2023 RI H2 Physics Prelims P4 Answers

1 ©Raffles Institution 9749/04 H2 Physics Prelim P4 (2023) Suggested solutions 1 In this experiment, you will investigate an electrical circuit. (a) Set up the circuit as shown in Fig. 1.1. Fig. 1.1 H is a crocodile clip that is free to move along the wire. Y is a resistor with resistance R. (b) Adjust length L to approximately 0.10 m. Measure and record L. L = 0.100 m (c) Close the switch. Measure and record the current I and the potential difference V. I = 85.93 mA V = 1.0135 V [1] Marker’s comments: • Many candidates converted current from mA to A wrongly which carried over to their table readings and calculations being wrong. • A small number of candidates connected the wires wrongly and ended up with wrong values/trend for the table values. • A significant number of candidates manipulated the equation wrongly, e.g., decided to plot V against L, without realising that it is not a linear relationship. A V H metre rule tape tape wire L Y

2 ©Raffles Institution 9749/04 (d) Repeat (b) and (c) for different values of L by varying the position of H. L /m I /mA V /V V I / 0.100 85.93 1.0135 11.79 0.200 80.65 1.0376 12.87 0.300 75.98 1.0715 14.10 0.400 71.20 1.0936 15.36 0.500 68.04 1.1116 16.34 0.600 64.17 1.1221 17.49 0.690 61.32 1.1393 18.58 [4] (e) V and L are related by the expression V R k L=+II where k is a constant. Plot a suitable graph to determine R and k. VV R k L R kL= +  = +II I Plot a graph of V I against L, where the gradient is k and the vertical intercept is R. Gradient 19.60 11.90 7.70 11.5 (3 s.f.)0.780 0.110 0.670 −= = = − 111.5 mk − =  From graph, vertical intercept = 10.65  10.65 R =  OR Using (0.780, 19.60) and gradient = 11.5 ( )( )19.60 11.5 0.780 10.63 C C =+ = 10.63 R =  R = 10.65  k = 11.5  m–1 [6] [Total: 11]

3 ©Raffles Institution 9749/04 /V I 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 19.0 20.0 21.0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 (0.110,11.90) (0.780,19.60) anomally L / m

4 ©Raffles Institution 9749/04 2 In this experiment, you will investigate the equilibrium of a metre rule. (a) (i) You have been provided with a metre rule with a spring attached, as shown in Fig. 2.1. Fig. 2.1 (ii) The length of the unstretched spring is L0, as shown in Fig. 2.2. Fig. 2.2 Measure and record L0. L0 = 4.2 cm [1] (b) Set up the apparatus as shown in Fig. 2.3. Fig. 2.3 The metre rule is placed on top of one of the rods. The distance x between the hole with the string and the centre of the rod is shown in Fig. 2.3. Set x to be about 50 cm and adjust the apparatus until the metre rule is horizontal and the spring is vertical and unstretched. metre rule spring string L0 rod of clamp boss boss rod of clamp bench stands metre rule spring string x

5 ©Raffles Institution 9749/04 Without changing the heights of the rods of the clamps, gradually shift one of the retort stands until x is 30 cm. The metre rule will tilt and the spring will stretch as shown in Fig. 2.4. (i) Make the necessary adjustment to the apparatus so that the spring remains vertical. Fig. 2.4 The length of the stretched spring is L1. The angle between the rule and the horizontal is , as shown in Fig. 2.4. Measure and record x and L1 and hence, determine sin. Extension of spring = L1 – L0 = 7.0 – 4.2 = 2.8 cm 2.8sin 0.093 30.0 e x = = = x = 30.0 cm L1 = 7.0 cm sin = 0.093 [2] rod of clamp rod of clamp metre rule spring string  L1 x

6 ©Raffles Institution 9749/04 (ii) Decrease distance x and repeat (b)(i). Extension of spring = L1 – L0 = 7.8 – 4.2 = 3.6 cm 3.6sin 0.15 24.5 e x = = = x = 24.5 cm L1 = 7.8 cm sin = 0.15 [1] (iii) It is suggested that the relationship between sin and x is given by: 2 1sin ( ) 2P xx =− l where l is the length of the metre rule and P is a constant. Determine the average value of P using your values in (b)(i) and (b)(ii). 1st set of readings : l 2 2 1sin ( ) 2 100 10.093 ( ) 2(30.0) (30.0) 4.19 P xx P P  =− =− = 2nd set of readings : l 2 2 1sin ( ) 2 100 10.15 ( ) 2(24.5) (24.5) 3.53 P xx P P  =− =− = < P > = ½ (4.19 + 3.53) = 3.86 cm P = 3.86 cm [2]

7 ©Raffles Institution 9749/04 (iv) Theory suggests that: mgP k= where k is the spring constant of the spring, g is 9.81 m s−2 and m is the mass of the metre rule with a value of 80 g. Calculate k. 2 1 (0.080)(9.81) (3.86 10 ) 20.3 N m mgP k k − − = =  = k = 20.3 N m−1 [2] (c) (i) The experiment is repeated for more values of x. Assuming the relationships in (b)(iii) and (b)(iv) are correct, state the graph that you would plot in order to determine the value of the spring constant k. Explain how k is determined from the graph. Plot a graph of sin against 2 1 2xx −l . Determine value of gradient (P). hence k = gradient mg

8 ©Raffles Institution 9749/04 (ii) Use the relationship in (b)(iii) to determine the value of x when  = 0. State the significance of this value of x. 2 2 2 2 1sin ( ) 2 100 10 ( ) 2 100 1 2 100 2 50 cm P xx P xx xx xx x  =− =− = = = l It represents the distance from the hole with the string to the centre of gravity of the metre rule (or position of the centre of gravity).

9 ©Raffles Institution 9749/04 3 In this experiment you will investigate the behaviour of an oscillating system. (a) Measure and record the length of the metal rod. length of metal rod = 0.302 m (b) (i) Measure and record the diameter d of the wire. zero-error of micrometer screw gauge: Nil d = 0.71 mm, 0.71 mm, 0.71 mm d = 0.71 mm [1] (ii) Measure and record the length of the wire. length of wire = 0.500 m [1] (iii) Coil the wire evenly on to the plastic tube to form a uniform spiral leaving two straight lengths of about 5 cm at the ends as shown in Fig. 3.1. Fig. 3.1 Measure the lengths of the straight parts and hence , calculate the length l of the wire in the spiral. l = 0.500 – 0.045 – 0.045 = 0.410 m l = 0.410 m [1] 5 cm 5 cm

10 ©Raffles Institution 9749/04 (iv) Estimate the percentage uncertainty in the value of l. l l  =  = 0.9 100 2.195 % 2.2 %41 percentage uncertainty in l = 2.2 % [1] (c) Bend one end of the wire by 90  from about 2 cm from the end of the wire as shown in Fig. 3.2. Using scotch-tape, attach the bent end to the centre of the metal rod as shown in Fig. 3.3. Fig. 3.2 Fig. 3.3 Attach the plasticine spheres to the ends of the metal rod such that their centres coincide with the ends of the rod as shown in Fig. 3.4. Fig. 3.4 2 cm 90 centre of rod use scotch-tape to attach wire to the rod metal rod plasticine sphere x plasticine sphere