Prelim H2P4 - soln

1 1 In this experiment, you will investigate how the resistance R of a thermistor varies with its temperature θ. (a) Construct the circuit shown in Fig. 1.1. Fig. 1.1 (b) Immerse the thermistor in a beaker of water. Measure and record the current I, potential difference V and temperature θ. I = .............................. V = .............................. θ = ……....................[1] (c) (i) Arrange the apparatus so that the water may be heated. Use the stand and clamp to ensure that the wires connected to the thermistor are kept well away from the source of heating. (ii) Use the heating apparatus to raise the temperature of the water by about 10 0C. After the temperature has stabilized, measure and record the new values of I, V and θ. I = .............................. V = .............................. θ = ……....................... 9749/04/ASRJC/2021Prelim [Turn Over M1 For Examiner’s Use V mA 11.1 mA 2.08 V 30.0 0C 17.4 mA 2.08 V 43.0 0C

2 (iii) Repeat (c)(ii) for θ varying from room temperature to 80 °C. Tabulate these results. Include the results from (b), (c)(ii), all the values of R, where R = V / I, and all the values of thermodynamic temperature T, where T = θ + 273. [6] θ / °C V / V I / mA R / Ω T / K ln (R/ Ω) 1 T / 10 3‒ K‒ 1 30.0 2.08 11.1 187 303.0 5.23 3.300 43.0 2.08 17.4 120 316.0 4.79 3.165 50.0 2.08 23.5 88.5 323.0 4.48 3.096 60.0 2.08 31.6 65.8 333.0 4.19 3.003 70.0 2.07 41.9 49.4 343.0 3.90 2.915 80.0 2.07 54.3 38.1 353.0 3.64 2.833 (d) The formula which relates R and T is where A is a constant, E is an energy characteristic of the thermistor, and k = 1.38 × 10 23‒ J K 1‒ . Plot a suitable graph to determine values for E and A. [7] R= Ae E kT ln R= E k ( 1 T )+ ln A Plot a graph of ln R against 1/T where gradient = E/k, and y-intercept = ln A. Hence Substituting (3.440 × 10 3‒ , 5.72) into y = mx + c: y-intercept c = 5.72 – 3.46 × 103 (3.440 × 10 3‒ ) = – 6.18 ln A = 6.18‒ A = e 6.18‒ = 2.07 × 10 3‒ Ω E = …………..……….. 9749/04/ASRJC/2021Prelim For Examiner’s Use P2 P3 P1 M2 A2 A4 A5 A3 A1 Gradient = 4.77 × 10 20‒ J 2.07 × 10 3‒ Ω

3 A = ……..…………….. 9749/04/ASRJC/2021Prelim [Turn Over For Examiner’s Use P4 P5 P6 3.60 3.80 4.00 5.80 4.20 5.60 5.40 4.40 5.20 4.60 4.80 5.00 2.800 2.900 3.000 3.100 3.200 3.300 3.400 3.500 (2.880, 3.78) (3.440, 5.72) x x x x x x ln (R/)

4 (e) Comment on any anomalous data or results you may have obtained. Explain your answer. ……..…………………………………………………………………………………….………… ……………..…………………………………………………………………………….………… ……………………...………………………………………..…………………………….……[1] [Total: 15 marks] 9749/04/ASRJC/2021Prelim M3 There are no anomalous data as all the plotted points lie close to the best fit line.

5 2 In this experiment, you will investigate the oscillations of a pendulum. (a) Set up the apparatus as shown in Fig. 2.1. The length l of the pendulum is approximately 70 cm. As the pendulum oscillates, a stop shortens the effective length l by an amount d. Mount the wooden rod horizontally so that it acts as a stop half-way down the pendulum. The stop should just touch the string when the pendulum rests in a vertical plane. (b) (i) Measure and record the value of l. l = ..………….………..……….. (ii) Measure and record the value of d. d = …………….………..…… [1] (iii) Gently displace the pendulum so that it performs small oscillations in a vertical plane perpendicular to the stop. Make and record measurements to determine the period T of these oscillations. T = = = 1.42 s 9749/04/ASRJC/2021Prelim [Turn Over d wooden blocks l stop M1 M2 A1 For Examiner’s Use Fig. 2.1 0.700 m 0.350 m

6 T = …………….………..…… [2] (c) The quantities d and T are related by the equation where k and l are constants, and g = 9.81 m s 2. (i) Calculate k. k = …………….……….. m s 2 [2] (ii) It is not accurate to draw a conclusion for the value of k based on only one reading as in c(i). It is a good practice to determine k graphically. Using the same apparatus, describe how you would obtain further measurements, and the graph that you would plot to determine k. [2] [Total: 7 marks] 9749/04/ASRJC/2021Prelim A2 A3 A4 A5 1.42 s For Examiner’s Use 9.41 Repeat the experiment with different d by changing the position of the wooden rod to obtain 6 sets of d and T. Plot a graph of T against (where gradient = and y-intercept = ), Determine gradient of the graph and find k using k = .

7 3 In this experiment, you will model the stability of a scoop of ice cream in a cone. (a) (i) Measure and record the diameter x and the height h of the cone, as shown in Fig. 3.1. Fig. 3.1 x = …..…………….…………. h = …..…………….……[1] (ii) Estimate the percentage uncertainty in your value of x. percentage uncertainty of x = = 15 % percentage uncertainty = …..…………….………….% [1] 9749/04/ASRJC/2021Prelim [Turn Over For Examiner’s Use M1 A1 cm cm 3.4 cm 12.8 cm 15

8 (b) (i) Place the ping-pong ball in the cone, as shown in Fig. 3.2. Tilt the cone until the ping-pong ball falls out, as shown in Fig. 3.3. The angle between the bench and the centre line of the cone is θ. The height of the top of the centre line above the bench is y. Fig. 3.2 Fig. 3.3 Measure and record θ and y. cm θ = …..…………….…………. y = …..…………….…………. [2] (ii) Calculate tan θ. tan 45 = 1.0 tan θ = …..…………….…………. [1] 9749/04/ASRJC/2021Prelim For Examiner’s Use M2 M3 A2 9.7 cm 1.0

9 (c) (i) You have been provided with a sheet of paper with the outline of another cone. Cut around the outline and assemble this cone. (ii) Repeat (a)(i) and (b). x = …..…………….…………. h = …..…………….…………. θ = …..…………….…………. y = …..…………….…………. tan θ = …..…………….…………. [2] (d) It is suggested that where k is a constant. (i) Use your values from (a)(i), (b) and (c)(ii) to determine two values for k. Give your values for k to an appropriate number of significant figures. first value for k = cm second value for k = cm first value for k = …..…………….…………. second value for k = …..…………….…………. [1] 9749/04/ASRJC/2021Prelim [Turn Over For Examiner’s Use M4 M5 A3 cm cm cm tan 63 = 2.0 2.9 cm 10.6 cm 63 9.2 cm 2.0 4.5 cm 6.6 cm

10 (ii) State whether the results of your experiment support the suggested relationship. Justify your conclusion by referring to your value in (a)(ii). ………………………………………………………………………………………………. ………………………………………………………………………………………………. ………………………………………………………………………………………………. ………………………………………………………………………………………………. …………………………………………………………………………………………… [1] (e) (i) Suggest two significant sources of error in this experiment. 1 …………………………………………………………………………………………….. ………………………………………………………………………………………………. ………………………………………………………………………………………………. ………………………………………………………………………………………………. 2 ……………………………………………………………………………………………. ………………………………………………………………………………………………. ………………………………………………………………………………………………. ………………………………………………………………………………………………. [2] (ii) Suggest an improvement that could be made to the experiment to address one of the error identified in (e)(i). You may suggest the use of other apparatus or a different procedure. ………………………………………………………………………………………………. ………………………………………………………………………………………………. ………………………………………………………………………………………………. …………………………………………………………………………………………….[1] (f) The experiment is repeated using a cone with fixed dimensions and spheres of different 9749/04/ASRJC/2021Prelim For Examiner’s Use For Examiner’s Use A4 A5 A6 A8 The criterion for the relationship to be valid