Cambridge A Level Physics 9702 — 2021 Feb/March Paper 3 · Variant 3

1 In this experiment, you will investigate the equilibrium of a wooden rod supported by a spring. (a) (i) Before assembling the apparatus, measure and record the length Co of the coiled section of the spring, as shown in Fig. 1.1. Co string loop spring string Fig. 1.1 Co = ................................................... cm [1] (ii) • Assemble the apparatus as shown in Fig. 1.2 with each nail held securely in a boss. stand upper nail string boss clamp C string loop holding split cork spring wooden rod bosses grooves lower nail x benchbench Fig. 1.2 • Adjust the bosses until the upper nail is approximately 35 cm above the bench and the lower nail is approximately 10 cm above the bench. • Position the string loop in one of the grooves near the middle of the rod. • Adjust the free end of the string so that the rod is parallel to the bench and then secure it in the split cork. • Measure and record the length C of the coiled section of the spring, as shown in Fig. 1.2. C = ......................................................... cm • Calculate E, where E = C − Co. E = ......................................................... cm [1] (iii) The distance from the centre of the lower nail to the groove with the string loop in it is x. Measure and record x. x = ................................................... cm [1] (b) Move the string loop into another groove and adjust the apparatus so that the rod is parallel to the bench. Measure C and x. Repeat until you have at least six sets of values of C and x. 1 Record your results in a table. Include values of E and 4 in your table. E [9] 1 (c) (i) Plot a graph of 4 on the y-axis against x on the x-axis. [3] E (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 E and x are related by the equation 1 4 = a x + b E where a and b are constants. Use your answers in (c)(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)(i) Value of Co to the nearest mm and in range 1.5cm to 3.0 cm 1 1(a)(ii) Value of C > Co 1 1(a)(iii) Value of x in range 14.0 to 33.0 cm 1 1(b) Six sets of readings of C and x with correct trend and without help scores 4 marks, five sets scores 3 marks etc. 4 Range: xmax - xmin ⩾ 14.0 cm 1 Column headings: 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 / E4 / cm–4 1 Consistency: All values of raw x must be given to the nearest mm 1 Significant figures: Values of 1 / E4 should be to the same s.f. (or one more than) the s.f. in the corresponding value of E. 1 Calculation: Values of 1 / E4 calculated correctly 1 Question Answer Marks 1(c)(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 which is being plotted. Scale markings should be no more than 3 large squares apart. 1 Plotting of points: All observations must be plotted on the grid. Diameter of plotted points must be ⩽ half a small square (no blobs). Plots must be accurate to within half a small square in both x and y directions. 1 Quality: All points in the table must be plotted (at least 5) for this mark to be awarded. Scatter of plots must be no more than ± 2.0 cm (to scale) from a straight line in the x direction. 1 1(c)(ii) Line of best fit: Judged 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 line along the full length One anomalous point is allowed only if clearly indicated (i.e. circled or labelled) by the candidate. Lines must not be kinked or thicker than half a square. 1 1(c)(iii) Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. Method of calculation must be correct. Both read-offs must be accurate to half a small square in both the x and y directions. 1 y-intercept: 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 = zero accurate to half a small square in y direction. 1 Question Answer Marks 1(d) a equal to candidate’s gradient, and b equal to candidate’s intercept. Values are not written as fractions. 1 Unit for a is dimensionally correct, e.g. cm–5 and unit for b is dimensionally correct, e.g. cm–4 1

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2 In this experiment, you will investigate the speed of air flowing through a hole. (a) • You are provided with a plastic bottle with the base cut off. The neck is sealed with a polythene sheet. Two lines are marked on the side of the bottle, as shown in Fig. 2.1. polythene sheet rubber band upper line lower line bottle Fig. 2.1 The distance between the lines is L, and the diameter of the bottle where the lines are marked is D, as shown in Fig. 2.2. bottle L D Fig. 2.2 • Measure and record L and D. L = ......................................................... cm D = ......................................................... cm [2] (b) (i) You have been provided with a pin and a thin nail. • Make a hole through the polythene sheet using the pin, as shown in Fig. 2.3. make hole here pin Fig. 2.3 • Measure and record the diameter d of the pin. d = ................................................... cm [1] (ii) Estimate the percentage uncertainty in your value of d. Show your working. percentage uncertainty = ......................................................... [1] (c) • Submerge the bottle in the bowl so that it is completely filled with water. • Tilt the bottle until it is vertical with its lower end approximately 1 cm below the water level in the bowl, as shown in Fig. 2.4. upper line bowl lower line water § 1 cm Fig. 2.4 • The water level in the bottle will fall. Start the stopwatch when the water level reaches the upper line, and stop the stopwatch when the water level reaches the lower line. Record the time t shown on the stopwatch. t = ......................................................... [2]

Mark scheme: 2(a) Value of L in range 2.5 cm to 3.5 cm and given to nearest mm or better 1 Value of D in range 6.0 to 9.0 cm and given to nearest mm or better 1 2(b)(i) Value of raw d to nearest 0.001 cm and final value in range 0.040 cm to 0.090 cm 1 2(b)(ii) Absolute uncertainty of 0.001 cm and correct method of calculation to obtain percentage uncertainty in d. If several readings have been taken, then the absolute uncertainty can be half the range, but not zero if values are equal. 1 2(c) Value for t in s, with unit 1 Evidence of repeat readings for t 1 2(d) Second values for d and t 1 Quality: second t shorter than first t 1 2(e)(i) Two values of k calculated correctly. 1 2(e)(ii) Justification based on sig. fig. in t and d 1 2(e)(iii) Sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate. 1 2(f) Correct calculation of S 1 Question Answer Marks 2(g)(i) Two k values are not enough to draw a valid conclusion Hole may not be same size as pin Difficult to measure D as bottle distorts Difficulty with 1 cm depth with reason, e.g. holding bottle steady (when timing) / seeing what the depth is Difficulty with measuring time with reason, e.g. lines are thick / difficult to judge when level passes line / difficult to see water level 4 max 4 2(g)(ii) Take more readings and plot a graph / calculate more k values and compare Measure hole itself, with detail of method Stand bottle on graph grid / use a more rigid named material for bottle / measure with bottle between blocks Place bottle on a support in the bowl / clamp bottle (after filling) / mark line 1 cm from bottom of bottle Video with timer in view (or frame by frame) / use coloured water 4 max 4

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