Cambridge A Level Physics 9702 — 2024 Oct/Nov Paper 3 · Variant 5

1 In this experiment, you will investigate the balancing of a metre rule. (a) • Set up the apparatus as shown in Fig. 1.1. 30.0 cm s 10.0 cm a 100 g mass mass A mass B rule bench pivot Fig. 1.1 • Use the adhesive putty to fix three 100 g slotted masses with their centres above the 10.0 cm mark on the rule, as shown in Fig. 1.1. • Place the rule on the pivot at the 30.0 cm mark. The 100 g masses and the pivot must remain at these positions throughout the experiment. • Place masses A and B on the rule. • The distance between the centre of A and the pivot is a. The distance between the centre of B and the centre of A is s. Adjust the position of A until a is approximately 20 cm. • Adjust the position of B until the rule is balanced. • Determine a and s. a = ......................................................... cm s = ......................................................... cm [1] (b) Change the position of A. Adjust the position of B until the rule is balanced. Determine a and s. Repeat until you have six sets of values of a and s. Do not use values of a less than 10.0 cm. 1 s Record your results in a table. Include values of and in your table. a a [10] s 1 (c) (i) Plot a graph of on the y‑axis against on the x‑axis. [3] a a (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y‑intercept of this line. gradient = ............................................................... y‑intercept = ............................................................... [2] (d) (i) It is suggested that the quantities a and s are related by the equation s P = + Q a a where P and Q are constants. Using your answers in (c)(iii), determine the values of P and Q. Give appropriate units. P = ................................................................ Q = ................................................................ [2] (ii) Theory suggests that (Z – R)d P = m where Z = 300 g, d = 20.0 cm, m = 50 g and R is a constant. Using your value of P, determine a value for R. Give an appropriate unit. R = ......................................................... [1] [Total: 20]

Mark scheme: Question Answer Marks 1(a) Final value of s is greater than a and (a + s) ⩽ 70.0 cm. 1 1(b) Six (or more) sets of readings of a (different values) and s with the correct trend (as a increases, s decreases) and without 5 help from supervisor scores 5 marks, five sets scores 4 marks, etc. Range: smin ⩽ 10.0 cm. 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/a / cm–1 and no unit for s / a. Consistency: All raw values of a and s must be given to the nearest mm. 1 Significant figures: 1 All values of s / a must be given to the same number of s.f. as (or one more than) the least number of s.f. in raw a and s values. Calculation: Values of s / a are correct. 1 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 Trend of points must be positive. All points in the table must be plotted (at least 5) on the grid for this mark to be awarded. It must be possible to draw a straight line that is within  0.2 m–1 (0.002 cm–1) on the 1 / a axis (normally x-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 five 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 small 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 five points left after the anomalous point is disregarded. 1(c)(iii) Gradient: 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 Δx / Δy). Gradient sign on answer line consistent with graph drawn. y-intercept: 1 Intercept read directly from the graph, with read-off at 1 / a = 0, accurate to half a small square in y direction. or Correct read-off from a point on the line 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)(i) Value of P = candidate’s gradient value and value of Q = candidate’s y-intercept value. 1 The values must not be written as fractions, roots or given to one significant figure. Correct unit for P: m or cm or mm 1 and no unit for Q. 1(d)(ii) Correct calculation of R with correct unit, e.g. g. 1

More questions on Turning effects of forces

2 In this experiment, you will investigate the oscillations of a wooden rod. (a) (i) You are provided with two identical wooden rods. The length of one rod is L and the diameter of the rod is d, as shown in Fig. 2.1. L d Fig. 2.1 (not to scale) • Measure and record L. L = ................................................................ • Using the micrometer, measure and record d. d = ................................................................ • The volume V of the rod is given by πd2L V = . 4 Calculate V. V = ................................................................ [2] (ii) Justify the number of significant figures that you have given for your value of V. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (b) (i) • Set up the apparatus as shown in Fig. 2.2. 22.0 cm boss 22.0 cm clamp rod spring S0 spring rod 22.0 cm 22.0 cm mass hanger string loop stand bench Fig. 2.2 (not to scale) • Clamp one rod at its midpoint so that it is parallel to the bench. • Slide the string loop onto the other rod. • Slide the springs onto the rods and adjust the positions of the springs so that each spring is 22.0 cm from the nearest end of the rod, as shown in Fig. 2.2. • Hang the mass hanger from the string loop. Adjust the position of the string loop so that it is at the midpoint of the lower rod. • The distance between the two rods is S0. Measure and record S0. S0 = ..................................................... m [1] (ii) Estimate the percentage uncertainty in your value of S0. Show your working. percentage uncertainty = ......................................................% [1] (iii) • Add a 100 g slotted mass to the mass hanger. • The distance between the two rods is now S1. Measure and record S1. S1 = ........................................................... m • The spring constant k of the arrangement is given by W k = S1 – S0 where W has the value 0.98 N. Calculate k. k = ..................................................... N m–1 [1] (c) • The total mass hanging from the string loop is M. Record M. M = .......................................................... kg • Move the lower rod a small distance downwards. Release the rod. The rod oscillates in a vertical plane. • Take measurements to determine the period T of the oscillations. T = ............................................................ s [2]

Mark scheme: 2(a)(i) Final L value in the range 89.0–91.0 cm with unit and L to nearest mm. 1 Final d value in the range 8.00–12.00 mm with unit and all raw values to the nearest 0.01 mm or all to the nearest 1 0.001 mm. 2(a)(ii) Justification for significant figures in V linked to significant figures in L and d. 1 2(b)(i) S0 in the range 0.030–0.150 m. 1 2(b)(ii) Percentage uncertainty based on an absolute uncertainty in S0 in range 0.2 cm (0.002 m) to 0.6 cm (0.006 m). 1 Correct method of calculation to find percentage uncertainty e.g. (absolute uncertainty / value from 2(b)(i))  100. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. 2(b)(iii) Correct calculation of k. 1 2(c) Final T in range 0.30 s ⩽ T ⩽ 0.70 s. 1 At least two measurements of nT where n ⩾ 5. 1 2(d) Second value of M and second value of T. 1 Second value of T > first value of T. 1 2(e) Two values of r calculated correctly. 1 The final r values must not be written as fractions or given to only to one significant figure 2(f) Calculation of percentage difference between candidate’s two values. 1 Comparison of percentage difference with 15% leading to a consistent conclusion. 2(g)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). 4 B Difficult to measure S0 or S1 with a reason e.g. ruler disturbs lower rod while measuring / parallax error / ruler moves during measurement as hand-held. C S0 and/or S1 vary along the length of the rods with reason e.g. springs are of different lengths / rods bend / rod(s) not uniform. D Difficult to measure time or T with reason e.g. difficult to judge / identify / tell / know the start or end of an oscillation. E Difficulty with oscillation(s) with reason e.g. springs move on rod / other modes of oscillation are present / mass hanger swings (or moves) on rod / mass (hanger) hits the stand. 1 mark for each point up to a maximum of 4. 2(g)(ii) A Take more readings and plot a graph or take more readings and compare values (not “repeat readings” on its own). 4 B Clamp ruler / pointers on rule or use calipers or measure between middles of rods / measure diameter of rod and take account in measurement. C Use springs of identical length (and spring constant) or adjust positions of springs so that the extensions of each spring are the same or move mass hanger to make rods parallel. D Fiducial mark at the centre of the oscillation or video / record / film with timer in view or view frame by frame or motion / position sensor located under the lower rod / mass hanger E Carve / use grooves in rod or method of attachment to rod e.g. tape / glue / use adhesive putty for the springs or string 1 mark for each point up to a maximum of 4.

More questions on Physical quantities