Cambridge A Level Physics 9702 — 2024 Feb/March Paper 3 · Variant 3

1 In this experiment, you will investigate the properties of a pendulum. (a) (i) • Assemble the apparatus as shown in Fig. 1.1 and Fig. 1.2. • Push the nail through the central hole in the pendulum and then into the plastic tube. • Secure the tube and nail in the boss, as shown in Fig. 1.1. boss nail pendulum plastic tube Fig. 1.1 • Ensure that the pendulum swings freely on the nail. stand nail passing through central hole boss pendulum bench Fig. 1.2 • Attach two 50 g slotted masses to the pendulum using the bolts and nuts. Use two holes which are the same distance x from the nail, as shown in Fig. 1.3. slotted mass x x bolt nail Fig. 1.3 • The distance from the centre of each bolt to the nail is x. • Measure and record x. x = ......................................................... [1] (ii) Push the bottom of the pendulum a short distance to one side and then release it. Take measurements to determine the period T of the oscillations. T = .......................................................... [2] (b) Vary x by using different holes and measure T. Repeat until you have six sets of values of x and T. Record your results in a table. Include values of x3 in your table. [9] (c) (i) Plot a graph of T on the y-axis against x3 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] (d) It is suggested that the quantities T and x are related by the equation T = a x3 + b 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] You may not need to use all of the materials provided.

Mark scheme: Question Answer Marks 1(a)(i) Value of x with consistent unit. 1 1(a)(ii) Value of T in range 0.80 s to 2.00 s, with unit. 1 1(a)(ii) Evidence of repeat measurements of T (at least two measurements of 5T). 1 1(b) Six sets of readings of x and T with correct trend and without help scores 4 marks, five sets scores 3 marks etc. 4 1(b) Range: 1 x min ⩽ 7 cm and xmax = 19 cm. 1(b) 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 3 / cm1.5. 1(b) Consistency: 1 All raw values of x must be given to the nearest mm. 1(b) Significant figures: 1 All values of x 3 given to same s.f. as x (or one more than s.f of x). 1(b) Calculation: 1 Values of x 3 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). 1(c)(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. 1(c)(i) Quality: 1 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  5 cm1.5 in the x direction from 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 4 points left after the anomalous point is disregarded. 1(c)(iii) Gradient: 1 Sign of gradient must match graph drawn. The hypotenuse of the triangle used must be greater than half the length of the drawn line. Method of calculation must be correct (not x / y). Both read-offs must be accurate to half a small square in both the x and y directions. 1(c)(iii) y-intercept: 1 Either Correct read-off from a point on the line substituted into y = mx + c or an equivalent expression, with read-off accurate to half a small square in both x and y directions. Or Intercept read directly from the graph, with read-off at x 3 = zero accurate to half a small square in y direction. 1(d) a equal to candidate’s gradient, and b equal to candidate’s intercept. Values must not be written as fractions or to 1 1 significant figure. 1(d) Units for a and b correct and consistent with value 1 (e.g. s cm–1.5 for a and s for b).

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2 In this experiment, you will investigate the frictional forces on a wooden strip. (a) (i) • You have been provided with two wooden strips. Select the thicker strip. Measure and record its length L. L = .......................................................... cm • Attach the slotted mass to one of the wider faces of the strip approximately 10 cm from one end using a small piece of adhesive putty, as shown in Fig. 2.1. slotted mass wooden strip dA Fig. 2.1 • The distance from the centre of the slotted mass to the nearest end of the strip is dA, as shown in Fig. 2.1. Measure and record dA. dA = .......................................................... cm [2] (ii) You have been provided with a smooth board. Support the board vertically on the bench using the stand, boss and clamp, as shown in Fig. 2.2. smooth board clamp wooden strip boss stand slotted mass bench θA • Lean the strip against the smooth board with the slotted mass nearer the lower end, as shown in Fig. 2.2. • Move the bottom of the strip away from the smooth board until the strip starts to slip. Gradually push the bottom of the strip back towards the board until it just stays in position by itself. • The angle between the strip and the bench is θA, as shown in Fig. 2.2. Measure and record θA. θA = ........................................................° [2] (iii) Estimate the percentage uncertainty in your value of θA. Show your working. percentage uncertainty = ......................................................% [1] (iv) The mass of the thicker strip is M. The value of M is written on the strip. • Record M. M = ............................................................ g • Calculate FA using M SdA FA = A where S is 100 g. FA = ......................................................... [1] (v) • Invert the thicker strip and lean it against the smooth board so that the slotted mass is nearer the upper end as shown in Fig. 2.3. dB θB Fig. 2.3 • The distance from the centre of the slotted mass to the lower end of the strip is dB. Measure and record dB. dB = .......................................................... cm • Move the bottom of the strip away from the smooth board until the strip starts to slip. Gradually push the bottom of the strip back towards the board until it just stays in position by itself. • The angle between the strip and the bench is θB, as shown in Fig. 2.3. Measure and record θB. θB = ............................................................. ° • Calculate FB, using M SdB FB = . B FB = ............................................................... [1]

Mark scheme: 2(a)(i) Value for L and in range 42.0 to 46.0 cm. 1 2(a)(i) Raw Value for dA to nearest mm and < 50.0 cm. 1 2(a)(ii) Value for A in range 30 to 80 and raw values to nearest degree, 1 2(a)(ii) Evidence of repeated measurements of A, 1 2(a)(iii) Uncertainty of 2 to 5 and correct method of calculation to obtain percentage uncertainty in A. 1 If several readings have been taken, then the absolute uncertainty can be half the range if working clearly shown, but not zero if the values are equal. 2(a)(iv) Correct calculation of FA. 1 2(a)(v) Values for dB , B and FB. 1 2(b) Second values for dA and A. 1 2(b) Second values for dB and B. 1 2(b) Quality: B > A. 1 2(c) 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(d) Calculation of percentage difference between candidate’s two k values. Comparison of percentage difference with 15% 1 leading to a consistent conclusion. 2(e)(i) A Two readings / k values are not enough to draw a (valid) conclusion. 4 B Board may not be vertical. C Difficult to measure dA (or dB), with reason (e.g. parallax / finding centre of mass). D Difficult to measure  without disturbing strip. E Board moves when strip is pushed. F Difficult to identify ‘just sticks’ position/angle, with reason (e.g. varies when repeating / bench surface is uneven). G Mass of putty not considered. 1 mark for each up to a maximum of 4. 2(e)(ii) A Take more readings and plot a graph / calculate more k values and compare. 4 B Use set square between board and bench / plumbline / fix board to wall. C Measure to edge of mass then add half the diameter / other workable method of avoiding parallax. D Measure distance of base of strip from board then calculate  / fix strip before using protractor / take photo and measure angle on it. E Clamp stand to bench / use two stands. F Put flatter surface on bench / sand bench. G Add mass of putty to the 100 g / use tape instead of putty. 1 mark for each up to a maximum of 4.

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