Cambridge A Level Physics 9702 — 2025 Oct/Nov Paper 3 · Variant 4

1 In this experiment, you will investigate the equilibrium of forces. (a) (i) ● Assemble the apparatus as shown in Fig. 1.1. stand boss L nail spring string N boss wooden strip hole S mass nail M bench W Fig. 1.1 ● Adjust the height of the upper boss so that the wooden strip is parallel to the bench. ● The distance between hole S and the lower nail is W. Measure and record W. W = ............................................................... ● The distance between the two nails is N. Measure and record N. N = ............................................................... ● The length of the coiled part of the spring is L, as shown in Fig. 1.1. Measure and record L. L = ............................................................... [3] (ii) Calculate Z, where W Z = . (N 2 + W 2) Z = ......................................................... [1] (b) Change W by moving the lower nail to another hole in the wooden strip. Adjust the height of the upper boss so that the wooden strip is parallel to the bench. Measure and record W, N and L. Repeat until you have six sets of values. Record your results in a table. Include values of Z in your table. [8] (c) (i) Plot a graph of L on the y-axis against Z 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] (d) It is suggested that the quantities L and Z are related by the equation L = aZ + b where a and b are constants. Use your answers in (c)(iii) to determine the values of a and b. Give appropriate units. a = ............................................................... b = ............................................................... [2] [Total: 20]

Mark scheme: Question Answer Marks 1(a)(i) Final value W in range 34.0 cm ⩽ W ⩽ 36.0 cm, with unit seen somewhere 1 1(a)(i) Final Value of N in range 30.0 to 55.0 cm, with unit seen somewhere 1 1(a)(i) Value of raw L to nearest mm, with unit seen somewhere 1 1(a)(ii) Correct calculation of Z 1 1(b) Six sets of readings of W (different values), N and L with correct trend and without help scores 4 marks, five sets scores 3 4 marks etc. Correct trend is L increases as W increases. 1(b) Range: 1 W min ⩽ 28.0 cm and Wmax ⩾ 45.0 cm 1(b) 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. W / cm. Z must have no unit. 1(b) Consistency: 1 All raw values of N must be given to the nearest mm. 1(b) Significant figures: 1 All values of Z given to the same number of sig. figs as (or one more than) the least s.f.in the corresponding values of N and W. 1(c)(i) Axes: 1 Axes must be labelled with the correct quantities. Scales must be chosen so that the plotted points occupy at least half the graph grid in both the x and y directions. Scale markings are no more than 2 cm (one large square) apart. Sensible scales must be used, no awkward scales (e.g. 3 : 10 or fractions). 1(c)(i) Plotting of points: 1 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(c)(i) Quality: 1 General trend of points must be positive. All points in the table must be plotted (at least 5) for this mark to be awarded. It must be possible to draw a straight line that is within ± 0.02 on the Z axis of all plotted points. 1(c)(ii) Line of best fit: 1 ‘Best fit’ is judged by the balance of all points on the grid (at least 5 points) about the candidate’s line. There must be an even distribution of points either side of the line along the full length. Lines must not be kinked or thicker than half a square. Some candidates may choose to identify an anomalous point. If they identify one point as anomalous (e.g. by circling or labelling) then this point is to be disregarded when judging the line of best fit. There must be at least 5 points left after the anomalous point is disregarded. 1(c)(iii) Gradient: gradient sign on answer line consistent with graph drawn. 1 The hypotenuse of the triangle used should 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. 1(c)(iii) y-intercept: 1 Either Intercept read directly from the graph, with read-off at x = 0, accurate to half a small square in y direction. Or Correct read-off from a point on the line is substituted into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both x and y directions 1(d) a equal to candidate’s gradient value, and b equal to candidate’s intercept value. 1 Values must not be written as fractions or to only one significant figure. 1(d) Units for a and b correct and consistent with readings 1 (e.g. cm for a and cm for b).

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2 In this experiment, you will investigate the motion of a sphere rolling along a track. (a) You are provided with a length of plastic channel. When the channel is positioned with its open side at the top, it forms a track with a pair of rails along which a sphere can roll. An end view of the channel is shown in Fig. 2.1. rail x rail channel Fig. 2.1 The distance between the rails is x. Measure and record x. x = ......................................................... [1] (b) (i) ● Set up the apparatus as shown in Fig. 2.2. bench box track wooden block Fig. 2.2 ● You are provided with two spheres. Place the smaller sphere on the track. If necessary, adjust the position of the wooden block until the sphere is able to roll along the full length of the track and into the box. ● Secure the block to the track with a small piece of adhesive putty as shown in Fig. 2.3. The block and track must remain in these positions for the rest of the experiment. adhesive putty h Fig. 2.3 ● The height of the raised end of the track above the bench is h, as shown in Fig. 2.3. Measure and record h. h = ......................................................... [1] (ii) Estimate the percentage uncertainty in your value of h. Show your working. percentage uncertainty = ..................................................... % [1] (c) (i) ● Measure and record the diameter d of the smaller sphere. d = ............................................................... x 2 ● Calculate 1 -` j . d x 2 1 -` j = ............................................................... d [1] (ii) ● Place the smaller sphere on the track at the raised end. ● Release the sphere. ● The time taken for the sphere to roll along the track into the box is t. Take measurements to determine t. t = ......................................................... [2] (d) Repeat (c) using the larger sphere. d = ............................................................... x 2 1 -` j = ............................................................... d t = ............................................................... [3] (e) It is suggested that the relationship between t, h, x and d is 2 2 t h = k f 5 + p x 2 1 - ` j d where k is a constant. (i) Using your data, calculate two values of k. first value of k = ............................................................... second value of k = ............................................................... [1] (ii) Justify the number of significant figures that you have given for your values of k. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1]

Mark scheme: 2(a) Final Value for x in range 1.40 cm to 2.00 cm, with unit seen somewhere. 1 2(b)(i) Raw value for h to the nearest mm, with unit 1 2(b)(ii) Absolute uncertainty of 1 or 2 mm and correct method of calculation to obtain percentage uncertainty in h. 1 If several readings have been taken, then the absolute uncertainty can be half the range if working shown clearly, but NOT zero if values are equal. 2(c)(i) Value for d in the range 1.80 to 2.00 cm 1 2(c)(ii) Final value of t in the range 3.00 to 10.00 s and 1 Raw values of time all to 0.1 s or all to 0.01 s, with unit seen somewhere 2(c)(ii) Evidence of repeat readings of t. 1 2(d) Second value of d 1 2(d) Second value of t 1 2(d) Value for second t less than first t. 1 2(e)(i) Two values of k calculated correctly. 1 Final values not written as fractions or given to only one significant figure. 2(e)(ii) Justification for significant figures in k linked to significant figures in t, h, x and d. 1 2(f) Calculation of percentage difference between candidate’s two k values. 1 Comparison of percentage difference with 30% leading to a consistent conclusion. 2(g)(i) 1 mark for each point up to a maximum of 4. 4 A Two readings are not enough to draw a conclusion owtte e.g. reference to relationship or not enough k values to draw a conclusion. B Difficulty with measurement of h e.g. large percentage / fractional uncertainty in h; Scale markings do not start at zero at end of ruler. C Difficult to determine t with reason. e.g. Difficult to judge when ball reaches end of track / goes into box D Difficult to measure d with reason, e.g. parallax E Problem with ball rolling / moving on track described e.g. ball falls off track / motion is uneven / (small) ball gets stuck in track (as diameter less than or close to x) F Problem with the track described e.g. Track bends with large ball / width of track varies along its length / box moves due to impact with ball (so distance rolled varies) 2(g)(ii) 1 mark for each point up to a maximum of 4. 4 A Take more readings (for different diameter balls) and plot a graph / calculate more k values and compare B Use calipers (to measure h) C Improved timing method: e.g. video (/ record / film) and with a timer (in view) / use frame-by-frame or pressure switch or light gate at end of track connected to timer D Use micrometer / calipers (to measure ball diameter) E Use larger diameter ball(s) / narrower track (to avoid ball sticking in track) Use (spirit) level to check width is horizontal (to avoid ball falling off) F Method to improve stability of track: e.g. use a metal track / place other supports under track

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