Cambridge A Level Physics 9702 — 2021 May/June Paper 3 · Variant 3

1 In this experiment, you will investigate an electrical circuit. (a) You have been provided with two identical wooden strips labelled A and B. Measure and record the length L of the wire between the nails on strip A, as shown in Fig. 1.1. nail wooden strip A wire nail L Fig. 1.1 L = ......................................................... [1] (b) ● Set up the circuit shown in Fig. 1.2. 1.5 V d.c. x wooden strip A A metre rule F G J x H wooden strip B Fig. 1.2 ● F, G, H and J are crocodile clips. Attach G to the wire on wooden strip A so that the distance x between the nail on strip A and G is approximately 30 cm, as shown in Fig. 1.2. ● Attach H to the wire on wooden strip B so that it is the same distance x from the nail on strip B. ● Close the switch. ● Record x and the ammeter reading I. x = ............................................................... I = ............................................................... ● Open the switch. [1] (c) Vary x and repeat (b) until you have six sets of readings of x and I. Include your values from (b). 1 Record your results in a table. Include values of in your table. I [9] 1(d) (i) Plot a graph of on the y-axis against x on the x-axis. [3] I (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ............................................................... y-intercept = ............................................................... [2] (e) It is suggested that the quantities I and x are related by the equation 1 = Px + Q I where P and Q are constants. Using your answers in (d)(iii), determine values for P and Q. Give appropriate units. P = ............................................................... Q = ............................................................... [2] (f) Theory suggests that ρA – P ( ρB 1) = Q L where ρA is the resistivity of the wire on strip A and ρB is the resistivity of the wire on strip B. ρA Calculate . ρB ρA = ......................................................... [1] ρB [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Final value of L with unit and in the range 60.0–70.0 cm. 1 1(b) Raw values of I with unit and to the nearest 0.1 mA and final value of I < 1 A. 1 1(c) Six sets of readings of x and I (different values) without help from the Supervisor and showing the correct trend (I decreases as x increases) scores 4 marks, five sets scores 3 marks, etc. 4 Range: xmin ⩽ 10.0 cm and xmax ⩾ 60.0 cm. 1 Column headings: 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. 1 / I / A–1 or 1 / I (A–1) and x / m. 1 Consistency: All values of x must be given to the nearest mm. 1 Significant figures: All values of 1 / I must be given to the same number of significant figures as, or one greater than, the number of significant figures in raw I. 1 Calculation: Values of 1 / I are correct. 1 Question Answer Marks 1(d)(i) Axes: Sensible scales must be used, no awkward scales (e.g. 3:10 or fractions). Scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Axes must be labelled with the quantity that is being plotted. Scale markings should be no more than three large squares apart. 1 Plotting of points: All observations in the table must be plotted on the grid. Diameter of plotted points must be ⩽ half a small square. Points must be plotted to an accuracy of half a small square in both x and y directions. 1 Quality: All points in the table (at least 5) must be plotted on the grid. Trend of points on graph must be correct. It must be possible to draw a straight line that is within 2.0 cm (to scale) on the x-axis of all plotted points. 1 1(d)(ii) Line of best fit: 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. There must be at least five points left after the anomalous point is disregarded. Lines must not be kinked or thicker than half a small square. 1 1(d)(iii) Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. Method of calculation must be correct, i.e. Δy / Δx. Gradient sign on answer line matches graph drawn. Both read-offs must be accurate to half a small square in both the x and y directions. 1 y-intercept: Correct read-off from a point on the line and substituted into y = mx + c. Read-off must be accurate to half a small square in both x and y directions. or Intercept read directly from the graph at x = 0, accurate to half a small square. 1 Question Answer Marks 1(e) Value of P = candidate’s gradient and value of Q = candidate’s intercept. Values must not be written as fractions. 1 Unit for P is correct (e.g. A–1 m–1 or mA–1 cm–1) and unit for Q is correct (e.g. A–1 or mA–1). 1 1(f) Correct calculation of ρA / ρB using PL / Q + 1. 1

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2 In this experiment, you will investigate the oscillations of a loaded wooden strip. (a) You have been provided with a rectangular wooden strip with a hole in its centre. ● Use some of the adhesive putty to attach the two 100 g masses as near as possible to one end of the strip, as shown in Fig. 2.1 and Fig. 2.2. SIDE VIEW d hole 100 g masses wooden strip Fig. 2.1 100 g masses adhesive putty TOP VIEW Fig. 2.2 ● The distance between the centre of the masses and the hole is d, as shown in Fig. 2.1. Measure and record d. d = ......................................................... [1] (b) Estimate the percentage uncertainty in your value of d. Show your working. percentage uncertainty = ......................................................... [1] (c) (i) ● Attach the two 50 g masses to the other end of the strip so that the distance between the centres of these masses and the hole is also equal to d. ● Set up the apparatus as shown in Fig. 2.3. wooden rod boss spring stand string loop nail boss holding nail b wooden strip 100 g masses 50 g masses bench Fig. 2.3 (not to scale) ● The distance between the string loop and the nail in the centre of the strip is b. Adjust the position of the string loop and spring until b is approximately 10 cm. ● Adjust the heights of the bosses until the strip is horizontal and the spring and string loop are vertical. ● Measure and record b. b = ......................................................... [1] (ii) Calculate α where b α = . d α = ......................................................... [1] (iii) Justify the number of significant figures that you have given for your value of α. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (d) ● Move the end of the strip with the 100 g masses down through a short distance. ● Release the end of the strip. The strip will oscillate up and down. ● Take measurements to determine the period T of these oscillations. T = ......................................................... [2] (e) ● Change the value of b to approximately 20 cm. ● Adjust the heights of the bosses until the strip is horizontal and the spring and string loop are vertical. ● Measure and record b. b = ............................................................... ● Repeat (c)(ii) and (d). α = ............................................................... T = ............................................................... [2]

Mark scheme: 2(a) Final value for d with unit and in the range 28.0–40.0 cm. 1 2(b) Percentage uncertainty based on absolute uncertainty in the range 2–6 mm. If repeat readings have been taken, then the absolute uncertainty can be half the range (but not zero) if the working is clearly shown. Correct method of calculation to obtain percentage uncertainty. 1 2(c)(i) Measurement of raw b to the nearest mm. Final value with unit and in the range 9.0–11.0 cm. 1 2(c)(ii) Correct calculation of α. 1 2(c)(iii) Justification for the number of significant figures in α linked to s.f. in b and d. 1 2(d) Final value for T with unit and in the range 1.50–2.50 s. 1 At least two measurements of nT where n ⩾ 5. 1 2(e) Second values of b and T. 1 Second value of T < first value of T. 1 2(f)(i) Two values of C calculated correctly. The final values must not be written as fractions. 1 2(f)(ii) Valid comment consistent with calculated values of C, testing against a criterion stated by the candidate. 1 2(g) Value of k correctly calculated from the second value of C and with consistent unit, i.e. N m–1 or kg s–2. 1 Question Answer Marks 2(h)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Masses falling off/masses stick to a small surface area/not enough adhesive putty for the masses/adhesive putty not strong enough to hold masses. C Difficult to judge when the wooden strip is horizontal/difficult to set wooden strip horizontal or difficult to judge or set the spring or string vertical. D Difficulty measuring d with a reason, e.g. finding/determining the centre of the mass/hole or difficulty measuring b with a reason, e.g. finding/determining the centre of the nail/holding the ruler parallel to the strip/set-up wobbly/holding ruler in mid-air. E Difficult to judge/determine/decide when an oscillation starts/finishes/is complete. F Different modes of oscillation/string moves during oscillation or strip bends/twists/flexes (during oscillation). 1 mark for each point up to a maximum of 4. 4 Question Answer Marks 2(h)(ii) A Take more readings and plot a graph or take more readings and compare C values (not “repeat readings” on its own). B Wider strip/named method for improving the adhesion of the masses, e.g. glue/tape with reference to masses. C Method of ensuring strip is horizontal, e.g. use a spirit level or method to ensure spring/string is vertical, e.g. use a plumb-line. D Improved method to measure b or d, e.g. add a scale to the strip/mark on the strip/clamp ruler. E Fiducial marker at the centre of the oscillation or video/record/film with timer in view/play back frame by frame. F Use a thicker/stiffer/laminated strip or sand to make rougher/add notch to wooden strip or rod/stick sandpaper to wooden strip or rod. 1 mark for each point up to a maximum of 4. 4

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