Cambridge A Level Physics 9702 — 2020 May/June Paper 3 · Variant 4

1 In this experiment, you will investigate the balance of a pivoted rule. (a) The apparatus has been partially assembled for you. ● Add the mass M to the apparatus as shown in Fig. 1.1. The mass M should be suspended approximately 15 cm from the nail. stand boss nail d metre rule upper stop lower stop string loop M syringe boss beaker tray bench Fig. 1.1 ● The distance between the nail and the string loop attached to M is d, as shown in Fig. 1.1. Measure and record d. d = ................................................... cm [1] (b) ● Pour water into the syringe until it is full. The rule will tilt until it touches the upper stop. The water will flow out of the syringe. ● The time between the water level passing the 50 cm3 mark on the syringe and the rule losing contact with the upper stop is t. Measure and record t. t = ...................................................... s [2] (c) Change d by moving M. All values of d should be less than 25 cm. Measure d and t. Repeat until you have six sets of values of d and t. 1 2 Record your results in a table. Include values of and t in your table. d [9] 2 1(d) (i) Plot a graph of t on the y-axis against on the x-axis. [3] d (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 t and d are related by the equation 2 a t = + b d where a and b are constants. Use your answers in (d)(iii) to 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: 1(a) Value of d in range 14.0–16.0 cm. 1 1(b) Value of t in range 10.00–20.00 s. 1 Evidence of repeated readings of t. 1 1(c) Six sets of readings of d and T showing the correct trend and without help from the Supervisor scores 4 marks, five sets scores 3 marks etc. 4 Range: dmin ⩽ 10.0 cm and dmax ⩾ 20.0 cm. 1 Column headings: Each column heading must contain a quantity, a unit and a separating mark where appropriate. The presentation of quantity and unit must conform to accepted scientific convention. e.g. 1 / d / cm–1 1 Consistency: All values of d must be given to the nearest 0.1 cm. 1 Significant figures: Number of significant figures for every value of 1 / d the same as, or one more than, the number of s.f. of d as recorded in table. 1 Calculation: Values of 1 / d calculated correctly. 1 1(d)(i) Axes: Sensible scales must be used, no awkward scales (e.g. 3:10). Scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Scales must be labelled with the quantity that is being plotted. Scale markings should be no more than three large squares apart. 1 Plotting of points: 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. 1 Question Answer Marks 1(d)(i) Quality: All observations in the table (at least 5) must be plotted on the grid. Trend of points must be correct. It must be possible to draw a straight line that is within ± 20 s2 in the t 2 direction of all plotted points. 1 1(d)(ii) Line of best fit: Judge by balance of all points on the grid (at least 5) about the candidate’s line. There must be an even distribution of points either side of the curve along the full length. If there are 6 or more points, allow one anomalous point only if clearly indicated by the candidate. Line must not be kinked or thicker than half a small square. 1 1(d)(iii) Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. The method of calculation must be correct. Do not allow Δx / Δy. Both read-offs must be accurate to half a small square in both the x and y directions. 1 y-intercept: Correct read-off from a point on the line and substituted into y = mx + c. Read-off must be accurate to half a small square in both x and y directions. or Intercept read directly from the graph with read-off at 1 / d = 0 accurate to half a small square. 1 1(e) Value of a equal to candidate’s gradient and value of b equal to candidate’s intercept. The values must not be fractions. 1 Correct units for a (e.g. cm s2) and b (s2). 1

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2 In this experiment, you will investigate the amplitude of oscillations of a mass suspended from a spring. (a) (i) ● Assemble the apparatus as shown in Fig. 2.1. boss wooden rod stand spring 100 g mass hanger two 100 g slotted masses bench Fig. 2.1 ● Pull the mass hanger and slotted masses down through a short distance. Release them so that they oscillate vertically. ● Measure and record the period T of the oscillations. T = ...................................................... s [1] (ii) Calculate the spring constant k using 4π2 M k = 2 T where M = 0.300 kg. k = ............................................... N m–1 [1] (b) ● Slide the two 100 g slotted masses to the top of the mass hanger as shown in Fig. 2.2. two 100 g slotted masses y Fig. 2.2 ● The height of the slotted masses above the base of the mass hanger is y, as shown in Fig. 2.2. Measure and record y. y = ..................................................... m [1] (c) ● Drop the two 100 g slotted masses. The masses and the mass hanger will oscillate vertically, as shown in Fig. 2.3. H Fig. 2.3 ● The distance between the lowest and highest positions of the oscillating mass hanger is H, as shown in Fig. 2.3. Measure and record H. H = ..................................................... m [2] (d) Estimate the percentage uncertainty in your value of H. Show your working. percentage uncertainty = ......................................................... [1] (e) Repeat (b) and (c) but this time sliding the two slotted masses approximately half-way up the mass hanger. y = ........................................................... m H = ........................................................... m [2]

Mark scheme: 2(a)(i) Value of T in the range 0.50–1.00 s. 1 2(a)(ii) Correct calculation of k. 1 2(b) Value of y to nearest 0.001 m and in range 0.050–0.150 m. 1 2(c) Value for H. 1 Evidence of repeated readings of H. 1 2(d) Percentage uncertainty in H based on an absolute uncertainty of 4–8 mm. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. Correct method of calculation to obtain percentage uncertainty. 1 2(e) Second values of y and H. 1 Quality: second H < first H. 1 2(f)(i) Two values of c calculated correctly and both values given to two or more significant figures. 1 2(f)(ii) Justification based on significant figures in H and y. 1 2(f)(iii) Valid comment consistent with calculated values of c, testing against a criterion stated by the candidate. 1 2(g) Correct calculation of g, with unit. 1 Question Answer Marks 2(h)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Mass oscillates horizontally as well as vertically. C y varies around the masses/other specific problem with y. D Difficult to judge end points of oscillation. E H decreases with time/oscillations damped. F Parallax error when taking measurements for H. G Difficult to raise masses to same position for repeats. 1 mark for each point up to a maximum of 4. 4 2(h)(ii) A Take more readings and plot a graph or take more readings and compare k values (not “repeat readings” on its own). B Valid method of restricting oscillation to vertical direction e.g. a guide. C Take several readings and average/clamp ruler vertically to measure y. D Video with rule in view and play back. E Use ‘peak-hold’ indicator to indicate maximum and minimum/use data logger with position sensor under mass hanger. F Hold rule in a clamp/other valid method to reduce parallax. G Use a stop e.g. horizontal piece of wood held by clamp. 1 mark for each point up to a maximum of 4. 4

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