2026 SAJC H2 Physics Prelim P4 ANNOTATED SOLUTION

1 1 In this experiment, you will investigate an electrical circuit. (a) You have been provided with two metre rules, F and G, with wires of different diameter attached. (i) The diameter of the wire attached to F is dF. Using the micrometer, measure and record dF. dF = …………………………….. [2] (ii) Set up the circuit as shown in Figure 1.1. Position connecting lead C so that distance x is 50.0 cm on both rules. Close the switch. The ammeter reading is I. Record x and I. x = ………………………………… I = …………………………..…….. [2] Open the switch. No zero error dF1 = 0.229 mm, dF2 = 0.231 mm; dave = 0.230 mm 0.230 mm 50.0 cm 90.6 mA

2 (b) Vary x and repeat (a)(ii). Present your results clearly. x / cm I / mA (1/ I)/ A-1 10.0 81.1 12.33 25.0 85.0 11.76 50.0 95.5 10.47 65.0 94.0 10.64 80.0 95.5 10.47 90.0 97.7 10.24 [3] (c) The quantities I and x are related by the expression: 1 𝐼𝐼 = 𝑃𝑃𝑃𝑃 + 𝑄𝑄 where P and Q are constants. Plot a suitable graph using a spreadsheet to determine P and Q. Sketch the graph in the space below. Write down the equation of the trendline.

3 (1/ I) / A-1 x / cm 12.542 0 (1/ I) = -0.0263 x + 12.542 P = ………………………………… Q = …………………………..…….. [3] (d) It is suggested that: 𝑃𝑃 𝑄𝑄 = �𝑑𝑑𝐺𝐺 2 𝑑𝑑𝐹𝐹 2 − 1� 𝐿𝐿 Where dG is the diameter of the wire attached to G and L = 1.000 m. Determine a value for dG. Show your working. dG = …………………………….. [2] [Total: 12 marks] Refer to Prelim_ datasetforceext answer. Plot graph of against x, where gradient = P and y- intercept = Q -0.0263 A-1 cm-1 12.5 A-1 dG = 2.5398 x 10-4 m = 0.254 mm (to 3 s.f.) { Note: actual dG measured using digital MSG = 0.190 mm } 0.254 mm

4 2 In this experiment, you will investigate stretched rubber bands. (a) Set up the apparatus as shown in Fig. 2.1.

5 Clamp the hacksaw blade with its teeth facing upwards. Place the rubber bands on the blade so that the tops of the rubber bands are approximately 8 cm apart. You may wish to use some of the Blu- Tack to secure the tops of the rubber bands on the blade. Suspend mass m from the rubber bands where m = 300 g. Record m. m = …………………………….. The angle between one of the rubber bands and the hacksaw blade is α, as shown in Fig. 2.1. The length of one of the stretched rubber bands is b. Measure and record α and b. α = ………………………..…….. b = ……………………………… [2] (b) Change m to 200 g. 300 g α1 = 73° α2 = 73° ; αave = 73° b1 = 10.5 cm b2 = 10.5 cm; bave = 10.5 cm 73° 10.5 cm

6 Adjust the position of the tops of the rubber bands on the blade so that b has the same value as in (a). Record m. m = …………………………..….. Measure and record α. α = …………….……………...…. [1] (c) It is suggested that sin α = Cm where C is a constant. Use your values from (a) and (b) to determine two values of C. first value of C = ………………………………. second value of C = ………………………...….. [2] (d) It is suggested that: 𝐶𝐶 = 𝑔𝑔 2𝑒𝑒𝑒𝑒 where e is the extension of the rubber band with extended length b, k is the force constant of this rubber bands and the acceleration of free fall g = 9.81 ms-2. Determine a value for k. Show your working. k = ………………………………. [3] (e) Suggest one significant source of error in this experiment. 200 g α1 = 42° α2 = 42° 42° C1 = = 3.19 kg-1 C2 = = 3.35 kg-1 3.19 kg-1 3.35 kg-1 Initial length of rubber band = 8.5 cm (to be measured) Extension e = 10.5 – 8.5 = 2.0 cm Cave = = 3.27 kg-1 Thus, k = = 75.0 N kg-1 75.0 N m-1 or kg s-2 In the measurement of angle ɑ, uncertainty arises due to the unsteadiness of the hand when holding the protractor. In the measurement of length b, uncertainty arises due to the unsteadiness of the hand when holding the rule. In the measurement of angle ɑ, uncertainty arises as the positioning of protractor is hindered by the clamp.

7 ………...……………………………………………………………………………………………… ………...……………………………………………………………………………………………… ………...……………………………………………………………………………………………… ………………….………………………………………………………………………………… [1] (f) A materials engineer is characterising the performance of a high- grade industrial material that does not obey Hooke’s Law. The measured Force-Extension data for the loading cycle only is recorded in the digital file: Prelim_datasetforceext.excel Imagine you are the engineer. (i) Use the engineer’s data to estimate the total work done during the loading phase. work done = ……………………………….J [1] (ii) Explain how you obtained the value of the total work done. …………………………………………………………………………………………………. ………………………………………………………………………………………………[1] (iii) When a sample of the material is tested for its mechanical properties, it is subjected to a force that gradually increases to a maximum value (loading), and then is smoothly decreased back to zero (unloading), as illustrated in the figure below. force extension loading Refer to Prelim_ datasetforceext answer 5.06 Area under the graph of force against extension.

8 unloading It is observed that the unloading curve does not retrace the loading curve, forming a distinct closed loop. Explain the physical significance of this closed loop. …………………………………………………………………………………………………. …………………………………………………………………………………………………. ………………………………………………………………………………………………[1] (iv) The loading curve of the material is modeled by the equation: 𝐹𝐹 = 𝐴𝐴 (𝑒𝑒𝐵𝐵𝐵𝐵 − 1) where: ● F is the loading force applied to the material, ● x, measured in metres, is the extension of the material, ● A is a constant equal to 2.0 N, ● B is a constant. Plot a suitable linear graph using the dataset to determine B. Sketch the graph in the space below. Write down the equation of the trendline. In (F/2 + 1) x /m 0.0154 The area enclosed between the 2 curves represents the energy dissipated as thermal energy (heat) within the material during one complete cycle of loading and unloading. Note: Area under Loading Curve represents total work done on material by the stretching force to deform it; Area under Unloading Curve represents work done by material as it returns to its original length (mechanical energy recovered). Refer to Prelim_ datasetforceext answer. Plot graph of against , where gradient = = gradient = 7.94 (as given by excel trendline eqn) (3 sf) Acceptable range of : 6.4 – 9.5

9 0 In (F/2 + 1) = 7.9439 x + 0.0154 B = …………………………. [2] [Total: 14 marks] 3 This experiment concerns a coupled pendulum system. Figure 3.1 shows six pendulums, 1, 2, 3, 4, 5 and 6, connected to a common string. When pendulum 1 is set swingling, the other pendulums move. You will investigate how these properties affect the behaviour of a coupled pendulum system: - The distance between pendulums - The tension in the common string - The difference in pendulum lengths - The mass of the pendulum bobs (a) (i) Set up two pendulums A and B as shown in Figure 3.2. Place the loops of the common string on the rods of the clamps. The distance x between the pendulum strings is shown. 7.94 m-1

10 Adjust the distance between the stands so that the common string is taut but not as taut as possible. Adjust the knots until each pendulum has a length equal to 45 cm and x is approximately 15 cm. Measure and record x. x = ……………………….. cm [1] Pull pendulum A towards yo