Cambridge A Level Physics 9702 — 2024 Oct/Nov Paper 3 · Variant 6

1 In this experiment, you will investigate the equilibrium position of a suspended cardboard sheet. (a) You are provided with a flat sheet of cardboard with a hole through it and two lines drawn near two of the edges. • Assemble the apparatus as shown in Fig. 1.1 with the bottom edge of the cardboard approximately 5 cm above the bench. Check that the cardboard swings freely on the knitting needle. stand knitting needle passing through hole in cardboard and held in boss boss cardboard lines drawn on cardboard bench ≈ 5 cm Fig. 1.1 • Use the sharp pencil to make a hole through the cardboard approximately half‑way along the longer line. • Pass the bolt through the slotted mass and then through the hole in the cardboard, as shown in Fig. 1.2. • Secure the bolt using the nut. x slotted θ mass Fig. 1.2 • The distance between the centre of the slotted mass and the intersection of the two lines is x, as shown in Fig. 1.2. Measure and record x. x = ............................................................... • The angle between the bottom edge of the cardboard and the horizontal is θ, as shown in Fig. 1.2. Use the wooden block and the protractor to measure θ. θ = ............................................................. ° [2] (b) Use the pencil to make another hole through the longer line and move the slotted mass and bolt to the new hole. Measure x and θ. Repeat until you have six sets of values of x and θ. 1 Record your results in a table. Include values of in your table. tan θ [10] 1 (c) (i) Plot a graph of on the y‑axis against x on the x‑axis. [3] tan θ (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 θ and x are related by the equation 1 = ax + b tan θ where a and b are constants. Using your answers in (c)(iii), determine the values of a and b. Give appropriate units. a = ............................................................... b = ............................................................... [2] [Total: 20]

Mark scheme: Question Answer Marks 1(a) Final value of x in range 12.0–16.0 cm, with unit. 1 Raw values to nearest degree and final value of in range 10°–30°. 1 1(b) Six (or more) sets of readings of x (different values) and with correct trend (x increases, decreases) and without help 5 from supervisor scores 5 marks, five sets scores 4 marks etc. Range: xmin ⩽ 5.0 cm and xmax ⩾ 20.0 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. x / cm. 1 / tan  must have no unit. Consistency: All values of raw x must be given to the nearest mm. 1 Significant figures: All values of 1 / tan given to same (or one more) number of s.f. as raw . 1 Calculation: Values of 1 / tan  calculated correctly. 1 1(c)(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 All points in the table must be plotted (at least 5) for this mark to be awarded. Trend of points must be positive. It must be possible to draw a straight line that is within  0.20 on the 1 / tan  axis (normally y-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 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 x / y). Gradient sign on answer line consistent with graph drawn. y-intercept: 1 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 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(d) a equal to candidate’s gradient value and b equal to candidate’s intercept value. 1 Values must not be written as fractions, roots or given to only one significant figure. Units for a and b correct and consistent with readings (e.g. cm–1 for a and no unit for b). 1

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2 In this experiment, you will investigate the motion of a conical pendulum. (a) • Set the compasses to a radius of approximately 9 cm and then use them to draw a circle on the sheet of paper. • Mark the centre of the circle with a cross. • Measure and record the diameter D of the circle. D = .................................................... cm [1] (b) (i) You are provided with a pendulum bob with a length of string attached. • Tie a knot in the string approximately 19 cm from the top of the bob. • Measure and record the distance p from the knot to the centre of the bob. p = .................................................... cm [1] (ii) Estimate the percentage uncertainty in your value of p. Show your working. percentage uncertainty = ......................................................% [1] (c) (i) • Place the paper with the circle on the bench. • Holding the knot, suspend the bob approximately 5 mm above the cross at the centre of the circle, as shown in Fig. 2.1. hand holding knot string bob paper Fig. 2.1 • Move the knot in small, slow circles so that the bob starts to move in a circle. • Adjust the movement of the knot until the bob moves just above the circle on the paper, as shown in Fig. 2.2. Fig. 2.2 • The period T of the rotation of the bob is the time the bob takes to travel through one complete circle. When this motion is steady, take measurements to determine T. T = ......................................................... [2] (ii) The angle between the string and the vertical when the bob follows this circular path is Φ, where Φ is given by D sin Φ = 2p. Calculate Φ. Φ = ........................................................° [1] (d) • Tie a knot in the string approximately 13 cm from the top of the bob. • Using this knot, measure and record p. p = .......................................................... cm • Using this knot, repeat (c). T = ............................................................... Φ = ............................................................. ° [3]

Mark scheme: 2(a) Raw D to nearest mm and final value for D in range 17.0–19.0 cm. 1 2(b)(i) Raw p to nearest mm. 1 2(b)(ii) Percentage uncertainty based on an absolute uncertainty in p in range 2–5 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)(i) Period determined correctly and final value for T with unit in range 0.60–1.10 s. 1 Evidence of repeated readings for T (at least two values of at least 5T). 1 2(c)(ii) Correct calculation of . 1 2(d) Second value for p. 1 Second value for 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, roots or given to only one significant figure. 2(e)(ii) Justification based on the significant figures in D, p and raw times. 1 2(f) Valid calculation of percentage difference between candidate’s two k 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 p with a reason e.g. parallax error / difficult to determine (judge) centre of bob / ruler not parallel to string. C Problem with matching bob movement to circle with reason e.g. difficult to judge whether path of bob matches circle drawn. D Difficult to keep (rotation) speed constant. E Problem with measurement of time with reason e.g. difficult whilst maintaining motion of bob / difficult to judge when one rotation is complete 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 k values (not “repeat readings” on its own). 4 B Measure bob diameter and knot to edge of bob / workable method of avoiding parallax. C Put paper lower down e.g. on floor and view from above / rotate inside a cylinder instead of above line (to judge path). D Valid method to maintain constant rotation e.g. use motor (instead of hand). E Video/film/record with timer in view or replay frame by frame or pointer or mark on circle e.g. radius line. 1 mark for each point up to a maximum of 4.

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