VJC 2024 H2 Physics CA2 Practical sample answers and common mistakes

2024 CA2 Physics P4 Mark Scheme 1 In this experiment, you will investigate the effect of friction on a simple pulley system. (a) You are provided with a spring of unstretched length 0L , as shown in Fig. 1.1. Fig. 1.1 Measure and record 0L . 0L = 4.1 cm [1] • Some students did not measure from the extreme ends of the rings. Read the question carefully! • When using ruler to measure length, instrument uncertainty = 0.1 cm. So L0 should be recorded to 1 dp. (b) Set up the apparatus as shown in Fig. 1.2. Fig. 1.2 L0 boss bench clamp boss mass hanger pvc pipe string retort standretort stand rod of clamp spring

Ensure that the pipe remains horizontal at all times, and that the strings on each side of the pipe are vertical and parallel with each other. The spring should only stretch minimally at this instant. (i) Place a 50 g slotted mass onto the mass hanger and slowly lower the mass hanger, allowing the spring to extend to a new equilibrium length 1L , Measure and record 1L . 1L = 6.1 cm [1] (ii) Calculate the extension 1x of the spring from its unstretched length, where =−1 1 0x L L = − = − =1 1 0 6.1 4.1 2.0 cmx L L 1x = 2.0 cm [1] • You should show the working for your calculation. (iii) Pull the mass hanger downwards by about 10 cm, causing the spring to extend further. Hold the hanger while allowing it to slowly rise upwards until the spring retracts to another equilibrium length 2L , where 2L is larger than 1L . Measure and record 2L . 2L = 11.3 cm (iv) Calculate the new extension 2x of the spring from its unstretched length, where =−2 2 0x L L = − = − =2 2 0 11.3 4.1 7.2 cmx L L 2x = 7.2 cm [1]

(c) Theory suggests that 1x and 2x are related by the expression =2 1 ln 2x x where  is a constant and  is the angle of contact (expressed in radians) between the string and the pipe, as shown in Fig. 1.3. Fig. 1.3 (i) State the value of θ for the set-up in Fig. 1.2.  =  rad [1] • Some students recorded the answer in degrees, when the question asked for radians. (ii) Determine a value for . ( ) ( )  −= = = 21 1ln ln 7.2 2.0 0.204 rad22 xx  = −10.204 rad [1] 

(iii) The experiment is repeated with different numbers of slotted masses to obtain more values of 1x and 2x . State how a straight line graph can be plotted and used to determine the value of , assuming the theory is correct. =2 1 ln 2x x  = 22 1 x ex  ( ) = 2 21x e x Plot a graph of 2x against 1x where the gradient is 2e and the vertical intercept is zero. Hence, ( ) = 1 ln gradient2 . or =2 1 ln 2x x  −=21ln ln 2xx  =+21ln ln 2xx Plot a graph of 2ln x against 1ln x where the gradient is 1 and the vertical intercept is 2 . Hence, ( ) = 1 vertical intercept2 . [2] Many students said to plot ln 2 1 x x vs . But  is a constant! (iv) State the value of  if the pipe is frictionless. Explain your answer. If the pipe is frictionless, =12xx , as the spring will retract back to an extension of 1x after being stretched further. Hence, ( ) ( )==21ln ln 1 0xx and this implies  = 0 . [2] Note:  is the coefficient of friction between the string and the pipe (You’re not expected to know. Hence,  = 0 when the pipe is frictionless. . [Total: 10]

2 In this experiment, you will investigate an electrical circuit. (a) Component Z in the circuit shown in Fig. 2.1 is a combination of resistors X. The values of the resistance of X is 2.2 . Fig. 2.1 Set up the circuit in Fig. 2.1 such that Z is a combination of X, X and Y connected in series. Draw this series combination. Calculate the effective resistance ZR of Z. Z 2.2 2.2 2.2 6.6 R = + + =  ZR = 6.6  [1] Close the switch. Adjust length L to obtain an ammeter reading I of approximately 0.10 A . Measure and record I and L. I = 99.7 mA (to 0.1 mA) L = 0.410 m (to 0.1 cm) [1] • For I, you should use the most sensitive setting possible, which is the 200 mA setting, which can measure to 0.1 mA. If you record in A, then you should record to 4 dp. Open the switch. A switch Z resistance wire on metre rule L E

(b) Vary ZR using different combinations of X, and repeat (a), keeping I constant throughout. Present your results clearly. Include drawings of the different combinations of X. Connections of X, X and Y Z / R / mL 6.6 0.410 4.4 0.590 2.2 0.800 1.5 0.868 1.1 0.880 3.3 0.750 [3] • Some students didn’t present their data in a table form. • Don’t do working in the table. That makes the table look very untidy. XX X Y XY X X X X X

(c) ZR and L are related by the expression =+ ZE R k LII where E is the electromotive force of the cell and k is a constant. Plot a suitable graph to determine a value for k. =−Z ER kL I Plot a graph of ZR against L where the gradient is −k and the vertical intercept is E I . gradient 11.1=− Resistance per unit length 1gradient 11.1 mk −= − =  k = 111.1 m − [5] • Some students plotted more complicated graphs, eg IR vs IL etc. Learn to identify the simplest possible graph to plot, in order to save time. • Some students forgot the units of k.

(d) The experiment is repeated using a resistance wire of the same material but with a smaller diameter. Sketch a line on your graph grid on Page 8 to show the expected result. Label this line W. [1] The resistance per unit length of a thinner wire will be higher. So for the same Rz, to get the same current, you need a shorter length of the resistance wire (i.e. L will be smaller). Also, y intercept = E I , which remains the same. These 2 facts combined means that the new line will be to the left of the old line, but with the same y intercept. So the new line will become steeper (draw and see for yourself). [Total: 11]

3 In this experiment, you will investigate how the following properties affect the period of the oscillation of a suspended closed loop wire. • the perimeter of the closed loop wire • the shape of the closed loop wire • the ratio of certain dimensions of the closed loop wire (a) (i) Bend the longer wire to form a square shape of length L, as shown in Fig. 3.1. Fig. 3.1 Measure and record L. L = cm [1] (ii) Estimate the percentage uncertainty in your value of L. percentage uncertainty in L = [1] • There is a lot of unavoidable inaccuracies in measuring L eg the copper wire is not straight etc. So L should be more than 0.1 cm. L = 13.0 cm 13.0 0.5100% 100% 3.8%13.0 L L   =  = 3.8%

(b) (i) Place the cork in the clamp and attach the clamp to the stand using the boss. Hang the wire square from the pin as shown in Fig. 3.2. Fig. 3.2 Gently displace the wire square and release it so that it oscillates as shown in Fig. 3.3. Fig. 3.3