Cambridge A Level Physics 9702 — 2025 Oct/Nov Paper 3 · Variant 1

1 In this experiment, you will investigate oscillations. You have been provided with a double spring and two single springs. (a) (i) • Slide the double spring and the two single springs onto the longer wooden rod. • Set up the apparatus as shown in Fig. 1.1. stand boss longer wooden rod single springs double spring ≈ 55 cm mass m bench Fig. 1.1 • Use the bosses to fix the wooden rod approximately 55 cm above the bench and parallel to the bench. • Hang a total mass of 270 g from the double spring. • The mass hanging from the double spring is m. Record m. m = ......................................................... [1] (ii) • Gently pull the mass down through a short distance. When released, the mass will oscillate. • Take measurements to determine the period T1 of the oscillations. T1 = ............................................................... • Remove the mass from the double spring. [2] (b) • Using the shorter wooden rod, hang mass m as shown in Fig. 1.2. shorter wooden rod with two notches Fig. 1.2 • Gently place the hook of the mass hanger near the centre of the shorter rod. • Carefully adjust the position of the mass hanger until the shorter rod is approximately parallel to the bench, as shown in Fig. 1.2. • Gently pull the mass down through a short distance. When released, the mass will oscillate. • Take measurements to determine the period T2 of the oscillations. T2 = ............................................................... • Remove the mass. [1] (c) Vary m. For each value of m, determine T1 and T2. Repeat until you have five sets of values of m, T1 and T2. Do not use values of m less than 200 g. Record your results in a table. Include values of T1 and T2 in your table. [8] (d) (i) Plot a graph of T2 on the y-axis against T1 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 T2 and T1 are related by the equation T2 = P T1 + 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]

Mark scheme: Question Answer Marks 1(a)(i) Value of m = 270 g with unit. 1 1(a)(ii) Final value of T1 in the range 0.5 s to 1.5 s with unit. 1 Repeats: at least two measurements of nT where n ⩾ 5. 1 1(b) T2 < T1 1 1(c) Five sets of readings of m (different values), T1 and T2 with correct trend (as m increases  T1 (average) increases  and 4 T2 (average) increases) and without help from Supervisor scores 4 marks, four sets scores 3 marks etc. Range of m : mmin ⩽ 220 g and mmax ⩾ 350 g. 1 Column headings: Each column heading must contain a quantity and a unit where appropriate. 1 The presentation of quantity and unit must conform to accepted scientific convention, e.g. m / g, nT1 / s, T1 / s, T1 / s , T10.5 / s0.5. Consistency: All raw values of time must be given to 0.1 s or all given to 0.01 s. 1 1 Calculation: Correct calculation of T1 . 1(d)(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(d)(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. Quality: Trend of points must be positive. 1 All points in the table must be plotted on the grid for this mark to be awarded. It must be possible to draw a straight line that is within 0.01 s½ (to scale) on the T1 axis (normally x-axis) of all plotted points. 1(d)(ii) Line of best fit: 1 ‘Best fit’ is judged by the balance of all points on the grid (at least 4 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 four points left after the anomalous point is disregarded. 1(d)(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. 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(e) P = candidate’s gradient value and 1 Q = candidate’s intercept value. Values must not be written as fractions or given to one significant figure. No units for P. Unit for Q s or s0.5. 1

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2 In this experiment, you will investigate the deformation of paper cylinders. (a) You have been provided with two pieces of paper. The width of a piece of paper is the length w of the shorter side, as shown in Fig. 2.1. w Fig. 2.1 • Select the smaller piece of paper. • Measure and record w. w = ......................................................... cm • Roll the paper into a cylinder and use two paper clips to hold the paper in place, as shown in Fig. 2.2. d w paper clips Fig. 2.2 • The diameter of the cylinder is d, as shown in Fig. 2.2. Adjust the paper and paper clips until d is as close as possible to 7.0 cm. • Measure and record d. d = ........................................................ cm [2] (b) (i) • Set up the apparatus as shown in Fig. 2.3. stand boss wooden rod springs y 200 g mass paper cylinder ≈ 10 cm bench paper clip Fig. 2.3 • Slide the loop of the upper spring onto the wooden rod. • Hang a mass of 200 g from the lower spring. • Adjust the height of the boss until the bottom of the mass is approximately 10 cm above the bench. • Place the paper cylinder so that the middle of the cylinder is under the mass, as shown in Fig. 2.3. • The length of the springs is y, as shown in Fig. 2.3. Measure and record y. y = ................................................... cm [1] (ii) Estimate the percentage uncertainty in your value of y. Show your working. percentage uncertainty = ......................................................% [1] (c) (i) • By adjusting the height of the boss, lower the mass to squash the middle of the paper cylinder until the bottom of the mass is 2.5 cm above the bench, as shown in Fig. 2.4. p 2.5 cm Fig. 2.4 (not to scale) • The length of the springs is p, as shown in Fig. 2.4. Measure and record p. p = ................................................... cm [1] (ii) Calculate (y – p). (y – p) = ................................................... cm [1]

Mark scheme: 2(a) Values of raw d to the nearest mm and final d in range 6.5 cm to 7.5 cm. 1 Repeats: Evidence of repeat readings of d. 1 2(b)(i) Values of raw y to the nearest mm and final value of y in the range 15..0 cm to 30.0 cm. 1 2(b)(ii) Absolute uncertainty in y in range 2 mm to 6 mm. 1 Correct method of calculation to find percentage uncertainty e.g. absolute uncertainty/value from (b)(i)  100. If repeated readings have been taken, then the uncertainty can be half the range if the working is clearly shown, but NOT zero if values are equal. 2(c)(i) Value of p < y 1 2(c)(ii) Correct calculation of (y − p). 1 2(d) Second values of w and d. 1 Second values of y and p. 1 Quality : Second value of p < First value of p. 1 2(e)(i) Two values of k calculated correctly. 1 The final k values must not be written as fractions or given to one significant figure. 2(e)(ii) Justification for significant figures in k linked to significant figures in w and (y − p). 1 2(f) Calculation of percentage difference between candidate’s two k values. 1 Comparison of percentage difference with 10% 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 wtte, e.g. reference to relationship B Difficulty with setting or measuring d, e.g. shape is not a circle or a perfect cylinder / diameter varies around the cylinder / paper clips flatten one side / damage paper with ruler or clips C Difficult to measure y or p with a reason, e.g. parallax error / springs moves when touched by rule / rule not steady / deciding position of end of the coiled section D Difficulty with squashing the cylinder, e.g. squashes in the middle and not at the edge / uneven deformation / difficult to locate mass on middle of cylinder E Difficult to set or measure h with a reason, e.g. metre rule is unwieldy / 30 cm ruler has snout / parallax error / to move boss and observe mass (at the same time) / boss does not move (mass smoothly) in small increments / when boss is tightened (mass rises) / mass base not parallel to bench. 2(g)(ii) 1 mark for each point up to a maximum of 4. 4 A Take more readings and plot a graph OR take more readings and compare k values. B Improved method to improve setting or measuring d, e.g. wrap around a proforma / use glue / tape (for cylinder) / mark a line where the two ends should meet (at 7) / place two blocks either side of the cylinder and measure between the blocks or photograph from above with a mm grid in view. C Improved method to measure y or p, e.g. rule with pointers / clamp ruler D Improved method to ensure whole of longer cylinder is squashed, e.g. Glue a plastic oblong to the mass hanger (to cover the whole cylinder). E Improved method to set or measure h, e.g. Video with rule in view during adjustment / depth gauge / vernier caliper / compare to a block of height 2.5 cm / rule with pointers / hang springs from jaw of a clamp to allow small adjustment in height of masses.

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