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

2. What is Physics? Extracted from New Physics at Work, book 1A
Physics is the scientific study of matter and energy and 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 principles for their design.
The study of physics helps us develop a scientific way of working and problem solving, e.g, proposing hypotheses and testing them against observations. It also helps us to develop a set of values and attitudes such as curiosity, honesty, respect for evidence, appreciation of achievement in physics and recognition of limitations.

3. Introduction 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.

4. Objectives of Studying Physics
Able to make observation
Able to understand how things behave in the observation
Able to understand what laws and theories about an observation
Able to apply the laws and theories in solving related problems

5. Steps of scientific study of physics
Observation (how things behave in our daily life )
Data collection (experiment measurement, data recording)
Data analysis (numerical analysis, graphical analysis)
Conclusion (Laws, Theories and Principles )

6. 1st Activity
Your teacher will throw an object. Observe and draw a diagram to show what you saw.
the object

7. Observation
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.
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8. Data Collection
Your 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

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

10. Conclusion
Make a conclusion about the relation of the two time measurements.
(about, approximate, exactly, twice)
_________________________________
The total time is about twice the time to the highest position.
The time to the highest position is about the same as the time returning to his hand from the highest position.

11. Summary of Introduction
We learn the following steps in scientific study of Physics.
Observation
Data Collection
Data Analysis
Conclusion    

12. 2nd activity
Your teacher will throw an object again, sketch (簡單描繪) how the object moves/flies.

13. 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.

14. 2nd activity
Length of string
Total time for ten cycles 1 2 3 4 5

15. 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.

16. Scientific Method of Study
The steps of scientific study of physics that you learned in previous lessons.
Observation
Data ___________
Data ____________ – Graphical Method
________________
Collection
Analysis
Conclusion

17. Data Collection
Data can be collected during observation or experiment.
Most often, data are collected during experiment as experiment can be better controlled.

18. Data Collected Length of string /cm Time for 10 cycles / s
Average time for 1 cycle /s 1 2 3 4 5

19. 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.

20. 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.
the length of string
average time for 1 cycle

21. Graphical Data Analysis
‘x’ is used to represent the first quantity and ‘y’ ______________.
the second
The name of the graph could be either
The graph of relationship between __ and y
Or The graph of y against ___ X X

22. Graphical Data Analysis
The graph of y against x x

23. Graphical Data Analysis
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.

24. Graphical Data Analysis
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 four

25. Graphical Data Analysis
The graph

26. Graphical Data Analysis
The graph

27. Graphical Data Analysis
A straight line or a curve can be drawn to show the relation between the two quantities.
A straight line represents the simplest relation.
If the line is a straight line, then y and x have a linear relationship.

28. Graphical Data Analysis
y = m x + c y x C
The graph of y against x
x : length of string
y : average time
The mathematical equation to represent the linear relationship between two quantities is
y = m x + c

29. Graphical Data Analysis
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
The graph of y against x

30. Graphical Data Analysis
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
The graph of y against x

31. Find the slope, m (2 points form)
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
Draw a right-angled triangle as shown in the diagram.
3.The slope, m, can be calculated by the following formula: y2 x2
(x2,y2)
Dy = y2-y1
(x1,y1) y1
Dx = x2-x1
(D, delta: difference in- …) x1

32. Example 1 What is the slope of the following graph ? 5 2 Steps :9 5 2 10
(2,5)
(10,9)
Dy = 9-5
Dx = 10-2
Steps :
Two points (2, 5) and (10,9) are chosen.
2. A triangle is drawn.
3. By two points form :

33. Class Practice: 8 6 4 10 (4,6) (10,8) 8-6 10-4 1 3 The slope, m = = 1.

34. Class Practice: (6,8) (18,14) 14-8 18-6 1 2 = The slope, m = 2. 1. 8 610
(4,6)
(10,8)

35. Example 1 : Discussion: 5 2 (10,9) 9 Dy = 9-5 (2,5) Dx = 10-2 10
Will there be any difference if (10,9) is the first point and (2,5) the second point in example 1 ?

36. Example
A 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 equation to describe the relationship between W (load) and L (length of spring).

37. (20, 16.0)
The graph of length of spring against load
(40, 20.0) 35
(60, 24.5) 30
(80, 28.0) 25
(100,31.5) 20
length of spring /cm 15 10 5 20 40 60 80
100
120
load /g

38. Does the line pass through all points ? Ans :___
The graph of length of spring against load 5 10 15 20 25 30 35 40 60 80
100
120
load /g
length of spring /cm
Does the line pass through all points ? Ans :___ No
The y-intercept is about _____cm
12.3
The slope :
0.195
The equation to describe the relationship is:
L = W

39. Equation : L = 0.195 W + 12.3 Discussion :
The graph of length of spring against load 5 10 15 20 25 30 35 40 60 80
100
120
load /g
length of spring /cm
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 = x )

40. Drawing the Best Fit Line
The graph of length of spring against load
Which line is the best? 35 30 25
length of spring /cm 20 15 10 5 20 40 60 80
100
120
load /g

41. Drawing the Best Fit Line
The graph of length of spring against load 5 10 15 20 25 30 35 40 60 80
100
120
load /g
length of spring /cm
Steps of drawing the best line.
From the data, find the mean values of both W and L (60, 24)
W :
( )/5
= 60
L :
( )/5
= 24

42. Drawing the Best Fit Line
The graph of length of spring against load 5 10 15 20 25 30 35 40 60 80
100
120
load /g
length of spring /cm
Steps of drawing the best line.
From the data, find the mean values of both W and L (60, 24)
On the graph paper, plot the mean point of (60,24).

43. Drawing the Best Fit Line
The graph of length of spring against load 5 10 15 20 25 30 35 40 60 80
100
120
load /g
length of spring /cm
Steps of drawing the best line.
From the data, find the mean values of both W and L (60, 24)
On the graph paper, plot the mean point of (60,24).
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.

44. Summary of Graphical Analysis

45. Summary of Graphical Analysis
1) Write the name of the graph (e.g The graph of Length of spring against load)
The graph of length of spring against load

46. Summary of Graphical Analysis
Write the name of the graph (e.g The graph of Length of spring against load)
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)
The graph of length of spring against load
length of spring /cm
load /g

47. Summary of Graphical Analysis
Write the name of the graph (e.g The graph of Length of spring against load)
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)
Properly draw the scale on the two axes
The graph of length of spring against load 35 30 25 20
length of spring /cm 15 10 5 20 40 60 80
100
120
load /g

48. Summary of Graphical Analysis
Write the name of the graph (e.g The graph of Length of spring against load)
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)
Properly draw the scale on the two axes
Plot the data points on the graph paper
The graph of length of spring against load 35 30 25 20
length of spring /cm 15 10 5 20 40 60 80
100
120
load /g

49. Summary of Graphical Analysis
Write the name of the graph (e.g The graph of Length of spring against load)
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)
Properly draw the scale on the two axes
Plot the data points on the graph paper
Find the mean values of all data for both horizontal and vertical axes (W : 60, L : 24)
The graph of length of spring against load 35 30 25 20
length of spring /cm 15 10 5 20 40 60 80
100
120
load /g

50. Summary of Graphical Analysis
Write the name of the graph (e.g The graph of Length of spring against load)
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)
Properly draw the scale on the two axes
Plot the data points on the graph paper
Find the mean values of all data for both horizontal and vertical axes (W : 60, L : 24)
Locate and plot the mean point (60,24)
The graph of length of spring against load 35 30 25 20
length of spring /cm 15 10 5 20 40 60 80
100
120
load /g

51. Summary of Graphical Analysis
Find the mean values of all data for both horizontal and vertical axes (W : 60, L : 24)
Locate and plot the mean point (60,24)
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.
The graph of length of spring against load 35 30 25 20
length of spring /cm 15 10 5 20 40 60 80
100
120
load /g

52. Summary of Graphical Analysis
Find the mean values of all data for both horizontal and vertical axes (W : 60, L : 24)
Locate and plot the mean point (60,24)
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.
Extend the line to the y-axis, find the y-intercept, c.
The graph of length of spring against load 35 30 25 20
length of spring /cm 15
12.3 10 5 20 40 60 80
100
120
load /g

53. Summary of Graphical Analysis
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.
Extend the line to the y-axis, find the y-intercept, c.
On the straight line, locate two points and find the slope m with the method of two-point form.
The graph of length of spring against load 35 30 25 20
length of spring /cm 15
12.3 10 5
=0.195 20 40 60 80
100
120
load /g

54. Summary of Graphical Analysis
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.
Extend the line to the y-axis, find the y-intercept, c.
On the straight line, locate two points and find the slope m with the method of two-point form.
Complete the equation.
y = m x + c
The graph of length of spring against load 35 30 25 20
length of spring /cm 15
12.3 10 5 20 40 60 80
100
120
load /g

55. Summary of Graphical Analysis
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.
Extend the line to the y-axis, find the y-intercept, c.
On the straight line, locate two points and find the slope m with the method of two-point form.
Complete the equation.
L = 0.195W+12.3
The graph of length of spring against load 35 30 25 20
length of spring /cm 15
12.3 10 5 20 40 60 80
100
120
load /g

56. Practice 1
For 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 7 9 11

57. Practice 2
For 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

58. 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 13 7 5

59. Curve Fitting : a Line or a Curve
The graph of s against t 35 30 25 20 S 15 10 5 2 4 6 8 10 12 14 16 18 t

60. Curve Fitting : a Line or a Curve
The graph of s against t 5 10 15 20 25 30 35 2 4 6 8 12 14 16 18 t 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.

61. Curve Fitting : a Line or a Curve
The graph of s against t 5 10 15 20 25 30 35 2 4 6 8 12 14 16 18 t S
In this situation, a curve is better than a line. But s and t is not linear related.

62. Discussion
How is the best fit line drawn ?

63. End of Introduction
Thank you !!