Lesson 4- Scientific Investigations

…………………depend on………… …………. Or The ……………..changes as the …………...changes

LESSON 4 SCIENTIFIC INVESTIGATIONS When physicists observe a particular physical phenomenon they will as questions as to how or why it happens . A hypothesis will be put forth and experiments or scientific investigations will be carried out to prove or disprove the hypothesis. If the experiments bear out the hypothesis, the hypothesis may come to regarded as theory or law of nature. If the don’t the hypothesis will be rejected or modified. In any experiment , the report on the experiment will be based on these guidelines and follows a sequence as shown in the following flow chart:

Hypothesis A general statement about the relationship between a manipulated variable and a responding variable. The hyphotesis should be written as : The greater the………, the greater the……. Or The bigger the…………., the smaller the….. Manupulated variable The quantity whose values we deliberately choose to change or a primary variable which causes other secondry variable to change. Responding variable The quantity whose value depend on the manipulated variable or a secondry variable which changes in response to the change in the manipulated variable. Fixed variable The quantity whose value is kept constant throughout the experiment.

Inference

Aim

Early assessment that is carried out to answer the questions raised.

A statement to show the investigation of the variables involve.

The inference should be written as :

The aim of the experiment should be written as:

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To investigate the relationship between ………..and ………………

Velocity,v /s Time , t / s

Apparatus List the apparatus and materials used so that at least a set of data for manipulated and responding variables can be determined.

Volume , V / m3

State the arrangement of the apparatus that can function by drawing a labeling diagram .

Pressure , P / Pa

The data shown in the table must be consistent in the number of decimal places in accordance with the respective measuring instruments. For example, Length, l / Time , t /s cm 0 12.8 2 25.6 4 39.4 6 52.2 8 75.0

Procedure State the method of controlling the manipulated variables State the method of measuring the responding variables Repeat the experiments at least four times. Tabulating the data Record the data in the following table Manipulated variable

Responding variable If the data too small or too big use the standard form number. For example Temperature θ /oC Density, ρ / kgm-3 x 104

Analysing the data Plot a graph of ( Responding variable) against (Manupulated variable)

10

20

30

40

50

9. 7

8. 5

7. 3

6. 6

5. 1

How to plot the graph ? The title of the graph must be shown. The axes of the graph must be labelled with the unit used. For example:

How to tabulate the data ? The table muast be neatly drawn and the data arranged in either and rows. The names and symbols of the manipulated and responding variables must be written together with the units. For example,

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The best straight line or the best curve graph is the line that passes through most of the points plotted such that it is balanced by the number of points above and below the line.The line also must smooth. The scale choosen must be easy to use. Scales such 1:1 , 1:2 , 1:5 ,1:10 ,1:100 are preffered in plotting a graph. Odd scales such as 1:3 , 1:4 , 1: 6 , 1:7 , 1: 30 should be avoided in plotting a graph. Make sure the area covered by the plotted points must not be less than 50% of the area of the graph paper.

It is not advisable to plot graph by joining point to point because the graph obtained is not smooth.

For example:

The scale on the axes must be uniform and clearly marked with value. For example:

How to analyse the data ? (a) Determine the relationship between two variables. Example :

All the points are marked with a symbol such as a cross or circle and the centre of the cross must accurately positioned.

y is directly proportional to x. or y α x or y = kx k = constant or y = mx m = gradient or y1 = y2 x1 x2

The best straight line or the best curve graph must be drawn.

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y increases linearly with x or y = mx + c m = gradient c = intercept on axis-y

Draw a suffiecienly large triangle to calculate the gradient of the graph. State value of the gradient with correct unit. The gradient of the graph is m

y decreases linearly with x or y = -mx + c m = gradient c = intercept on axis-y

= y2 - y 1 x 2 - x1 = QR QR

(c) Determine the certain values from the graph. Certain important values can be obtained from the graph plotted by drawing a horizontal line or by extrapolating the graph.

y is inversely proportional to x atau y α 1 x atau y = k x k = constant atau y1 x1 = y2 x2

(d) State the precautions should be taken For example: The circuit connentions must be taken Off the switch when taking the raeding of the meters. Make sure the amplitude of oscillation is small.

(b) Determine the gradient of the graph Example

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TUTORIA 1

Which of the following is the best way to tabulate the data ?

A Voltage, V Current, I

0

5

10

15

20

0

1.7

2.5

3.4

4.2

B Time,t /s Density, ρ / kgm3

2

4

6

8

10

20 00

50 00

80 00

1 100 0

1 400 0

C Period,T /s Distanc e,d /m

1 0.5

1 5.3

1 9.8

27.9

36.0

2.5

3.3

4.6

5.8

6.9

D Object distanc e ,u / cm Image distanc e, v / cm

5.1

8.7

1 1.6

16.5

18.6

2.3

5

6.9

9

11.6

2

Which of the following scales is the most suitable to plot a graph? A

1 cm : 3 unit

B

1 cm : 5

C 1 cm : 6 unit 8.8 unit

D

1 cm :

unit

3 Which of the following is the best graph ?

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Which of the following graphs describes the relationship between a and m .

4

5

Which of the following graphs show that y increases linearly with x?

7

An experiment is carried out to find the relationship between mass and acceleration of a trolley on a wooden runway. The experiment is repeated by adding the number of trolleys. The responding variable in this experiment is

A the length of the wooden runway. B acceleration C mass

Hooke’s law states that applied force F is directly proportional to the extension x of spring if its elastic limit is not exceeded. Which of the following graphs shows the Hooke’s Law?

8

In a simple pendulum experiment, the length of the pendulum and time for 20 oscillations are recorded. The length of the pendulum is a A B C

6

The acceleration,a of an object is inversely proportional to the mass,m of the object under constant force.

9

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manipulated variable responding variable fixed variable

Based on the graph above, what is the gradient of the graph?

A C E

- 1.5 0.7 1.5

D

B - 0.7 1.0

The equation of the graph above is

10 What is the unit of the gradient of the graph above? A C

m ms2

B D

A P = 10Q + 5 2Q + 10 C P = -2Q + 10 5Q – 10

2

m s ms- 2

11 A student plot a graph for a physical quantity , Q on axis-y against a physical quantity ,R on axis –x The relationship between Q and R is given by as Q - aR = b , where a and b are constants. The gradient of vthe graph is A a

B

B

P=

D

P=

14 The following figure shows a graph U versus V.

R

b Q C

b

D

Which of the following shows the correct relationship between U and V?

a

12 The resistance R and temperature T for an electric conductor is given as R = r + aT with r as the resistance at 0oC dan a as a constant. A graph of R against T is shown .

A B

U=-mV +m n C U=mV + n n D U=-nV +m m 15 The pressure ,P of the gas is directly proportional to the absolute temperature, T of the gas. When P = 100 ,T = 50. What is the value of P when T = 400.

What is the resistance ,R of the conductor at a temperature 60oC ? A C E

35 86 180

B D

U=mV +m n

47 93

13

26

A

0.8A

B

C

200

D

E

2000

125 800

16 Boyle’ s law state that the pressure of the gas is inversely proportional to the volume of the gas. The pressure of a buble under sea surface is 120 cm Hg Pa and its volume is 15.8 cm3. When the buble rises to the surface of the sea the pressure of the buble is 76 cm Hg. What is the volume of the buble at the surface of the sea?

cm3

A 10.0 cm3 cm3 C 124.8 cm3 E

B

25.0

D

309.1

19 A student carries out an experiment to find out the relationship between the change in length , y , of a spring and mass, m , of the load on the spring. The arrangement of the apparatus for the experiment is shown in Figure 1 . The length of the spring when a load is placed on the piston is l .

577.2 cm3

17 An object is released from a height , h and the time taken to reach the ground is t.2 h/m 20 x t/s 2 4 If h is directly proportional to t , what is the value of x in the table above.

2

A

10 m

B

40 m

C

80 m

D

160

E

240 m

At the beginning of the experiment there is no load. The length of the spring is lo . The actual length of lo is shown in Figure 2. The experiment is repeated by using load with mass , m , equal to 0.5 kg , 1.0 kg , 1.5 kg , 2.0 kg and 2.5 kg. The actual lengths of the spring when the different masses are used are shown in Figure 3, Figure 4 , Figure 5 , Figure 6 and Figure 7.

m 18 Newton’s universal law of gravitation states that the gravitational force of attraction, F between two point masses is inversely proportional to the square of the distance ,R between them. If the distance between them is 3R, what is the gravitational force of attraction ? A 9F B 3F C F D F 3 E

F 9

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Tabulate your results for m ,l and y in the space below. (a) Based on the aim and the procedure of the experiment state the: (i) manipulated variable ______________________________ __ (ii) responding variable ______________________________ ___ (iii) constant variable

(c) On the graph paper , plot a

graph of y against m. ______________________________ __

(d) Based on your graph, state the relationship between y and m

(b) Measure the length of the spring in Figure 2. lo = ___________________

. ______________________________

Measure the lengths l of the spring in Figure 3 , Figure 4 , Figure 5 , Figure 6 and Figure 7 when different load are used.

___ ______________________________ ___

In each case, calculate the change in length, y , of the spring where; y = ( lo – l )

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30

Graph T2 against l

T2 / s2

5

4

3

2

1

l / cm

0

20

40

60

80

100

31 l/cm

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A student carries out an experiment to investigate the relationship between the length of a simple oscillating pendulum ,l , with its period, T. The experiment is repeated using different lengths,l, and their corresponding periods, T, are recorded. A graph of T2 against l , is then plotted as shown above. (a) Based on the graph, (i) State the relationship between T2 with l. …………………………… ……………..

(c) State one precaution for this experiment. …………………………………… ………… …………………………………… …………

…………………………… …………….. (ii) Calculate period,T, when the length l = 45 cm. (Show your working)

(iii) Calculate the gradient of the graph.

21 The graph above represents graph W against V , where W and V are the distances on a wooden rod. (a)

(b)

Using the value of the gradient obtained from (a)(iii) and the equation,

Based on the graph state the: (i) manipulated variable ______________________________ __

calculate the acceleration

(ii) responding variable

due to gravity , g.

______________________________ ___

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(b) Calculate the gradient of the graph.

State one appropriate hypothesis for an investigation. (c) With the use of apparatus such as pendulum bob , string and other apparatus, describe an experimental framework to test your hyphothesis. In your description, state clearly the following: (i) Aim of the experiment (ii) Variables in the experiment (iii) List of apparatus and materials (iv) Arrangement of the apparatus (v) The procedure of the experiment which include the method of controlling the manipulated variable and the method of measuring the responding variable (vi) Way you would tabulate the data (vii) Way you would analysis the data (b)

(c) Determine the intercept on (i) axis- W ........................................ ............ (ii)

axis-V ........................................

............. (d) State the equation of the line ............................................... ................

22 Pak Abu has a pendulum clock as shown in the diagram below.

Every day it was observed that the clock was slow about 2 minutes. Pak Ali raised the position of the bob to correct the clock. Based on the observations: (a) State one suitable inference that can be made.

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