Topic 0 - Practical Skills
Name:_____________________________________ Date:
_________________
Assess yourself with these criteria
Teacher Comments
What you need to do to improve
Making measurements and resolution
· Micrometer
· Vernier callipers
· Use of fiducial marks
· Improving Precision
· Improving Accuracy
· Improving Reproducability and repeatability
A simple measurement (really simple)
Sources of Uncertainty – random and systematic errors
Handling Uncertainty
· Absolute, fractional and percentage uncertainties
· Combining uncertainties
Drawing Graphs and interpreting graphs
· Using error bars on a graph
· Determining uncertainties in the gradient and intercept
#
Assignment Title
Student Self-Assessment
Teacher Comment
Grade (1-4)
(1 = high)
0.1
Sources of error – pendulum timing
0.2
Uncertainty in Readings
0.3
Handling Uncertainty
0.4
Practical measurements with errors
0.5
Drawing and interpreting graphs
0.6
Assessed Experiment
/ 20 marks
Making Measurements
Resolution is the fineness to which an instrument can be read.
e.g. the resolution of a stop watch is 0.01 s
The uncertainty in a measurement is at best equal to the
resolution. e.g. the uncertainty in any reading of a stop watch is
+/– 0.01 s
The resolution is taken as the smallest division capable of
being read. (This may be different to the uncertainty)
Vernier Calliper
The vernier calliper contains a vernier scale. This scale
enables readings to be made with a much greater resolution. As a
result, the precision of readings can be increased.
With a pair of vernier callipers, you can measure short lengths
i.e. 0 to 15 cm. It has a resolution of 0.002 cm, or 0.02mm. A pair
of vernier calipers consists of a Main Scale (top) and a Vernier
Scale (bottom / moving) as shown in the diagram to the right.
The outside jaws, are used to measure the outer dimensions of an
object and the inner jaws for the inner ones. The stem is used to
measure the depth of a hole.
To take measurements
1. To measure, gently grip the object with the straight edges of
the outside or inside jaws.
2. First read the main scale, and note down the
reading before the 0 on the vernier scale, as
shown in the diagram right. The reading on it is 2.8 cm,
as the .8 after the 2 on the main scale is before
the 0 on the vernier scale.
3. For the second place of decimal, look at the vernier scale.
Find a marking on the vernier scale that coincides exactly with the
reading on the main scale. In the diagram below, the 6 on
the vernier scale coincides exactly with a line on the main scale
(it does not matter with which line on the main scale
this line coincides). So the second place of the decimal would 6.0,
ie .060cm or 0.6mm.
4. To get the total reading, add the two readings i-e 2.8+.060.
The final reading is 2.860cm or 28.60mm.
Lab Work – Vernier Scale Practise
Determine the measurement of the following examples, and then
have a go at measuring some objects yourself using a pair of
Vernier Callipers. Make sure you compare your measurements to those
that other students of the teacher can take. You could also check
your reading with a digital calliper. You must take at least seven
correct readings.
Object
Your reading
Comparison reading
Correct?
Screwgauge Micrometer
A screwgauge micrometer is used to measure very short readings
i.e. 0 to 2.5cm. It has a resolution of 0.001cm or 0.01 mm. Like
the vernier scale, the micrometer has two scales, main scale (on
the sleeve) and the circular scale (on the thimble). Each division
on the main scale represents 1 mm. Each division on the thimble
represents a distance of 0.01mm.
How to take measurements
1. Turn the thimble until the object is nearly gripped. Then use
the ratchet knob to fully close the anvil and spindle. DO NOT
overtighten. This can cause two problems; the object you are
measuring becomes squashed slightly, so the reading is reduced; the
thread of the screwgauge becomes warped, so all future measurements
have a zero-error (more on this later).
2. Read the main scale on the sleeve. This reading would be in
millimeters. In the diagram below, the reading is 5.5mm. The top
row of the sleeve gives whole mm, and the bottom row of the sleeve
gives half mm. These ½ mm are only read if they are clearly visible
(they become clearly visible when the thimble has rotated fully
past 49).
3. Then read the line on the circular scale that coincides with
the line on the main scale. In the diagram below, the 28th line on
the circular scale coincides with the line. So, the reading would
be 0.28mm.
4. Then add 5.5 with 0.28 and you will obtain your answer in
millimeters.
How to avoid error
When fully closed with no object to measure, the zero on the
vernier scale i.e. circular scale coincides exactly the
horizontal line then no error exists (a). This should be the case
for all new micrometers, though older ones may, through misuse,
have zero error.
If the zero is below the horizontal line than
a positive zero error exists and can be avoided
by subtracting the error from the final
reading (b)
While if the zero is above the horizontal line than
a negative zero error exists and can be avoided by
measuring the error and adding the error into
the final reading (c).
Lab Work – Micrometer Scale Practise
Determine the measurement of the following examples, then have a
go at measuring some objects yourself using a screwgauge
micrometer. Make sure you compare your measurements to those that
other students of the teacher can take. You must take at least
seven correct readings.
Object
Your reading
Comparison reading
Correct?
(Answers from previous page6.146. 3.880.227. 7.383.618.
5.980.839. 1.57 8.08)
The space below has been left for you to make further note
regarding the use of and measurements with Vernier Calipers and the
Screwgauge Micrometer.
Lab Work – Using a fiducial mark – increasing accuracy and
reliability
In this experiment a fiducial mark is going to be used to help
increase the accuracy of measurements.
In the broadest sense, a fiducial marker or fiducial is an
object placed in the field of view of an imaging system which
appears in the image produced, for use as a point of reference or a
measure. It may be either something placed into or on the imaging
subject, or a mark or set of marks in the reticle of an optical
instrument.
Within the practicals you will undertake on this course,
fiducial markers are used to create a fixed reference point against
which measurements can be taken, be it measurements of length or
timing.
(bulldog clippendulum bob)Equipment needed
· Retort stand, clamp and boss
· Pendulum bob attached to a length of string
· Bulldog clip (which will act as our fiducial mark)
· Stopwatch
Set up the equipment as shown in the diagram to the right.
The length of the string is not important, but do record the
length.
1. Remove the bulldog clip and swing the pendulum.
2. Record the time for one complete swing. time for one swing
=
3. Record the time for 20 complete swings and find the average
time for one swing.
average time for one swing =
4. Add the bulldog clip. This will act as a fiducial mark to
provide a fixed reference point.
5. Observe the time it takes for the pendulum to pass the
bulldog clip and record the time for one complete swing.
time for one swing =
6. Record the time for 20 complete swings and find the average
time for one swing.
average time for one swing =
7. Comment on the impact that using a fiducial mark had upon the
measurement.
8. Comment on the impact that taking multiple readings and
finding the average had upon the measurement.
9. If you have a digital camera (e.g. a camera phone, iPad,
table etc) with the capability of advancing a video one frame at a
time, repeat the experiment and record the swings with the timer in
the picture. You should be able to achieve very high precision
(down to 1ms) in your measurements.
Apps such as CMV (CoachMyVideo.com) for iPad/iPhone and AndroVid
Video Trimmer (for Android) are useful and free.
Sources of Uncertainty
In metrology, physics, and engineering, the uncertainty or
margin of error of a measurement, is a range of values likely to
enclose the true value. There are a variety of origins of
uncertainty summarised below:
19
1. Personal Careless Error (Human error)
· introduced by experimenter.
· while discussing this was sometimes acceptable at GCSE level,
do not cite this as a source of error at A level. Rather, take care
with your experiment to ensure that you do not introduce error. You
will be assessed on your ability to do this.
2. Determinate (Systematic) Error
· uncertainty that is inherent in the measurement devices (hard
to read scales, etc.) – i.e. the resolution of the instrument
· often caused by poorly or mis-calibrated instruments
· cannot reduce by repeated measurements
3. Indeterminate (Random) Errors
· may be natural variations in measurements caused by factors
beyond reasonable control
· may be result of operator bias, variation in experimental
conditions (e.g. temperature), or other factors not easily
accounted for.
· may be minimized by repeated measurement and using an
arithmetic mean (average) as the best estimate of the true
value.
Practical Steps to take to minimise uncertainty
Bookmark or otherwise this guide so that you can easily refer to
it when doing investigations
· First look at your measuring instrument. What is its precision
(resolution)? (Usually this is the smallest scale division on the
instrument, but sometimes you can do better than this e.g. reading
a typical temperature to ± 0.5 ºC between the divisions of a
thermometer – you can still use your common sense!) This is your
best case scenario.
· Then ask yourself: “Are my readings really that good?”
Consider whether there are other factors (other random errors)
restricting the precision further? This may be obvious with a
single reading, but does become obvious over multiple readings.
Again use your common sense!
· Generally you will have instinctively realised if your
measurements are less reliable and you will have done repeat
readings. (There are rare occasions where repeat readings are
unnecessary, or even daft.)
· With repeat readings the range of your readings will usually
be bigger than the precision of the instrument and this gives you a
better idea of the uncertainty in your measurements (the precision
is then ignored and the range from the repeats is considered).
Example: timing a trolley rolling a fixed distance from rest
down a slope using a manual stopwatch
· Initial reading: 1.27 sec. Precision of stopwatch: ± 0.01
sec
· Clearly it is very unlikely that your measurement is this
precise –– your reaction time is involved. So you will do repeat
measurements and find a mean value as the best estimate of the true
value.
· Readings: 1.27 s; 1.28 s; 1.35 s. Mean value = 1.30 s.
· In fact the ‘true result’ is likely to lie somewhere between
1.27 and 1.35 s.
· The uncertainty is ± 0.4s. This is half the range (1.35 -1.27
= 0.08) of the readings so we write: mean value = 1.30 ± 0.4s.
Assignment 0.1 – Sources of error – pendulum timing – due
……………
First, categorise the following sources of error according to
whether they are random, systematic or both.
· Lag time and hysteresis – some measuring devices require time
to reach equilibrium and display a stable figure (such as
thermometers), and taking a measurement before the instrument is
stable will result in a measurement that is generally too low
· Instrument drift – most electronic instruments have readings
that drift over time.
· Parallax – this error can occur whenever there is some
distance between the measuring scale and the indicator used to
obtain a measurement. If the observer's eye is not squarely aligned
with the pointer and scale, the reading may be too high or low
(some analogue meters have mirrors to help with this
alignment).
· Physical or environmental variations
· Failure to calibrate or check zero of instrument
· Instrument resolution – all instruments have finite precision
that limits the ability to resolve small measurement
differences.
· Failure to account for a factor – the most challenging part of
designing an experiment is trying to control or account for all
possible factors except the one independent variable that is being
analyzed. For instance, you may inadvertently ignore air resistance
when measuring free-fall acceleration.
· Incomplete method – one reason that it is impossible to make
exact measurements is that the measurement is not always clearly
defined. For example, if two different people measure the length of
the same rope, they would probably get different results because
each person may stretch the rope with a different tension
Secondly, referring back to the Pendulum Timing experiment
conducted earlier. On a single side of A4 discuss the potential
sources of error that contributed to the uncertainty of the period
of the pendulum. Discuss whether each source of error was random or
systematic and how each source of error affected the accuracy,
repeatability and reproducibility of the measurement. Discuss how
the precision and accuracy differ.
You may need to read up further on the meaning and use of the
underlined terms. Hand in a well presented document.
Affix your final version of the essay here.
Percentage uncertainties
Clearly a ± 1mm uncertainty in a length of 12mm has more effect
than a ± 1mm uncertainty in a length of 123mm and a ± 0.1mA
uncertainty in a current of 0.5mA is more worrying than a ± 0.1mA
uncertainty in a current of 50.0 mA.
This is why we work out the percentage uncertainty of a
measurement. This is the most useful indicator of uncertainty.
Small percentage uncertainties (<5%) are typically excellent
results, especially in a school science lab. Larger than 20%
uncertainties are poor results.
The rules for combining uncertainties
· When measurements are added, subtracted, you can add their
absolute uncertainties or their percentage uncertainties.
· When measurements are multiplied together or divided you can
ONLY add their percentage uncertainties.
· If a measurement is raised to a power then you multiply the
percentage uncertainty by the power.
· Using these rules enables you to work out the overall
percentage uncertainty in a quantity that you have calculated from
your measurements. This can then be converted into an actual ±
value of uncertainty in your final value.
Uncertainties in gradients of graphs
· If there is very little scatter in your points, so that you
can be highly certain of the position of your best fit line, then
the uncertainty in your gradient is due to your precision in
measuring the lengths of the sides of your triangle. Here, using
larger triangles, (minimum 80mm sides) helps reduce uncertainty.
Again, selecting scales such that your data points cover the
maximum space on your A4 paper helps to reduce uncertainty.
· Measure the actual lengths of the horizontal and vertical
sides of your gradient triangle; assume that you can measure them
to a precision of ±1mm; work out the corresponding percentage
uncertainty for each side; then add those 2 percentage
uncertainties together to get the percentage uncertainty in your
gradient.
· If there is a lot of scatter then you should probably draw
another likely best fit line at a steeper/shallower angle and
compare its gradient with your original line to give you the likely
uncertainty.
Assignment 0.2: Uncertainty in Readings – due …………………
1. What is the minimum resolution of each of the following
apparatus:
a. Metre rule
b. 25ml measuring cylinder
c. 50 N spring balance
d. 25 N spring balance
e. Thermometer
f. Analogue ammeter
2. What is the minimum uncertainty when using:
a. Metre rule
b. 25ml measuring cylinder
c. 50 N spring balance
d. Thermometer
3. John uses a metre rule to measure the width of the room by
repeatedly drawing a pencil line at the 100cm mark then moving the
ruler to measure from there. He gets a value of 4677 mm
Suggest an estimated uncertainty
calculate the percentage uncertainty:
%
4. What is minimum percentage uncertainty in the following
measurements:
a. Standard Lab Thermometer reading 26°
b. Thermometer reading 76°
c. Metre rule reading 3 mm
d. Metre rule reading 320 mm
e. 50 N spring balance reading 20N
Assignment 0.3 – Handling Uncertainty due …………………..
It is suggested that working out is completed on a separate
piece of paper and the final answers are copied to the spaces
below. Hand in the working out with the answers, ensuring the
working out is well organised and easy to follow.
1. Convert the following to relative uncertainties:
a. 2.70 ± 0.05 cm /1
b. 12.02 ± 0.08 cm/1
2. Convert the following to absolute uncertainties:
a. 3.5 cm ± 10 % /1
b. 16 s ± 8 %/1
3. Complete the following, determining the appropriate
uncertainty:
a. (2.70 ± 0.05 cm) + (12.02 ± 0.08 cm)/1
b. (2.70 ± 0.05 cm) − (12.02 ± 0.08 cm)/1
c. (2.70 ± 0.05 cm) + (3.5 cm ± 10 %)/1
4. Complete the following, determining the appropriate
uncertainty:
a. (2.70 ± 0.05 cm) × (12.02 ± 0.08 cm)/1
b. (12.02 ± 0.08 cm) ÷ (16 s ± 8 %)/1
c. (3.5 cm ± 10 %) × (2.70 ± 0.05 cm) ÷ (16 s ± 8 %)/1
5. Complete the following, determining the appropriate
uncertainty:
a. 2 × (2.70 ± 0.05 cm)/1
b. 2 × (16 s ± 8 %)/1
c. (12.02 ± 0.08 cm)2/1
6. Complete the following determining the appropriate
uncertainty:
a. (12.02 ± 0.08 cm)2 ÷ (3.5 cm ± 10 %)/1
b. (12.02 ± 0.08 cm)2 + (3.5 cm ± 10 %) × (2.70 ± 0.05 cm)/1
c. [(3.5 cm ± 10%) + (2.70 ± 0.05 cm)] / (16 s ± 8%)/1
d. 4π2/(0.034 ± 0.004 s2/cm)/1
7. Determine the perimeter and area of a rectangle of length 9.2
± 0.05 cm and width 4.33 ± 0.01 cm, stating the percentage and
absolute uncertainty.
/1 Mark: /19
Assignment 0.4: Using a micrometer screw gauge and Vernier
callipers, digital balance and combining errors
Tip: Show all raw measurements clearly. Show all subsequent
steps in your working clearly. Underline final answer with units,
to a suitable number of significant figures. Include the percentage
error for all final answers. Marks awarded for presentation.
1. Find the volume of the Perspex block
2. Find the density of Perspex
3. Find the mean diameter of the ball bearing.
4. Calculate the volume of the ball bearing.
5. Calculate the density of the steel of the ball bearing.
6. Find the area of a sheet of A4 paper.
7. Find the volume of a sheet of A4 paper. Explain how you did
this to make it accurate.
8. Find the density of water. (Tip – use a measuring
cylinder)
9. Copper has a density of 8.0 g cm-3. By measurement find the
volume of copper in the copper pipe, and calculate the mass of the
pipe.
10. Use a top pan balance to find the mass of the copper
pipe.Account for any discrepancy between the measured and
calculated mass.
Drawing and interpreting graphs
The standard for drawing graphs in A level Physics is set out
here (adapted from AQA GCE Physics A Teacher Resource Bank ISA/PSA
Guidance). Please ensure all graphs drawn meet this standard.
Regularly refer to this page until you are familiar with the
standard required and confident at producing suitable graphs.
· Graphs should be plotted on A4 graph paper with either 1 mm or
2 mm squares (it is advisable that you purchase a pad of suitable
graph paper).
· Graph scales should have sensible divisions on which points
can be easily plotted and read multiples of 1, 2, 5, 8 (i.e. not
generally in multiples of 3, 4, 6, 7, 9 etc).
· Axes should be labelled with the plotted quantity and unit, ie
quantity/unit.
· The scale should be chosen so that the plotted points occupy
as large an area of the paper as possible. A scale would be deemed
too small if the plotted points do not occupy at least half the
length of each axis. In some cases this will require starting
either or both axes at a suitable non-zero value.
· Notwithstanding the previous point, ensure that a y-intercept
(i.e. 0, c) can be plotted, therefore an x-axis with a non-zero
start point should be an extremely rare exception.
· It is good practice to ensure that all graphs have an
appropriate title that describes the data shown.
· The plotted points should be represented as a small horizontal
cross ‘+’ (preferred) or a small diagonal cross ‘×’ (less
accurate). Generally, a plotted point would be deemed as correctly
plotted if it is a distance of 0.5 mm or less from the correct
position. A sharp pencil is needed.
· Lines of best fit:
· Where the plotted points suggest a straight line, the line
should be drawn with approximately equal numbers of points on
either side of the line. Points which are obviously anomalous
should not unduly influence the line (do indicate that an anomalous
point has been ignored when drawing the line of best fit).
· If the plotted points suggest a curve, a smooth curve should
be drawn.
· Where a gradient is to be calculated, a suitably large
triangle should be used (at least 8cm on the smallest side).
· Where a gradient is taken from two points on the graph, the
points must be sufficiently far apart to be equivalent to a ‘large’
triangle as defined above.
· Where the line of best fit is a smooth curve, the gradient at
a point may be found by drawing a tangent to the curve at that
point.
· Where an intercept is required this can either be read
directly from the axis or, in the case of axes not starting from
zero, a suitable calculation may be required.
Plotting Error Bars on graphs
Data that you plot on a graph will have experimental
uncertainties. These should be shown on a graph with error bars,
and used to determine uncertainties in the slope and intercept.
Consider a point with coordinates and. Often does not have an
error to plot, but be sure before you make this assumption.
(a) Plot a point, circled, at the point
(b) Draw lines from the circle to (if relevant , ), , and and
put bars on the lines, as shown in the diagram right. These are
called error bars.
http://www.rit.edu/cos/uphysics/graphing/graphingpart1.html
Use the space below to make further notes regarding drawing
graphs and determining the error of their gradients.
Assignment 0.5 – Graphing and interpreting data due ……………………
For each of the following sets of data, you need to do the
following:
1. Process the data (if relevant) by calculating average values,
absolute and percentage errors. EXT: Dataset 4 requires the natural
log ln(x) to be calculated of one of the variables to be
plotted.
2. Plot a suitable graph on A4 graph paper, including (if
relevant) error bars.
3. Calculate gradient and intercept.
4. EXT: Determine the equation of the graph in the form y = mx +
c
All work should be neatly presented, with clear titles, properly
laid out tables, appropriately drawn graphs. Work should be secured
together ready for submission.
Space has been left for you to complete working out and attach
your graphs. Graphs should be completed on A4.
Data set 1 – simple linear relationship (no error bars needed on
points)
Current /mA
Voltage /V
0
1.49
2
1.47
5
1.44
8
1.41
10
1.39
13
1.36
16
1.33
20
1.29
22
1.27
25
1.24
28
1.21
Data set 2 – data with multiple repeats, requires average to be
calculated and then plotted with error bars
Height to fall /m
Time /s
1
2
3
0.2
0.25
0.22
0.20
0.4
0.72
0.30
0.27
0.6
0.72
0.37
0.35
0.8
0.04
0.42
0.40
1.0
0.56
0.43
0.43
1.2
0.31
0.50
0.50
1.4
0.46
0.53
0.55
1.6
0.50
0.58
0.58
1.8
0.19
0.60
0.59
2.0
0.62
0.63
0.64
For this, calculate the average time and then calculate time2.
Plot height vs time2.
Data set 3 – data with a large scatter
Hubble’s 1929 Cepheid Variable data
Distance /Mpc
Recessional velocity /km s-1
0.032
170
0.034
290
0.45
200
0.5
290
0.5
270
0.63
200
0.8
300
0.9
650
0.9
150
0.9
500
1
920
1.1
450
1.1
500
1.4
500
1.7
960
2
500
2
850
2
1090
EXTENSION: Data set 4 – data with an exponential
relationship
Radioactive Decay of Protactinium-234
Time /s
Activity /count
1
2
3
0
382
510
530
10
445
372
320
20
381
461
431
30
413
377
366
40
236
388
332
50
249
309
311
60
166
243
201
70
167
246
156
80
132
290
266
90
247
183
199
100
79
95
196
Plot a graph of time vs. ln (average activity)
For further reading and activities have a look at
http://www.batesville.k12.in.us/physics/apphynet/Measurement/Measurement_Intro.html
1
Topic 0
-
Practical Skills
Name:_____________________________________ Date:
_________________
Assess yourself with these
criteria
Teacher Comments
L
K
J
What you need to do to
improve
Making measurements
and resolution
·
Micrometer
·
Vernier callipers
·
U
se of fiducial marks
·
Improving Precision
·
Improving Accuracy
·
Improving R
eproducability and repeatability
A simple measurement (really simple)
Sources of Uncertainty
–
random and systematic
errors
Handling
Uncertainty
·
Absolute, fractional and p
ercentage uncertainties
·
Combining uncertainties
Drawing Graphs and
interpreting
graphs
·
Using error bars on a graph
·
Determining uncertainties in the gradient and
intercept
#
Assignment Title
Student
Self
-
Assessment
Teacher Comment
Grade (1
-
4)
(1 =
high)
0.
1
Sources of error
–
pendulum timing
0.
2
Uncertainty in Readings
0.3
Handling Uncertainty
0.4
Practical measurements
with errors
0.5
Drawing and interpreting
graphs
0.6
Assessed Experiment
/ 20 marks
