Cambridge A Level Physics 9702 — 2015 May/June Paper 3 · Variant 5

1 In this experiment, you will investigate how the voltage across components in a circuit varies as the resistance of the circuit is changed. (a) (i) Set up the circuit as shown in Fig. 1.1. + ï 15 1 V1 V x wire 10 1 metre rule crocodile clips V V2 Fig. 1.1 Attach the crocodile clips to the wire so that the distance x is approximately 30 cm. (ii) Measure and record x. x = ..................................................[1] (b) (i) Close the switch. (ii) Record the voltmeter readings V1 and V2. V1 = ....................................................... V2 = ....................................................... [1] (iii) Open the switch. (c) Change x and repeat (a)(ii) and (b) until you have six sets of readings of x, V1 and V2. V2 Include values of in your table. V1 [10] V2 (d) (i) Plot a graph of on the y-axis against x on the x-axis. [3] V1 (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ..................................................... y-intercept = ..................................................... [2] (e) The quantities V2, V1 and x are related by the equation V2 Ax Q = + V1 P B where P = 15 Ω, Q = 10 Ω and A and B are constants. Use your answers in (d)(iii) to determine values for A and B. Give appropriate units. A = ........................................................ B = ........................................................ [2] You may not need to use all of the materials provided.

Mark scheme: 1 (a) (ii) Value of x to the nearest mm with unit, and in range 25.0 cm < x < 35.0 cm. [1] (b) (ii) Values of V1 and V2 in range 0.100 V – 2.500 V with unit. Ignore negative sign(s). [1] (c) Six sets of readings of x, V1 and V2 scores 5 marks, five sets scores 4 marks etc. [5] Minor help from supervisor –1, major help –2. Inconsistent trend –1 (correct trend is V2 increases and V1 decreases as x increases). Range: [1] Range of values of x > 60.0 cm. Column headings: [1] Each column heading must contain a quantity and a unit where appropriate. The presentation of quantity and unit must conform to accepted scientific convention e.g. x / m and V2 / V1 (no unit). Consistency: [1] All values of raw V must be given to 0.001 V. Significant figures: [1] The number of significant figures for V2 / V1 must be the same as (or one more than) the least number of significant figures in the corresponding values of V2 and V1. Calculated values: [1] V2 / V1 calculated correctly to the number of s.f. given by the candidate. (d) (i) Axes: [1] Sensible scales must be used. Awkward scales (e.g. 3:10) are not allowed. Scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Scales must be labelled with the quantity that is being plotted. Scale markings should be no more than three large squares apart. Plotting: [1] All observations must be plotted. Diameter of plotted points must be < half a small square (no “blobs”). Plotted points must be accurate to within half a small square. Quality: [1] All points in the table must be plotted on the grid for this mark to be awarded. All points must be ± 0.025 (to scale) on the V2 / V1 axis of a straight line. (ii) Line of best fit: [1] Judge by balance of all points on the grid about the candidate’s line (at least 5 points). There must be an even distribution of points either side of the line along the full length. Allow one anomalous point only if clearly indicated by the candidate. (iii) Gradient: [1] The hypotenuse of the triangle must be greater than half the length of the drawn line. The method of calculation must be correct. Both read-offs must be accurate to half a small square in both the x and y directions. y-intercept: [1] Either: Check correct read-off from a point on the line and substituted into y = mx + c. Read-offs must be accurate to half a small square in both x and y directions. Or: Check read-off of the intercept directly from the graph (accurate to half a small square). (e) Value of A = 15 × candidate’s gradient and value of B = 10 / candidate’s y-intercept. [1] Do not allow fractions or final answer to 1 s.f. Units for A (Ω m–1 or Ω cm–1 or Ω mm–1) and B (Ω) dimensionally correct. [1]

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2 In this experiment, you will investigate the motion of a metal bar. (a) Use the loops on one piece of string to arrange the string on a wooden rod as shown in Fig. 2.1. The loops of the string on the rod should be approximately 18 cm apart. Repeat for the other rod and string. wooden rod §18 cm string Fig. 2.1 (b) Set up the apparatus as shown in Fig. 2.2. wooden rod boss 50 cm metal rod stand 50 cm Fig. 2.2 The two wooden rods should be parallel, equal heights above the bench and 50 cm apart. The two strings supporting the metal rod should be 50 cm apart. (c) (i) Measure and record the angle θ as shown in Fig. 2.3. e metal rod Fig. 2.3 θ = ........................................................ [1] (ii) Estimate the percentage uncertainty in your value of θ. percentage uncertainty = ........................................................ [1] θ (iii) Calculate the value of cos . 2 θ cos = ........................................................ [1] 2 (d) (i) Move the metal rod to the left. Release the metal rod and watch the movement. The metal rod will move to the right and then to the left again, completing a cycle as shown in Fig. 2.4. Fig. 2.4 (ii) The time taken for one complete cycle is T1. By timing several of these complete cycles, determine an accurate value for T1. T1 = ........................................................ [2] (e) (i) Move the centre of the metal rod towards you through a small distance. Release the metal rod and watch the movement. The metal rod will move away from you and then back towards you completing a cycle as shown in Fig. 2.5. Fig. 2.5 (ii) The time taken for one complete cycle is T2. By timing several of these complete cycles, determine an accurate value for T2. T2 = ........................................................ [1]

Mark scheme: 2 (c) (i) Value of raw θ to the nearest degree, with unit, in range θ < 90°. [1] (ii) Percentage uncertainty in θ based on absolute uncertainty of 2 to 5°, and correct method of calculation. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. [1] (iii) Correct calculation of cos (θ / 2) correct to 2 s.f. [1] (d) (ii) Value of T1 with unit and in range 0.5 s < T1 < 1.5 s. [1] Evidence of repeats here or in (e)(ii) or (f)(ii). [1] (e) (ii) Value of T2 with unit in range 0.5 s < T2 < 1.5 s. [1] (f) (ii) Second value of θ. [1] Second values of T1 and T2. [1] Second value of T1 > first value of T1 and Second value of T2 < first value of T2. [1] (g) (i) Two values of k calculated correctly. [1] (ii) Correct justification of s.f. in k linked to s.f. in θ and T1 and T2 (or θ and raw times) [but not cos (θ / 2)]. [1] (iii) Sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate. [1] (h) (i) Limitations (4 max.) (ii) Improvements (4 max.) Do not credit A Two readings not enough to draw a Take many readings for different “repeat readings”/ valid conclusion angles and plot a graph/ “few readings” take more readings and compare k values B Difficult to measure angle with Trace on a card/use graph reason e.g. hand shakes/curve at paper/project onto screen and bottom/position of zero measure angle/use uncertain/parallax/rod gets in the trigonometry/take photo and way/thick string/holding protractor measure angle/clamp protractor without a stand Use thinner string C Difficult to maintain gap (between Method to prevent movement of strings or stands) or angle with stands e.g. G clamp reason e.g. stands move/string stands/mark positions of stands slips on bench Make indentations around/in the rod(s) so the strings do not slide/method of fixing string to rod D Movement of rod not confined to Electromagnetic release Fans/air conditioning the wanted oscillation/rod rotating E Difficult to obtain time with reason Video with timer/frame by frame e.g. high damping/time too short /no. of oscillations too Longer rod/longer string/heavier few/friction between string and rod rod (loses energy) Large uncertainty in time F Difficult to identify/judge end or Count to highest point of oscillation middle/fiducial/reference marker at middle

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