Introduction of Physics Shatin Tsung Tsin Secondary School Mr. C.K. Yu & Mr. Tai Kin Fai.

Introduction of Physics Introduction of Physics

Shatin Tsung Tsin Secondary SchoolShatin Tsung Tsin Secondary School

Mr. C.K. YuMr. C.K. Yu

&&

Mr. Tai Kin FaiMr. Tai Kin Fai

What is Physics? Extracted from New Physics at Work, book 1A

Physics is the scientific study of matter and energy Physics is the scientific study of matter and energy and the relations between themand the relations between them. Microwave oven, mobile phone, seat-belt and crumple zone in safe car design, X-rays machine, and nuclear reactor are but a few of the appliances/devices that we encounter in daily life that draw on physics principlesphysics principles for their design.

The study of physics helps us develop a scientific way of develop a scientific way of working and problem solvingworking and problem solving, e.g, proposing hypotheses and testing them against observations. It also helps us to develop a set of values and attitudesdevelop a set of values and attitudes such as curiosity, honesty, respect for evidence, appreciation of achievement in physics and recognition of limitations.

Introduction1) What is Physics?

2) What is needed before a microwave oven is invented or designed?

3) What do you expect after studying physics?

Physics is the scientific study of matter and energy and the relations between them.

A physics principle for its design is needed.

It helps develop a set of values and attitudes in physics and recognition of limitations.

Objectives of Studying PhysicsObjectives of Studying Physics

1. Able to make observation

2. Able to understand how things behave in the observation

3. Able to understand what laws and theories about an observation

4. Able to apply the laws and theories in solving related problems

Steps of scientific study of physics

1.1. ObservationObservation (how things behave in our daily life )

2.2. Data collectionData collection (experiment measurement, data

recording)

3.3. Data analysisData analysis (numerical analysis, graphical analysis)

4.4. ConclusionConclusion (Laws, Theories and Principles )

1st ActivityYour teacher will throw an object. Observe and draw a diagram to show what you saw.

the object

ObservationObservation

After the object left teacher’s hand, it moved faster/slower and faster/slower upwards.

After it reached the highest/lowest point, it moved faster/slower and faster/slower downwards.

======== ========

========

======== ========

Data CollectionData CollectionYour teacher will throw the object three times. The

object will return to his hand. Measure and record the following quantities with your group-mates.

Time to highest position Total Time

1

2

3

Simple DataData AnalysisAnalysis

Analyze the data, discuss with your group-mates and make a conclusion about the measurement.

ConclusionConclusionMake a conclusion about the relation of the

two time measurements.(about, approximate, exactly, twice)_____________________________________________________________________________________________________________________________________________________________________

The total time is The total time is about twice the time about twice the time to the highest position. to the highest position. The time to the highest position is The time to the highest position is about the same as the time returning about the same as the time returning to his hand from the highestto his hand from the highest position. position.

Summary of Introduction

We learn the following steps in scientific study of Physics.

ObservationData CollectionData AnalysisConclusion

2nd activity Your teacher will throw an object again, sket

ch (簡單描繪 ) how the object moves/flies.

2nd activity

Now, your teacher will do the activity several times.

Discuss with your group-mate what you will measure first and put down the quantities in the table.

Make some measurements and record in a table.

2nd activity

Length of string Total time for ten cycles

1

2

3

4

5

2nd activity

What is the length of the string so that it takes 1 second to complete one cycle?

Do you know how to analyze these data to find the answer of this question?

This procedure is called Data Analysis. Let’s look at the way to analyze the data in next lesson.

Scientific Method of Study

The steps of scientific study of physics that you learned in previous lessons.

1. Observation

2. Data ___________

3. Data ____________ – Graphical Method

4. ________________

CollectionCollection

AnalysisAnalysis

ConclusionConclusion

Data CollectionData Collection

Data can be collected during observation or experiment.

Most often, data are collected during experiment as experiment can be better controlled.

Data CollectedData CollectedLength of string

/cm

Time for 10 cycles / s

Average time for 1 cycle /s

1

2

3

4

5

Data Collection

1) Why is it better to take the total time for 10 cycles?

__________________________________

2) How many times of measurement or repetitions are necessary?

__________________________________

To reduce the reaction time error.

At least three times. The more the better.

Graphical Data Analysis

Data can be analysed numerically (nu’/me/ri/cal-adj., nu/’me/ri/cal/ly-adv.) or/and graphically. We will use graphical method to find out the relation between two quantities, e.g. in the previous activity.

1. the length of string

2. average time for 1 cycle


‘x’ is used to represent the first quantity and ‘y’ ______________. the second

XX

The name of the graph could be either The graph of relationship between __ and y The graph of relationship between __ and y Or Or The graph of y against ___The graph of y against ___

Graphical Data AnalysisThe graph of y against x

x

y


• Plotting (繪製 ) a graph means drawing a graph with some sets of values of x and y.

• The values x and y may be the data collected in daily life or in experiments. For example, x represents the length of string and y the time for one cycle.


Length of string/m　

Average time for 1 cycle/s

1 0.85 2.16

2 0.73 1.70

3 0.64 1.60

4 0.35 1.18

How many sets of data are there in the above table? Ans : There ___________ sets of data.

are fourare four


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Length of string/m

aver

age

tim

e/s

The graph of average time against length of string

The graph


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Length of string/m

aver

age

tim

e/s

The graph of average time against length of string

The graph


A straight line or a curve can be drawn to show the relation between the two quantities.

A straight line represents the simplest A straight line represents the simplest relation.relation.

If the line is a straight line, then y and x have a linear relationship.


x : length of string y : average time The mathematical equation to represent the linear relationship between two quantities is y = y = mm x + x + cc

y = m x + c

y

x

C

The graph of y against xThe graph of y against x


m is the slope (斜率 ) of the graph.

c is the y-intercept (y 軸交截 )

y = m x + c

y

x

C



If c is zero,. i.e. the line passes the origin (0,0) , then y is directly proportional to (直接正比於 ) x, and m is the proportional constant (正比常數 ).

y = m x + c

y

X

C


Find the slope, m (2 points form)

y1

x1

(x1,y1)

y2

x2

(x2,y2)

y = y2-y1

x = x2-x1

1.On the graph line, choose two points.

Their locations are (x1, y1) and (x2, y2).

(x1, y1) is the first

point and (x2, y2) is

the second point

2.Draw a right-angled triangle as shown in the diagram.

3.The slope, m, can be calculated by the following formula:

x

y

xm

12

12

x-

y - y =

(delta: difference in- …)

Example 1

0.5 = 8

4 =

2 - 10

5 - 9 =m , slope the

9

5

2 10

(2,5)

(10,9)

y = 9-5

x = 10-2

What is the slope of the following graph ?

Steps : 1.Two points (2, 5) and (10,9) are chosen.2. A triangle is drawn. 3. By two points form :

Class Practice:

The slope, m =

8

6

4 10

(4,6)

(10,8)

8-6 10-4

= 13

Class Practice:

(6,8)

(18,14)

2.

The slope, m = 14-8 18-6

= 12

Example 1 : Discussion:

9

5

2 10

(2,5)

(10,9)

y = 9-5

x = 10-2

Will there be any difference if (10,9) is the first point and Will there be any difference if (10,9) is the first point and (2,5) the second point in example 1 ?(2,5) the second point in example 1 ?

ExampleA spring (彈簧 )was loaded with weights (W) in g. The length of the spring (L) is measured for each different load.

Load, W (g) 20 40 60 80 100

Length of Spring, L (cm) 16.0 20.0 24.5 28.0 31.5

Objective : To find an equationequation to describe the relationship between W (load) and L (length of spring).

The graph of length of spring against load

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120

load /g

len

gth

of

sp

rin

g /

cm

(20, 16.0)

(40, 20.0)

(60, 24.5)

(80, 28.0)

(100,31.5)


0

5

10

15

20

25

30

35

0 20 40 60 80 100 120

load /g

len

gth

of

sp

rin

g /

cm

Does the line pass through all points ? Ans :___NoNo

The y-intercept is about _____cm12.3

The slope :

096

3.12310.195

The equation to describe the relationship is: L = 0.195 W + 12.3


0

5

10

15

20

25

30

35

0 20 40 60 80 100 120load /g

len

gth

of

sp

rin

g /

cm

Equation : L = 0.195 W + 12.3

Discussion : What is the original length of the spring without being loaded? Answer : ____________What is the length of the spring if it is loaded with 200 g? Answer :_____________

12.3 cm

51.3 cm (L = 0.195 x 200 + 12.3)


0

5

10

15

20

25

30

35

0 20 40 60 80 100 120load /g

len

gth

of

sp

rin

g /

cm

Drawing the Best Fit Line

Which line is the best? Which line is the best?

Drawing the Best Fit Line The graph of length of spring against load

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120load /g

len

gth

of

sp

rin

g /

cm

Steps of drawing the best line.

1) From the data, find the mean values of both W and L (60, 24)

W : (20+40+60+80+100)/5 = 60L :(16+20+24.5+28+31.5)/5 = 24

Drawing the Best Fit Line Steps of drawing the best

line.1) From the data, find the mean

values of both W and L (60, 24)

2) On the graph paper, plot the mean point of (60,24).


0

5

10

15

20

25

30

35

0 20 40 60 80 100 120load /g

len

gth

of

sp

rin

g /

cm

Drawing the Best Fit Line The graph of length of spring against load

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120load /g

len

gth

of

sp

rin

g /

cm

Steps of drawing the best line.

1) From the data, find the mean values of both W and L (60, 24)

2) On the graph paper, plot the mean point of (60,24).

3) Draw a straight line passing through the mean point, and adjust the line so that data points on both sides of the mean points should be evenly distributed (平均地分佈 ) around the straight line.

Summary of Graphical Analysis

The graph of length of spring The graph of length of spring against loadagainst load


1) Write the name of the graph (e.g The graph of Length of spring against load)


load /g

len

gth

of

sp

rin

g /

cm



2) Select the vertical axis (Y-axis) and horizontal axis (X-axis), draw an arrow on each axis and label the two axes (Length of spring/cm, load/g)


0

5

10

15

20

25

30

35

0 20 40 60 80 100 120

load /g

len

gth

of

sp

rin

g /

cm




3)Properly draw the scale on the two axes


0

5

10

15

20

25

30

35

0 20 40 60 80 100 120

load /g

len

gth

of

sp

rin

g /

cm




3) Properly draw the scale on the two axes

4)Plot the data points on the graph paper


0

5

10

15

20

25

30

35

0 20 40 60 80 100 120

load /g

len

gth

of

sp

rin

g /

cm





4) Plot the data points on the graph paper

5)Find the mean values of all data for both horizontal and vertical axes (W : 60, L : 24)


0

5

10

15

20

25

30

35

0 20 40 60 80 100 120

load /g

len

gth

of

sp

rin

g /

cm





4) Plot the data points on the graph paper

5) Find the mean values of all data for both horizontal and vertical axes (W : 60, L : 24)

6)Locate and plot the mean point (60,24)


0

5

10

15

20

25

30

35

0 20 40 60 80 100 120

load /g

len

gth

of

sp

rin

g /

cm

Summary of Graphical Analysis 5) Find the mean values of all data

for both horizontal and vertical axes (W : 60, L : 24)

6) Locate and plot the mean point (60,24)

7)Draw a straight line to pass through the mean point. Ensure that there are points above and below the straight line on both sides of the mean point.


0

5

10

15

20

25

30

35

0 20 40 60 80 100 120

load /g

len

gth

of

sp

rin

g /

cm

Summary of Graphical Analysis 5) Find the mean values of all data

for both horizontal and vertical axes (W : 60, L : 24)

6) Locate and plot the mean point (60,24)

7) Draw a straight line to pass through the mean point. Ensure that there are points above and below the straight line on both sides of the mean point.

8)Extend the line to the y-axis, find the y-intercept, c.

12.3


0

5

10

15

20

25

30

35

0 20 40 60 80 100 120

load /g

len

gth

of

sp

rin

g /

cm

Summary of Graphical Analysis 7) Draw a straight line to pass

through the mean point. Ensure that there are points above and below the straight line on both sides of the mean point.

8) Extend the line to the y-axis, find the y-intercept, c.

9)On the straight line, locate two points and find the slope m with the method of two-point form.

12.3

12

12

W-

L - L = W

m =0.195


0

5

10

15

20

25

30

35

0 20 40 60 80 100 120

load /g

len

gth

of

sp

rin

g /

cm




9) On the straight line, locate two points and find the slope m with the method of two-point form.

10)Complete the equation. y = m x + c

12.3


0

5

10

15

20

25

30

35

0 20 40 60 80 100 120

load /g

len

gth

of

sp

rin

g /

cm




9) On the straight line, locate two points and find the slope m with the method of two-point form.

10)Complete the equation. L = 0.195W+12.3

12.3

Practice 1For the data in the following table, plot y

against x and draw the best straight line graph; and find the slope and the equation to describe the relationship between x and y.

x 1 2 3 4 5

y 3 5 7 9 11

Practice 2For the data in the following table, plot S

against t and draw the best straight line graph; and find the slope and the equation to describe the relationship between S and t.

t 20 40 60 80

s 36 46 56 66

Practice 3

In an experiment, the temperature (T/oC) of alcohol is recorded at different time (t /min) and the results are recorded in the table below.

t/min 10 15 20 25 30

T/oC 15 13 10 7 5

The graph of s against t

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16 18t

S

Curve Fitting : a Line or a Curve

Curve Fitting : a Line or a CurveThe graph of s against t

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16 18t

S

A line may be drawn but the points are quite far away from the graph.

But the points are quite close to the curve.

Curve Fitting : a Line or a CurveThe graph of s against t

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16 18t

S

In this situation, a curve is better than a line. But s and t is not linear related.

Discussion

How is the best fit line drawn ?

End of IntroductionEnd of Introduction

Thank you !!Thank you !!

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Introduction of Physics Shatin Tsung Tsin Secondary School Mr. C.K. Yu & Mr. Tai Kin Fai.

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