Cambridge A Level Physics 9702 — 2025 Oct/Nov Paper 3 · Variant 6

1 In this experiment, you will investigate the phase difference between the oscillations of two mass–spring systems. (a) • Assemble the apparatus as shown in Fig. 1.1. stand stand boss boss rod of clamp rod of clamp springs springs mass z mass A mass B bench Fig. 1.1 • Mass A and mass B are each 200 g. • Add a mass z of 40 g to mass B. Record the value of z. z = ............................................................ g • M is given by M = 200 g + z. Calculate M. M = ............................................................ g • Pull both A and B down a short distance and release them together. Observe the oscillations. A and B initially oscillate in phase (both moving up and down together), then their oscillations go out of phase and then become in phase again. • The time from A and B oscillating in phase to the next time they oscillate in phase is P. Measure and record P. P = ............................................................... [2] (b) Change z and determine P. Repeat until you have six sets of values of z and P. 1 1 Record your results in a table. Include values of M, and in your table. M P [10] 1 1 (c) (i) Plot a graph of on the y-axis against on the x-axis. [3] P M (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 P and M are related by the equation 1 a = + b P M 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) Value of P in range 5.00 to 15.00 s, with unit seen somewhere 1 Evidence of repeated measurement of P 1 1(b) Six sets of readings of z (different values) and P with correct overall trend and without help scores 5 marks, five sets scores 5 4 marks etc. Correct trend is P decreases as z increases. Range: at least one reading of z ⩽ 10 g and at least one reading of z ⩾ 70 g 1 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. 1 / M (g-½) Consistency: 1 All raw values of P must be given to the nearest 0.01 s or all to the nearest 0.1 s. Significant figures: 1 All values of 1 / M must be given to 3 s.f. or 4 s.f. Calculation: 1 1 / M calculated correctly 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). 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. Quality: 1 General trend of points must be negative. 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  0.001 g–1/2 on the 1 / M 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: 1 Gradient sign on answer line consistent with graph drawn. 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) Value of a = candidate’s gradient value and 1 Value of b = candidate’s y-intercept value. The values must not be written as fractions or given to only one significant figure. Units for a and b correct and consistent with readings 1 (e.g. g½s-1 for a and s-1 for b)

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2 In this experiment, you will investigate the tension in a string. (a) • Set up the apparatus as shown in Fig. 2.1. stand boss nails bosses d nail ≈ 52 cm string ≈ 37 cm mass hanger ≈ 31 cm and masses G-clamp bench Fig. 2.1 • The mass hanger and masses should have a total mass M of 0.400 kg. • The distance between the two lower nails is d, as shown in Fig. 2.1. Measure and record d. d = .................................................... cm [1] (b) The tension in the string is T. Calculate T using T = Mg, where g = 9.81 N kg–1. T = ...................................................... N [1] (c) (i) • Hook the newton meter on the string half-way between the two lower nails and pull it horizontally with a force F of 5.0 N, as shown in Fig. 2.2. newton meter x Fig. 2.2 • The force F causes the string to deflect a distance x, as shown in Fig. 2.2. Measure and record x. x = .................................................... cm [2] (ii) Estimate the percentage uncertainty in your value of x. Show your working. percentage uncertainty = ......................................................% [1] (iii) Calculate y, where 2 d 2 y = ex + o. 4 y = .................................................... cm [1] (d) • Add slotted masses to the mass hanger so that the total mass M is 0.700 kg. • Repeat (b), (c)(i) and (c)(iii). T = ............................................................ N x = .......................................................... cm y = .......................................................... cm [3]

Mark scheme: 2(a) Raw values of d to the nearest mm and final value in range 5.00 to 7.00 cm. 1 2(b) Correct calculation of T given to 3 or 4 significant figures 1 2(c)(i) Raw value (s) of x to nearest mm 1 Evidence of repeat readings of x 1 2(c)(ii) Absolute uncertainty of 2 mm to 6 mm and correct method of calculation to obtain percentage uncertainty in x. 1 If several readings have been taken, then the absolute uncertainty can be half the range, provided the working is shown clearly, but not zero if values are equal. 2(c)(iii) Correct calculation of y 1 2(d) Second value of T 1 Second value of x 1 Quality – second x less than first x 1 2(e)(i) Two values of k calculated correctly. 1 Final values not written as fractions or given only to one significant figure. 2(e)(ii) Justification based on the significant figures in T, x and y. 1 2(f) Calculation of percentage difference between candidate’s two k values. 1 Comparison of percentage difference with 20% 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 F with reason, e.g. maintaining steady reading or 5.0 N / keeping newton meter steady / checking value of F at the same time as measuring x / holding newton meter horizontally / zero error on newton meter C x has a large percentage uncertainty. D Difficulty with x with reason e.g. parallax / no reference point at start or end position / hard to hold ruler steady / checking newton meter at the same time as measuring x (award checking newton meter/checking value of F only once). E Friction over nails affects T. F Difficulty with d with reason e.g. nails not aligned vertically / judging the centre of the nails 2(g)(ii) 1 mark for each point up to a maximum of 4. 4 A Take more readings (for different values of M) and plot a graph OR calculate more k values and compare. B Clamp newton meter / use (spirit) level to ensure newton meter is horizontal / video / record / film with newton meter and ruler in view / use mass hanger over pulley C Increase d / increase F / decrease T D Use of a vertical reference e.g. plumb line / string between bottom two nails / grid behind string / clamped pointer (for x) or clamped ruler (for x) E Replace nails with pulleys / use smoother string with example e.g. waxed thread / nylon string F Use plumb line / measure from the top of one nail to the top of the other nail owtte / use (vernier) caliper and subtract or add diameter (award plumb line only once).

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