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- 1. LESSON 4 - SCIENTIFIC INVESTIGATIONS Hypothesis When physicists observe a particular physical phenomenon they will as questions as to how A general statement about the relationship or why it happens . A hypothesis will be put between a manipulated variable and a forth and experiments or scientific responding variable. investigations will be carried out to prove or disprove the hypothesis. If the experiments The hypothesis should be written as : bear out the hypothesis, the hypothesis may The greater the………, the greater the……. come to regarded as theory or law of nature. If Or the don’t the hypothesis will be rejected or The bigger the…………., the smaller the….. modified. In any experiment , the report on the Manipulated variable experiment will be based on these guidelines and follows a sequence as shown in the The quantity whose values we deliberately choose following flow chart: to change or a primary variable which causes other secondary variable to change. Responding variable The quantity whose value depend on the manipulated variable or a secondary variable which changes in response to the change in the manipulated variable. Fixed variable The quantity whose value is kept constant throughout the experiment. Aim A statement to show the investigation of the variables involve. The aim of the experiment should be written as: To investigate the relationship between ………..and ……………… Inference Apparatus Early assessment that is carried out to answer the questions raised. List the apparatus and materials used so that at least a set of data for manipulated and responding The inference should be written as : variables can be determined. …………………depend on……………………. Or State the arrangement of the apparatus that can The ……………..changes as the function by drawing a labeling diagram . …………...changes Procedure State the method of controlling the manipulated variables 21
- 2. State the method of measuring the responding variables Repeat the experiments at least four times. If the data too small or too big use the standard form number. Tabulating the data For example Record the data in the following table Temperature θ /oC 10 20 30 40 50 Density, ρ / kg m-3 9.7 8.5 7.3 6.6 5.1 Manipulated variable Responding variable x 104 How to plot the graph ? The title of the graph must be shown. The axes of the graph must be labeled with the unit used. For example: Analyzing the data Plot a graph of ( Responding variable) against (Manipulated variable) How to tabulate the data ? The scale chosen must be easy to use. The table must be neatly drawn and the data Scales such 1:1 , 1:2 , 1:5 ,1:10 ,1:100 are arranged in either and rows. proffered in plotting a graph. The names and symbols of the manipulated and Odd scales such as 1:3 , 1:4 , 1: 6 , 1:7 , 1: 30 responding variables must be written together with should be avoided in plotting a graph. the units. For example, Make sure the area covered by the plotted points must not be less than 50% of the area of the graph Velocity, v / s paper. Time , t / s For example: Volume , V / m3 Pressure , P / Pa The data shown in the table must be consistent in The scale on the axes must be uniform and clearly the number of decimal places in accordance with marked with value. the respective measuring instruments. For example: For example, Length, l / cm Time , t /s 0 12.8 2 25.6 4 39.4 6 52.2 8 75.0 22
- 3. or y α x All the points are marked with a symbol such as a cross or circle and the centre of the cross must or y = kx k = constant accurately positioned. or y = mx m = gradient or y1 = y2 x1 x2 The best straight line or the best curve graph must be drawn. 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. y increases linearly with x or y = mx + c m = gradient c = intercept on axis-y y decreases linearly with x or y = -mx + c m = gradient c = intercept on axis-y It is not advisable to plot graph by joining point to point because the graph obtained is not smooth. y is inversely proportional to x or y α 1 x or y = k x k = constant or y1 x1 = y2 x2 How to analyze the data ? (a) Determine the relationship between two variables. Example : y is directly proportional to x. (b) Determine the gradient of the graph 23
- 4. Example Draw a sufficiently large triangle to calculate the gradient of the graph. State value of the gradient with correct unit. The gradient of the graph is m = y2 - y1 x2 - 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. (d) State the precautions should be taken For example: The circuit connections must be taken Off the switch when taking the reading of the meters. Make sure the amplitude of oscillation is small. 24
- 5. TUTORIAL 4 4 Which of the following graphs show that y increases linearly with x? 1 Which of the following is the best way to tabulate the data ? A Voltage,V 0 5 10 15 20 Current,I 0 1.7 2.5 3.4 4.2 B Time,t /s 2 4 6 8 10 2000 5000 8000 11000 14000 Density,ρ / kgm-3 5 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 C Period, T 10.5 15.3 19.8 27.9 36.0 of the following graphs shows the Hooke’s /s Law? Distance, d 2.5 3.3 4.6 5.8 6.9 /m D Object 5.1 8.7 11.6 16.5 18.6 distance ,u / cm Image 2.3 5 6.9 9 11.6 distance, v / cm 2 Which of the following scales is the most suitable to plot a graph? 6 The acceleration, a of an object is inversely proportional to the mass, m of the object A B 1 cm : 3 unit 1 cm : 5 unit under constant force. C D 1 cm : 6 unit 1 cm : 8.8 unit Which of the following graphs describes the relationship between a and m . 3 Which of the following is the best graph ? 25
- 6. 7 12 An experiment is carried out to find the The resistance R and temperature T for an electric conductor is given as R = r + aT with relationship between mass and acceleration of a trolley on a wooden runway. r as the resistance at 0oC and a as a The experiment is repeated by adding the constant. number of trolleys. A graph of R against T is shown . The responding variable in this experiment is A the length of the wooden runway. B acceleration C mass What is the resistance ,R of the conductor at a 8 In a simple pendulum experiment, the length temperature 60oC ? of the pendulum and time for 20 oscillations are recorded. A B 35 47 The length of the pendulum is a C D 86 93 E 180 A manipulated variable B responding variable 13 C fixed variable 9 Based on the graph above, what is the gradient of the graph? The equation of the graph above is A B - 1.5 - 0.7 A B P = 10Q + 5 P = 2Q + 10 C D 0.7 1.0 C D P = -2Q + 10 P = 5Q – 10 E 1.5 14 The following figure shows a graph U versus V. 10 What is the unit of the gradient of the graph above? A B m m2 s C D ms2 ms- 2 Which of the following shows the correct 11 A student plot a graph for a physical quantity , relationship between U and V? Q on axis-y against a physical quantity ,R on axis –x A U=mV +m The relationship between Q and R is given by n as Q - aR = b , where a and b are constants. The gradient of the graph is B U=-mV +m n Aa B R C U=mV + n b Q n C D b a D U=-nV +m m 26
- 7. 15 The pressure ,P of the gas is directly 9 proportional to the absolute temperature, T of the gas. When P = 100 ,T = 50. What is the value of P 19 when T = 400. A student carries out an experiment to find out the relationship between the change in A B 0.8A 125 length , y , of a spring and mass, m , of the C D 200 800 load on the spring. The arrangement of the E 2000 apparatus for the experiment is shown in Figure 1 . The length of the spring when a 16 Boyle’ s law state that the pressure of the gas load is placed on the piston is l . is inversely proportional to the volume of the gas. The pressure of a bubble under sea surface is 120 cm Hg Pa and its volume is 15.8 cm3. When the bubble rises to the surface of the sea the pressure of the bubble is 76 cm Hg. What is the volume of the bubble at the surface of the sea? A B 10.0 cm3 25.0 cm3 C D 124.8 cm3 309.1 cm3 E 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 2 , what is the value of x in the table above. At the beginning of the experiment there is no A B 10 m 40 m load. The length of the spring is lo . The actual C D 80 m 160 m length of lo is shown in Figure 2. E 240 m The experiment is repeated by using load with mass , m , equal to 0.5 kg , 1.0 kg , 1.5 kg , 18 Newton’s universal law of gravitation states 2.0 kg and 2.5 kg. The actual lengths of the that the gravitational force of attraction, F spring when the different masses are used are between two point masses is inversely shown in Figure 3, Figure 4 , Figure 5 , proportional to the square of the distance ,R Figure 6 and Figure 7. between them. If the distance between them is 3R, what is the gravitational force of attraction ? A 9F B 3F CF DF 3 EF 27
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- 9. 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. (b) Measure the length of the spring in Figure 2. (d) Based on your graph, state the lo = ___________________ relationship between y and m . 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 ) 29
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- 11. Graph T2 against l T2 / s2 5 4 3 2 1 l / cm 0 20 40 60 80 100 31 l/cm
- 12. ……………………………………………… 20 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. ………………………………………….. ………………………………………….. (ii) Calculate period, T, when the length l = 45 cm. (Show your working) 21 The graph above represents graph W against V , where W and V are the distances on a wooden rod. (a) Based on the graph state the: (i) manipulated variable (iii) Calculate the gradient of the graph. ________________________________ (ii) responding variable _________________________________ (b) Using the value of the gradient obtained (b) Calculate the gradient of the graph. from (a)(iii) and the equation, calculate the acceleration due to gravity , g. (c) Determine the intercept on (i) axis- W .................................................... axis-V (ii) State one precaution for this experiment. (c) ..................................................... ……………………………………………… (d) State the equation of the line 32
- 13. ............................................................... 22 Pak Ali 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. (b) 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 hypothesis. 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 33

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