Cambridge A Level Physics 9702 — 2013 Oct/Nov Paper 3 · Variant 5

1 In this experiment, you will investigate the motion of a swinging bob and a wooden rod. (a) Measure and record the distance L between the end of the rod and the end of the hook as shown in Fig. 1.1. wooden rod hook L Fig. 1.1 L = ..............................................m [1] (b) (i) Set up the apparatus as shown in Fig. 1.2. split cork in clamp nail in clamp stand stand string L wooden rod bob bench Fig. 1.2 The distance between the bottom of the split cork and the centre of the bob should be equal to the value of L in (a). (ii) Reduce the distance between the bottom of the split cork and the centre of the bob For by approximately 3 cm. Examiner’s Use (iii) Measure and record the distance D between the bottom of the split cork and the centre of the bob, as shown in Fig. 1.3. D Fig. 1.3 D = ...................................................m (iv) Calculate x where x = L – D. x = ...................................................m (c) (i) Move the bob towards you. Release the bob and watch the movement. The bob will move away from you and back towards you, completing a swing. (ii) Move the bottom of the wooden rod towards you. Release the rod and watch the movement. The rod will move away from you and back towards you, completing a swing. (iii) Move the bob and the bottom of the rod towards you. Release the bob and the rod at the same instant and watch the movement. The bob and the rod will swing backwards and forwards becoming out of step. Eventually they will, for a short time, move together in step. (iv) Repeat (iii) and count the number n of swings of the bob between releasing the bob and rod and when they are back in step. Record n. n = ..................................................[1] (d) Decrease D and repeat (b)(iii), (b)(iv) and (c)(iv) until you have six sets of values of D, For x and n. Examiner’s Your values of D should be in the range D 40 cm. Use n + 1 2 Include values of in your table. n [10] n + 1 2(e) (i) Plot a graph of on the y-axis against x on the x-axis. [3] n (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ...................................................... y-intercept = ...................................................... [2] For Examiner’s Use (f) The quantities n and x are related by the equation For 2 Examiner’s n + 1 Use = – Px + Q n where P and Q are constants. Use your answers in (e)(iii) to determine the values of P and Q. Give appropriate units. P = ...................................................... Q = ...................................................... [2] You may not need to use all of the materials provided. For Examiner’s Use

Mark scheme: 1 (a) Value for L in the range 0.500–0.600 m. [1] (c) (iv) Value for n in the range 3–8. [1] (d) Six sets of readings of D and n scores 5 marks, five sets scores 4 marks etc. [5] Help from Supervisor –1. Range of D: Dmin < 45 cm and Dmax > 50 cm. [1] Column headings: [1] Each column heading must contain a quantity and a unit where appropriate. The unit must conform to accepted scientific convention e.g. D/m. Consistency: [1] All values of D must be given to the nearest mm. Significant figures: [1] Every value of ((n + 1)/n)2 should be given to 2 or 3 s.f. Calculation: [1] Values of ((n + 1)/n)2 calculated correctly. (e) (i) Axes: [1] 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. Plotting of points: [1] All observations in the table must be plotted. Diameter of plotted point must be ≤ half a small square (no “blobs”). Work to an accuracy of half a small square. Quality: [1] All points in the table must be plotted on the grid for this mark to be awarded. All points must be no more than 0.04 of ((n + 1)/n)2 from a straight line. (e) (ii) Line of best fit: [1] Judge by balance of all points on the grid about the candidate’s line (at least 5 points) 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 by the candidate. Line must not be kinked or thicker than half a small square. GCE AS LEVEL – October/November 2013 9702 35 (iii) Gradient: [1] The hypotenuse of the triangle must be at least 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. The method of calculation must be correct. y-intercept: [1] Either: Check 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: Check read-off of the intercept directly from the graph. (f) Value of P = –(candidate’s gradient). Value of Q = candidate’s intercept. [1] Unit for P (e.g. m–1) consistent with value and no unit for Q. [1] [Total: 20] 3

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2 In this experiment, you will investigate the motion of a water-filled ball in a container of water. (a) Place the rubber bands on the cylindrical container approximately 10 cm apart, as shown in Fig. 2.1. The top rubber band should be level with the surface of the water. 5 cm rubber bands 10 cm cylindrical container bench Fig. 2.1 (b) (i) You have been provided with a ball, a syringe and a beaker of water. Draw water from the beaker into the syringe and empty the contents into the hole in the ball. Determine the volume V0 of water that is required to fill the ball. (1 ml = 1 cm3) You may have to fill the syringe more than once. V0 = .......................................... cm3 [1] (ii) Describe how you determined the value of V0. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[1] (iii) Hold the ball so that no water leaks out and use the syringe to remove 5 cm3 (5 ml) of water from the ball. (iv) Use the Blu-Tack to seal the hole in the ball to prevent the water escaping. (v) Calculate the volume V of water remaining in the ball. For Examiner’s Use V = ...........................................cm3 [1] (vi) Estimate the percentage uncertainty in your value of V. percentage uncertainty = ..................................................[1] (c) (i) Hold the ball so that its bottom is on the surface of the water, as shown in Fig. 2.2. ball rubber band cylindrical container water Fig. 2.2 (ii) Release the ball. It will fall and then return to the surface. For Move the lower rubber band to the lowest position reached by the bottom of the ball Examiner’s as shown in Fig. 2.3. Use x rubber band Fig. 2.3 (iii) Measure and record the distance x between the rubber bands. x = ............................................ cm [2] (d) (i) Remove another 5 cm3 (5 ml) of water from the ball. (ii) Repeat (b)(iv), (b)(v), and (c). V = ............................................... cm3 x = ................................................ cm [3]

Mark scheme: 2 (b) (i) Value for V0 in range 25.0 – 35.0 cm3. [1] (ii) Evidence of two volumes added together. [1] (v) Correct calculation of V. [1] (vi) Absolute uncertainty in V in range 1 cm3–3 cm3. If repeated readings have been taken, then the uncertainty can be half the range (but not zero if values are equal). Correct method of calculation to find percentage uncertainty. [1] (c) (iii) Value(s) of x. [1] Evidence of repeat readings of x (either here or in (d)(ii)). [1] (d) (ii) Second value of V. [1] Second value of x. [1] Quality: second value of x less than first value of x. [1] (e) (i) Two values of k calculated correctly. [1] (ii) Justification of s.f. in k linked to significant figures in x and V. [1] (iii) Sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate. [1] GCE AS LEVEL – October/November 2013 9702 35 (f) (i) Limitations (4 max) (ii) Improvements (4 max) Do not credit A Two readings not enough (to Take more readings and plot ‘few readings’/‘take more draw a conclusion) a graph/take more readings, readings and calculate calculate more k values and average’/‘only one reading’/ compare ’repeat readings’ on its own B Difficult to remove correct Use syringe with longer ‘nozzle too short’ on its own amount of water because air nozzle/needle drawn into syringe Tilt/invert ball C Blu-tack not sticky Use e.g. sellotape/small cork enough/water leaks from ball/ to seal hole syringe D Difficult to judge lowest depth Line up both sides of rubber Parallax measuring x with reason e.g. parallax band with ball error/difficult to move head Take measurements at eye Use mirror behind ball level E Difficult to judge lowest depth Video experiment with scale Moves too fast/too quickly because ball at maximum depth for a short time Use motion sensor/high- speed cameras/slow-motion cameras Use light sensors F Large uncertainty in value of Use a smaller syringe/ V/scale divisions on syringe measure mass/weight of ball too large and water G Difficult to release ball without Method of releasing ball e.g. Clamp ball applying force/difficult to hold cut string attached to ball Use card/plastic gate the ball on the surface of the water Do not allow ‘use a computer to improve the experiment’. [Total: 20]

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