Cambridge A Level Physics 9702 — 2017 Oct/Nov Paper 3 · Variant 3

1 In this experiment, you will investigate the rotational motion of a mass. (a) You have been provided with a 10 g mass hanger and several 10 g slotted masses. Set up the apparatus as shown in Fig. 1.1. clamp wooden blocks boss string 40.0 cm stand mass m bench Fig. 1.1 Adjust the string so that the distance between the bottom of the wooden blocks and the top of the mass hanger is 40.0 cm. The combined mass m of the mass hanger and slotted masses must be 70 g. (b) (i) Twist the mass through ten complete turns as shown in Fig. 1.2. 10 turns Fig. 1.2 (ii) When the mass is released, it will rotate one way and then rotate the other way. This motion will continue until the mass comes to rest. At this point, the mass will continue to swing slightly with very little rotation. Release the mass. Measure and record the time a taken for the mass to come to rest. a = ..................................................[1] (iii) Change the distance between the bottom of the wooden blocks and the top of the mass hanger to 20.0 cm. (iv) Repeat (b)(i). Release the mass. Measure and record the time b taken for the mass to come to rest. b = ..................................................[1] (v) Change the distance between the bottom of the wooden blocks and the top of the mass hanger to 40.0 cm. (c) Change m and repeat (b) until you have six sets of values of m, a and b. You may include your results from (b). a2 Record your results in a table. Include values of in your table. b [10] a2(d) (i) Plot a graph of on the y-axis against m on the x-axis. [3] b (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 a, b and m are related by the equation a2 + Q = Pm b where P and Q are constants. Using your answers in (d)(iii), determine the values of P and Q. Give appropriate units. P = ...................................................... Q = ...................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(b)(ii) Value of a with unit and in the range 5.00–60.00 s. 1 1(b)(iv) Evidence of repeated readings. 1 1(c) Six sets of readings of m (different values), a and b showing the correct trend (as m increases, a and b also increase) and without help from the Supervisor scores 5 marks, five sets scores 4 marks etc. 5 Range: Values of m must include 10 g and 70 g. 1 Column headings: Each column heading must contain a quantity and a unit where appropriate. The presentation of the quantity and unit must conform to accepted scientific convention e.g. a2 / b / s. 1 Consistency: All raw values of time must be given to 0.1 s or all to 0.01 s. 1 Significant figures: All values of a2 / b must be given to the same number of s.f. as (or one more than) the number of s.f. in raw values of time. If raw times recorded to nearest 0.01 s, allow number of significant figures of a2 / b to be one less than the number of significant figures of the raw times. 1 Values of a2 / b calculated correctly. 1 Question Answer Marks 1(d)(i) Axes: Sensible scales must be used, no awkward scales (e.g. 3:10 or fractions). 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 must be plotted on the grid. Diameter of plotted points must be ⩽ half a small square (no “blobs”). Points must be plotted to an accuracy of half a small square. 1 Quality: All points in the table must be plotted on the grid for this mark to be awarded. It must be possible to draw a straight line that is within 10 g on the mass axis (x-axis) of all plotted points. 1 1(d)(ii) Line of best fit: Judge by balance of all points on the grid about the candidate’s line (at least 5). There must be an even distribution of points either side of the line along the full length. Allow one anomalous point only if clearly indicated (i.e. circled or labelled) by the candidate. There must be at least five points left after the anomalous point is disregarded. Lines must not be kinked or thicker than half a small square. 1 Question Answer Marks 1(d)(iii) Gradient: The hypotenuse of the triangle used should be greater than half the length of the drawn line. The 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: Correct read-off from a point on the line 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 x = 0, accurate to half a small square in the y direction. 1 1(e) Value of P = candidate’s gradient and value of Q = candidate’s intercept. The values must not be fractions. 1 Unit for P correct (s g–1 or s kg–1) and unit for Q correct (s). 1

More questions on SI units

2 In this experiment, you will investigate the equilibrium of a metre rule supported by springs. (a) (i) Set up the apparatus as shown in Fig. 2.1. boss rod of clamp spring metre rule loop of string loop of string c bench Fig. 2.1 Adjust the position of the bosses until the metre rule is parallel to the bench. The loops of string supporting the rule should be vertical and as close to the ends of the rule as possible. The distance between these loops is c. (ii) Measure and record c. c = ........................................... cm [1] (b) Suspend a mass m of 0.100 kg from the loop of string as shown in Fig. 2.2. The distance between the string loop below boss A and the string loop supporting the mass is x. Move the mass so that x is approximately 80 cm. Adjust the height of boss B until the rule is parallel to the bench as shown in Fig. 2.2. boss A boss B z y x mass m Fig. 2.2 The lengths of the coiled sections of the springs are y and z as shown in Fig. 2.2. (c) (i) Record m. m = ................................................. kg (ii) Measure and record x. x = ........................................... cm [1] (iii) Measure and record y. y = ................................................ cm (iv) Measure and record z. z = ........................................... cm [1] (d) Estimate the percentage uncertainty in your value of z. percentage uncertainty = ..................................................[1] c -(e) (i) Calculate x b 2 l. c x - = ........................................... cm [1] b 2 l z - y (ii) Calculate ^ h. Give an appropriate unit. m z - y ^ h = ..................................................[1] m z - y(f) Justify the number of significant figures that you have given for your value of ^ h. m .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[1]

Mark scheme: 2(a)(ii) Value of c in the range 95.0–100.0 cm. 1 2(c)(ii) Value of x in the range 75.0–85.0 cm. 1 2(c)(iv) Value(s) of raw z to the nearest mm. 1 2(d) Percentage uncertainty in z based on absolute uncertainty of 2–5 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)(i) Correct calculation of (x – c / 2). 1 2(e)(ii) Correct calculation of (z – y) / m and consistent unit e.g. cm kg–1. 1 2(f) Justification for s.f. in (z – y) / m linked to s.f. in z, y and m or (z – y) and m. 1 2(g)(ii) Second value of x. 1 Second value of z. 1 Quality: second value of z greater than first value of z (provided m in (g) > (c)). 1 2(h)(i) Two values of k calculated correctly. 1 2(h)(ii) Valid comment consistent with calculated values of k, testing against a criterion stated by the candidate. 1 Question Answer Marks 2(i)(i) A Two readings/too few readings/only two readings not enough to draw a (valid) conclusion. B Difficult to read x/c on rule owing to thickness of string. C Difficult to measure y/z/spring with reason e.g. parallax, difficult to judge where end of coiled section is/easy to knock/difficult to hold ruler still. D Difficult to judge/adjust rule to be parallel to bench/horizontal (not ‘rule is not parallel to bench’). E Large percentage uncertainty in (z – y). 1 mark for each point up to a maximum of 4. 4 2(i)(ii) A Take more readings (for different added masses) and plot a graph/take more values of k and compare. B Use thread/wire/thin(ner) string or any other valid method. C Use clamped ruler/use pointer(s) on rule or spring/use (vernier) calipers. D Use a (spirit) level/use ruler and set square with detail. E Larger difference between masses/larger x value/springs with smaller spring constant. 1 mark for each point up to a maximum of 4. 4

More questions on Errors and uncertainties