use an elevator during an evacuation
- Do not use the central stairwell as emergency
exit
- Gather for a head count at the ldquoFire Assembly
Pointrdquo behind the Geology-Botany building
- Do not enter the building again until it has
been declared safe to enter by the local Fire Department
14
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 501-503
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 502
Room 503Room 501
15
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
16
Experiment 7 Rotational MotionA wheel and an axle are heavy and they are not fixed with the
clamp Therefore during the experiment do not move the wheel
or the axle and beware of the loaded mass ndash when it moves it
may hit you or your partners
Laboratory Room 503
Personnel amp Staff Security Issue
17
Experiment 11 Electrical Measurement
bull Be careful about electronic devices eg multimeters or
resistors before connecting them to a power supply
Check whether devices work well before doing the
experiment
Laboratory Room 503
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
Personnel amp Staff Security IssueEvacuation Procedure
In Case of FireWhen you hear fire alarm or are
instructed to leave the building you should
- Bring valuable items eg money or cellphone
- Follow the staff who carries the ldquoPhysics
Room XXXrdquo sign
- Leave the building quickly and calmly to the
nearest ldquoFire Exitrdquo
- Do not use an elevator during an evacuation
- Do not use the central stairwell as emergency
exit
- Gather for a head count at the ldquoFire Assembly
Pointrdquo behind the Geology-Botany building
- Do not enter the building again until it has
been declared safe to enter by the local Fire Department
14
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 501-503
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 502
Room 503Room 501
15
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
16
Experiment 7 Rotational MotionA wheel and an axle are heavy and they are not fixed with the
clamp Therefore during the experiment do not move the wheel
or the axle and beware of the loaded mass ndash when it moves it
may hit you or your partners
Laboratory Room 503
Personnel amp Staff Security Issue
17
Experiment 11 Electrical Measurement
bull Be careful about electronic devices eg multimeters or
resistors before connecting them to a power supply
Check whether devices work well before doing the
experiment
Laboratory Room 503
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 501-503
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 502
Room 503Room 501
15
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
16
Experiment 7 Rotational MotionA wheel and an axle are heavy and they are not fixed with the
clamp Therefore during the experiment do not move the wheel
or the axle and beware of the loaded mass ndash when it moves it
may hit you or your partners
Laboratory Room 503
Personnel amp Staff Security Issue
17
Experiment 11 Electrical Measurement
bull Be careful about electronic devices eg multimeters or
resistors before connecting them to a power supply
Check whether devices work well before doing the
experiment
Laboratory Room 503
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
Personnel amp Staff Security Issue
16
Experiment 7 Rotational MotionA wheel and an axle are heavy and they are not fixed with the
clamp Therefore during the experiment do not move the wheel
or the axle and beware of the loaded mass ndash when it moves it
may hit you or your partners
Laboratory Room 503
Personnel amp Staff Security Issue
17
Experiment 11 Electrical Measurement
bull Be careful about electronic devices eg multimeters or
resistors before connecting them to a power supply
Check whether devices work well before doing the
experiment
Laboratory Room 503
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
Personnel amp Staff Security Issue
17
Experiment 11 Electrical Measurement
bull Be careful about electronic devices eg multimeters or
resistors before connecting them to a power supply
Check whether devices work well before doing the
experiment
Laboratory Room 503
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
Personnel amp Staff Security Issue
18
Experiment 19 Interference and Diffraction of Light
bull Be careful when using a laser do not aim it at
personrsquos eyes
Laboratory Room 503
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 505-507
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 506
Room 507Room 505
19
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
Personnel amp Staff Security Issue
20
Experiment 8
Speed of sound in air
bull Be careful when pulling up the
pipe higher than your height
bull Check the electrical wires before
connecting them in a circuit
Experiment 20 Radioactivity
bull Do not touch radioactive substances
without protection and do not put
them in your mouth
bull Radioactive source should be used
carefully to avoid damage (If
damage occurs inform instructors or
staffs immediately)
Laboratory Room 505-507
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
Personnel amp Staff Security Issue
21
Experiment 21
Heat Capacity
This experiment involves
heat students should use
provided equipment to
hold a pot or any hot
equipment and beware of
the stream coming from
the tube end
Students must wear heat
protection gloves while
doing the experiment
Laboratory Room 505-507
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
Personnel amp Staff Security IssueFIRE ESCAPE PLAN
General Physics Laboratory Room 601-603
Department of Physics Faculty of Science Chulalongkorn University
Fire Escape Plan Fire Exit
fire extinguisher Fire Alarm
fire extinguisher
Hallway Hallway
Hallway Faculty Office
Room 602
Room 603Room 601
22
What to do if a fire starts
If flames are contained in a small space and they are small enough to extinguish by oneself use a portable fire extinguisher to extinguish them
Press the fire alarm located near the fire exit
If not be able to extinguish fires leave the building immediately Close all doors and call emergency security radio center 02-2180000 or Banthat Thong Fire Station 02-214104302-2141049 or 199 or Medical Emergency Call National Institute for Emergency Medicine (EMS) 1669
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
Personnel amp Staff Security Issue
23
Experiment 17
Lenses and Spherical
Mirrors
bull Beware of dropping
or damaging lenses
or mirrors
Laboratory Room 601
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
24
Experiment 4
Simple Harmonic Motion
and Hookersquos Law
bull Beware not to drop loaded
masses on your feet
bull Do not pull or push a
spring too hard
Laboratory Room 202
Personnel amp Staff Security Issue
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
25
Comments Form
The comment form is available at every lab room in a box near the entrance door
Student can evaluate or comment on each lab and drop the form into the box nearby
Not necessarily do or return the form during the lab You can take the form home and drop it at any lab room next time you come to the lab
Your comments are important and useful to make things better
Comment can also be sent to physicslabchulaacth
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
26
Error analysis and graph
bull Types of errors
bull Preliminary description of error analysis
bull Propagation of uncertainties
bull How to report and use uncertainties
bull Straight line
Note that the following details appear in
Lab books 2304191
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
27
Types of errors
bull Personal error
ndash Individual mistake - must be avoided or minimized
bull Systematic error (ONE WAY error)
ndash Instruments that always give too high or too low value (corrected
by instrument calibration)
ndash Example the measuring tape that its end start from 1 not 0
Without this notice length will always be TOO SHORT
ndash We cannot reduce systematic error merely by taking an average
bull Statistical error (TWO WAY error)
ndash Reading that is randomly sometimes too high sometimes too
low
ndash Taking an average can reduce this random errorness
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
Accuracy and Precision
Not accurate not precise
Not accuratebut precise
Quite accurate
(around the
target) but not precise
Accurate and
precise
We want this one
in doing the measurement
28
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
29
Preliminary Description of
Error Analysis
use error in the sense of ldquouncertaintyrdquo error
do not involve lsquomistakersquo in a scientific
measurement
no scientific measurement can yield exact
value
knowing the uncertainty is important
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
30
Example Is the crown made of gold
Perform the density measurement of the crown
gold = 155 gcm3 and alloy = 138 gcm3
Measurement report Student A Student B
Best estimate of crown 15 gcm3 139 gcm3
Uncertianty() for crown 15 gcm3 02 gcm3
135 165
137 141Student A
(not sure)
Student B
(certainly NO)
138 gcm3 155 gcm3alloy gold
density
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
31
Estimating uncertainties in repeatable
measurements
Same quantities obtained from several readings
repeating
Best estimate = average value
Standard deviation () is 68 confidence limit
Uncertainty of the mean () is
2
1
( )
1
N
i
i
x x
N
68 of 100 readings will fall
within and x S D x S D
N
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
32
Propagation of uncertainties
Question If A = 15 1 and B = 10 2 what is the maximum and
minimum value of A+B (which give the range of answer)
14 A 16 8 B 12
Answer So maximum of A+B is 16+12 = 28 and minimum of A+B
is 14+8 = 22
Question What about the maximum and minimum value of A-B
Is it 16-12=4 and 14-8=6 respectively
Answer No the maximum of A-B is maxA ndash minB = 16-8 = 8
The minimum of A-B is minA ndash maxB = 14-12 = 2
A BA B
Maximum uncertainty
Example (15-10) (1+2) = 5 3
which gives maximum value of 8 and
minimum value of 2
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
Propagation of uncertainties
33
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A x B
14 A 16
8 B 12
Max = 16 x 12
= 192
Min = 14 x 8
= 112
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A x B = 150 and 2667 of this is
40 So our answer is 15040 which
is close to the exact answer on the
left
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
Propagation of uncertainties
34
Question If A = 15 1
and B = 10 2 what is the
maximum and minimum of
A B
14 A 16
8 B 12
Max = maxA minB
= 168 = 2
Min = minA max B
= 14 12
= 117
Another way of thinking is that
A has uncertainty around 667
(this come from 115 x 100)
B has uncertainty around 20
(210 x 100)
So we would expect maximum
uncertainty of around 2667
A B = 15 and 2667 of this is
04 So our answer is 15 04
which is close to the exact answer
on the left
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
35
What we did on two previous slides are equivalent to the following
formula
maximum uncertainty products or quotients
A x B = (a x b) AB AB = (ab) AB
the ratio added up
example W = 13 01 cm and L= 21 03 cm
area = WL = 13 x 21 = 273 cm2
Uncertainty of area WL= [(0113) + (0321)] x 273
= 0600054 = 06 cm2
b
b
a
a
ba
AB
b
b
a
a
ba
BA
Propagation of uncertainties
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
36
Statistical uncertainties (when your data is an average of many readings and uncertainty is the standard error or mean) Starting from
A =a a B=b b
sums or differences
products
quotients
2 2( ) ( ) ( )A B a b a b
2 2A a a a b
B b b a b
Propagation of uncertainties
2 2a b
AB ab aba b
Prove it yourself that statistical uncertainties is always
LESS THAN the maximum uncertainty
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
37
more example
q =
max uncertainty
stat uncertainty
Read more in your lab manual
zy
baq
|||||||||| z
z
y
y
b
b
a
a
q
q
2222
z
z
y
y
b
b
a
a
q
q
Propagation of uncertainties
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
38
How to report and use uncertainties
bull Always include the units
(measured value of x) = best estimate uncertainty
bull Rule for stating uncertainties
In an introductory laboratory experimental
uncertainty usually be rounded to one significant
figure
example (measured of g) = 982 002385 ms2
should be reported as 982 002 ms2 or the
mass of 524 04637 g should be reported as 52
05 g
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
39
How to report and use uncertainties
bull Rule for stating answers
The last significant figure in any stated answer
should usually be of the same order of
magnitude (in the same decimal position) as the
uncertainty
Example
best estimate uncertainty stated answer
92855 005 9286 005
92855 05 929 05
92855 5 93 5
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
40
How to report and use uncertainties
bull Using scientific notation for a very
large or small value
Example
1 (measured charge) = 159x10-19 5x10-21 C
should report as (159 005 ) x 10-19 C
2 1857000 40000
1857 x 106 4 x 104
( 186 004 ) x 106
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
41
Straight line
bull Linear equation y = m x + c
m is slope and c is y-intercept
They can be evaluated using either graphical
analysis or statistical analysis (lab 2)
bull Usually data are plotted to see if they satisfy
linear equation (straight line)
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
42
000
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60
x
y
di
di2 = (yline- ydata)
2 is minimum
Best fit for a straight line
bull Number of data
points above the line
is about the same to
that of under the line
bull Summation of the
vertical distances for
each data point to the
line is minimum
bull Number of data points above the line is about the same to that of
under the line
bull Summation of the vertical distances for each data point to the line is
minimum
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
43
Homework
bull Read the Introduction part in the lab book
bull Bring your calculator and learn how to use it
to get the mean and standard deviation of a
set of data
wwwphysicslabscchulaacth
44
wwwphysicslabscchulaacth
44