Cambridge A Level Physics 9702 — 2024 Oct/Nov Paper 3 · Variant 1

1 In this experiment, you will investigate the equilibrium position of a wooden strip. Some of the apparatus has been set up for you. (a) • Set up the apparatus as shown in Fig. 1.1. adhesive putty stand string string wrapped spring around screw rod of clamp boss string loop ≈ 15 cm wooden strip bench Fig. 1.1 • Ensure the rod of the clamp is approximately 15 cm above the bench. • Arrange the wooden strip so that the bottom of the strip rests against the base of the stand. • Use adhesive putty to fix the string centrally on the wooden strip in line with the spring. • Wrap the string around the screw. • Arrange the block and protractor as shown in Fig. 1.2. L0 protractor θ 0 adhesive putty block Fig. 1.2 • The length of the coiled section of the spring is L0, as shown in Fig. 1.2. The angle between the lower edge of the wooden strip and the horizontal is θ0, as shown in Fig. 1.2. Adjust the apparatus until θ0 is between 75° and 85°. You may wish to move the protractor along the block. • Measure and record L0 and θ0. L0 = ............................................................... θ0 = ............................................................. ° [1] (b) • Make a hook from one paper clip and hang nine paper clips from it as shown in Fig. 1.3. paper clip nine paper clips Fig. 1.3 • The mass of all ten paper clips is m. Measure and record m. m = ......................................................... [1] (c) • Using the mass hanger and slotted masses, hang a mass of 40 g from the string loop. • Hang the paper clips from the string loop as shown in Fig. 1.4. L θ paper clips mass hanger and masses Fig. 1.4 • The total mass hanging from the string loop is M. The angle between the wooden strip and the horizontal is θ, as shown in Fig. 1.4. The length of the coiled section of the spring is L, as shown in Fig. 1.4. Determine and record M. M = ............................................................... • Measure and record θ and L. θ = ............................................................. ° L = ............................................................... • Calculate e where e = (L – L0). e = ............................................................... [1] (d) Vary M. The total mass M may be made from slotted masses only or from m and slotted masses. For each value of M, measure and record M, θ and L. Repeat until you have six sets of values. Record your results in a table. Include values of e and sin θ in your table. [9] (e) (i) Plot a graph of e on the y‑axis against sin θ 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] (f) It is suggested that the quantities e and θ are related by the equation e = P sin θ + Q where P and Q are constants. Using your answers in (e)(iii), determine the values of P and Q. Give appropriate units. P = ............................................................... Q = ............................................................... [2] [Total: 20]

Mark scheme: Question Answer Marks 1(a) Value(s) of raw 0 to the nearest degree and final 0 value in the range 75° ⩽ o ⩽ 85°. 1 1(b) Value of m in range 3.0 g ⩽ m ⩽ 6.0 g with unit and to at least 0.1 g. 1 1(c) Correct calculation of e with correct unit. 1 1(d) Six (or more) sets of readings of M (different values) and with correct trend (as M increases, decreases) and without 4 help from supervisor scores 4 marks, five sets scores 3 marks etc. Range: Mmax – Mmin ⩾ 30 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. L / cm , M / g , e / cm,  / °, sin . Consistency: 1 All values of raw L must be given to the nearest mm. Significant figures: 1 Values of sin must be given to the same number of s.f. (or one more than) the number of s.f. in the corresponding raw  values. Calculation: Values of sin are correct. 1 1(e)(i) Axes: 1 Axes must be labelled with the required 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 negative. 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  0.25 cm (to scale) on the e axis (normally y-axis) of all plotted points. 1(e)(ii) Line of best fit: 1 ‘Best fit’ is judged by the balance of all points on the grid (at least 5 points on the grid) 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(e)(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 x / y). Gradient sign on answer line consistent with graph drawn. y-intercept: 1 Intercept read directly from the graph, with read-off at sin = 0, accurate to half a small square in y direction. or Correct read-off from a point on the line is substituted correctly into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both x and y directions. 1(f) P = candidate’s gradient value and Q = candidate’s intercept value. 1 Values must not be written as fractions, roots or given to only one significant figure. Correct and consistent units for P (e.g. cm or m or mm) and Q (e.g. cm or m or mm). 1

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2 In this experiment, you will investigate oscillations. (a) You have been provided with a board of width w and thickness x, as shown in Fig. 2.1. board hole hole x w Fig. 2.1 (not to scale) Measure and record w and x. w = ............................................................... x = ............................................................... [1] (b) (i) • Set up the apparatus as shown in Fig. 2.2. stand d clamp boss rod of clamp through curved board hole in board bench Fig. 2.2 • Ensure the rods of the clamps are the same height above the bench. • Slide the rods of the clamps through the holes in the board as shown in Fig. 2.2. Ensure that each end of the board touches a stand. • The distance between the inside edges of the stands is d, as shown in Fig. 2.2. Adjust the apparatus until d is in the range 92 cm to 99 cm. • Measure and record d. d = .................................................... cm [2] (ii) Estimate the percentage uncertainty in your value of d. Show your working. percentage uncertainty = ......................................................% [1] (c) • Place the spring in the middle of the curved board. • Displace the spring a short distance to one side, as shown in Fig. 2.3. spring board Fig. 2.3 • Release the spring. The spring will roll from side to side on the board. • Take measurements to determine the period T of these oscillations. T = ...................................................... s [2] (d) • Adjust the apparatus until d is in the range 66 cm to 74 cm. Ensure that the board does not touch the bench. • Measure and record d. d = ......................................................... cm • Repeat (c). T = ............................................................ s [3] (e) It is suggested that the relationship between T and d is (T – a) = kd where a is 0.70 s and 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) Value of w on answer line in the range 6.0–8.0 cm with unit 1 and value of x on answer line in the range 1–4 mm with unit. 2(b)(i) Value(s) of raw d to the nearest mm. 1 Final value of d in the range 92.0–99.0 cm. 1 2(b)(ii) Percentage uncertainty based on an absolute uncertainty in d in range 2–10 mm. 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(c) Value of T in the range 1.0–2.0 s. 1 Repeats: At least two measurements of time. 1 2(d) Second value of d. 1 Second value of T. 1 Second value of T < first value of T. 1 2(e)(i) Two values of k calculated correctly. 1 The final k values must not be 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 or time and d. 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) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). 4 B Difficulty with measuring x with a reason e.g. x is a small value and minimum rule marking 1 mm / rule is not precise enough / rule unwieldly / large percentage uncertainty. C Difficult to measure d with a reason e.g. rule hand held / rule may not be horizontal / parallax. D Difficult to determine T with a reason e.g. number of oscillations is small / identifying start or end point of oscillation. E Difficulty with spring e.g. rolls at an angle / falls off strip / loops restrict movement / spring slides as well as rolling. F Difficulty with board e.g. board twists / does not touch stand because of boss / roughness restricts rolling / stands move during the experiment / board hard to bend. 1 mark for each point up to a maximum of 4. 2(g)(ii) A Take more readings (for different values of d) and plot a graph / take more readings and compare k values (not “repeat 4 readings” on its own). B Improved method to measure x e.g. (vernier/digital) calipers or micrometer screw gauge. C Improved method to measure d e.g. clamp rule (with pointers). D Improved method to measure T e.g. fiducial marker at centre of oscillation or video / film / record with timer in view. E Improved method of release e.g. use of a stop / card gate. F Use G-clamps to fix the stands / add weights to stands. 1 mark for each point up to a maximum of 4.

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