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

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.

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.

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

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 )

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

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. ======== ======== ======== ======== ========

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

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

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.

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

2nd activity Your teacher will throw an object again, sketch (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. Observation Data ___________ Data ____________ – Graphical Method ________________ Collection Analysis Conclusion

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

Data Collected Length 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. the length of string average time for 1 cycle

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

Graphical Data Analysis The graph of y against x x

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.

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

Graphical Data Analysis The graph

Graphical Data Analysis The graph

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.

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

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

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

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

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 :

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

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

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 ?

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).

(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

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 = 0.195 W + 12.3

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 = 0.195 x 200 + 12.3)

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

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

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).

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.

Summary of Graphical Analysis

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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.

Discussion How is the best fit line drawn ?

End of Introduction Thank you !!