Cambridge A Level Physics 9702 — 2022 May/June Paper 3 · Variant 1

1 In this experiment, you will investigate the motion of a spring system. You have been provided with two springs connected by string. (a) ● Set up the apparatus as shown in Fig. 1.1. boss wooden rod upper spring stand upper string loop upper mass string lower string loop lower spring G-clamp bench lower mass m Fig. 1.1 ● The lower mass is m. Arrange all of the slotted masses so that m is 250 g and the remaining slotted masses are in the upper string loop. ● Pull the lower mass down through a short distance. ● Release the mass. The system will oscillate. ● Determine the period T of the oscillations of the upper mass. T = ......................................................... [2] (b) ● Transfer some of the slotted masses from the lower string loop to the upper string loop. ● Record the value of the upper mass. upper mass = ............................................................... ● Record the value of m. m = ............................................................... ● Determine the period T of the oscillations of the upper mass. T = ............................................................... [1] (c) Change m by moving slotted masses between the two string loops and then determine T. Repeat until you have six sets of values of m and T. You may include your results from (a) and (b). Record your results in a table. Include values of T in your table. [9] (d) (i) Plot a graph of T on the y-axis against m on the x-axis. [3] (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 T and m are related by the equation T = Pm + Q where P and Q are constants. Using your answers in (d)(iii), determine the values of P and Q. Give appropriate units. P = ............................................................... Q = ............................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Value of T with unit and in the range 0.850–1.300 s. 1 nT measured at least twice with n ⩾ 5. 1 1(b) Total mass (upper mass + m) is 450 g with consistent unit. 1 1(c) Six sets of readings of m and time with correct trend (T increases as m increases) and without help from the Supervisor scores 4 marks, five sets scores 3 marks etc. 4 Range: mmax – mmin ⩾ 300 g. 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. m / g, T / s, T / s½. 1 Consistency: Raw values of time either all given to the nearest 0.1 s or all given to the nearest 0.01 s. 1 Significant figures: All values of T must be given to the same number of s.f. as (or one more than) the number of s.f. in raw times. 1 Calculation: Correct calculation of T. 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 the x and y directions. Axes must be labelled with the quantity that is being plotted. Scale markings are no more than 2 cm (one large square) 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 must be plotted (at least 5) on the grid for this mark to be awarded. Trend of points must be positive. It must be possible to draw a straight line that is within  25 g ( 0.025 kg) on the m axis of all plotted points. 1 1(d)(ii) Line of best fit: Judge by the 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 (i.e. circled or labelled) by the candidate. There must be at least 5 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. Both read-offs must be accurate to half a small square in both the x and y directions. Method of calculation must be correct (not x / y). Gradient sign on answer line matches graph drawn. 1 y-intercept: Correct read-off from a point on the line and substituted into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both x and y directions. or Intercept read directly from the graph, with read-off at m = 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. The values must not be fractions. 1 Unit for P: s½ kg–1 or s½ g–1 and unit for Q: s½. 1

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2 In this experiment, you will investigate the equilibrium of a metre rule. You have been provided with a metre rule and a tube. (a) (i) ● The distance between the centre of the hole in the metre rule and the 50 cm mark on the metre rule is L, as shown in Fig. 2.1. L 50 cm mark hole metre rule string loop Fig. 2.1 Determine L. Give your value in metres. L = ........................................................... m ● The outer diameter of the tube is d, as shown in Fig. 2.2. tube d Fig. 2.2 Measure and record d. Give your value in metres. d = ........................................................... m [1] (ii) Calculate the cross-sectional area A of the tube where πd2 A = . 4 A = .................................................... m2 [1] (b) (i) ● Add sand to the tube as shown in Fig. 2.3. tube sand x Fig. 2.3 ● The height of sand in the tube is x. Adjust the amount of sand in the tube until x is approximately 12 cm. ● Measure and record x. Give your value in metres. x = ........................................................... m ● Push the stopper securely into the tube. ● Set up the apparatus as shown in Fig. 2.4. Place the beaker containing water inside the tray. y hook rod of clamp stopper boss stand beaker water tray h bench Fig. 2.4 (not to scale) ● Using the hook, suspend the tube from the string loop and place the tube in the water. ● The distance between the bottom of the tube and the surface of the water in the beaker is h. Adjust the apparatus so that the rule is balanced on the rod of the clamp, the rule is parallel to the bench and the value of h is approximately 5 cm. ● The distance between the rod of the clamp and the hole in the rule is y. Measure and record h and y. Give your values in metres. h = ........................................................... m y = ........................................................... m [2]

Mark scheme: 2(a)(i) Raw d value(s) to the nearest mm and value of d in the range 0.020–0.030 m. 1 2(a)(ii) Correct calculation of A. 1 2(b)(i) Value of h in the range 0.040–0.060 m. 1 Value of y. 1 2(b)(ii) Percentage uncertainty in h based on an absolute uncertainty in the range 2–5 mm. If several readings have been taken, then the absolute uncertainty can be half the range (but not zero) provided the working is clearly shown. Correct method of calculation to obtain percentage uncertainty. 1 2(b)(iii) Correct calculation of C. 1 2(b)(iv) Justification for significant figures in C linked to significant figures in L, d, h,  and M. 1 2(c) Second value of x. 1 Second value of y. 1 Second value of y > first value of y. 1 2(d) Two values of k calculated correctly. The final k values must not be written as fractions. 1 2(e) Calculation of percentage difference between candidate’s two k values. Comparison of percentage difference with 10% leading to a consistent conclusion. 1 Question Answer Marks 2(f)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficulty with measuring d with a reason e.g. tube surface is curved/parallax error/tube not flat on rule. C Difficulty with measuring h with a reason e.g. measuring outside beaker/tube not vertical/parallax error/refraction effects/distortion/tray obscures view. D Difficulty with measuring x with a reason e.g. sand surface not level/tube and rule not parallel/holding rule and tube at the same time. E Difficulty with measuring/judging/setting y with a reason e.g. judging centre of rod/balance is achieved over a range of y/difficult finding balance point/hard to balance/difficult to adjust ruler to horizontal. 1 mark for each point up to a maximum of 4. 4 2(f)(ii) A Take more readings (for different amounts of sand) and plot a graph or take more readings and compare k values (not “repeat readings” on its own). B Use calipers/micrometer screw gauge/travelling microscope/blocks either side. C Improvements to tube e.g. mark tube/place rubber band around tube to mark position/use a graduated tube. D Improved method for x or h e.g. clamp tube/use rule with pointers/use shallower tray or remove tray. E Use a triangular pivot. 1 mark for each point up to a maximum of 4. 4

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