Cambridge A Level Physics 9702 — 2011 Oct/Nov Paper 3 · Variant 6

1 In this experiment, you will investigate the equilibrium of a mass and pulley system. Use (a) The apparatus has been set up in an arrangement similar to that shown in Fig. 1.1. pulley pulley central knot H bench Fig. 1.1 (b) Measure and record the height H of the central knot above the bench. H = ............................................. m [1] (c) (i) Suspend the mass hanger from the central loop as shown in Fig. 1.2. m mass h hanger bench Fig. 1.2 (ii) Record the central suspended mass m. m = ............................................ kg [1] (iii) Measure and record the height h of the central knot above the bench, as shown in For Fig. 1.2. Examiner’s Use h = .................................................. m (iv) Calculate the deflection y, where y = (H – h). y = .................................................. m (d) Change m by adding masses to the hanger suspended from the central loop and repeat (c)(ii), (c)(iii) and (c)(iv) until you have six sets of values for m, h and y. 1 1 Include in your table of results values for 2 and 2. y m [10] 1 1 (e) (i) Plot a graph of 2 on the y-axis against 2 on the x-axis. [3] y m (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 relationship between y and m is For Examiner’s 1 p Use 2 = 2 – q y m where p and q are constants. Using your answers from (e)(iii), 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

Mark scheme: 1 (b) Measurement for H in range 0.200 m to 0.900 m. [1] (c) (ii) First measurement of m, to nearest 0.001 kg and in the range 0.045 to 0.055 kg. [1] (d) Six sets of values for h and m scores 5 marks, five sets scores 4 marks etc. [5] Incorrect trend then –1. Help from supervisor –1. Range: [1] m values must include 0.070 kg or less, and 0.220 kg or more. Column headings: [1] Each column heading must contain a quantity and a unit where appropriate. There must be some distinguishing mark between the quantity and the unit. 1 e.g. y–2/m–2, 1/m2(1/kg2) but not 2 2 . m / kg Consistency of presentation of raw readings: [1] All values of h must be given to the nearest mm. Significant figures: [1] Every value of 1/y2 must be given to the same s.f. as (or one more than) the s.f. in y. Calculation: [1] 1/y2 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 which is being plotted. Plotting: [1] All observations must be plotted. Check that the points are correctly plotted. Work to an accuracy of half a small square. Do not accept ‘blobs’ (points with diameter greater than half a small square). Quality: [1] Scatter of points must be less than ± 50 m─2 (± 0.005 cm─2) on the 1/y2 axis about a straight line. All points must be plotted (at least 5) for this mark to be scored. (ii) Line of best fit: [1] Judge by balance of all the points (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. Allow one anomalous point if clearly indicated by the candidate. Line must not be kinked or thicker than half a square. GCE AS/A LEVEL – October/November 2011 9702 36 (iii) Gradient: [1] The hypotenuse must be at least half the length of the drawn line. Both read-offs must be accurate to half a small square or better in both x and y directions. The method of calculation must be correct. Do not allow ∆x/∆y. Intercept: [1] Either: Check correct read-off from a point on the line, and substitution into y = mx + c. Read-off must be accurate to half a small square or better in both x and y directions. Allow ecf of gradient value. Or: Check the read-off of the intercept directly from the graph. (f) p = value of gradient and q = ─ (value of intercept). [1] Both values must be from (e)(iii). Do not allow fractions. Correct consistent units for p (e.g. kg2 m─2) and q (e.g. m─2). [1] [Total: 20]

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2 In this experiment you will investigate the range of a steel ball projectile. Use (a) You are provided with a length of tube with a wooden block at each end. Mount the tube in clamps, with the tray of sand positioned below its lower end, as shown in Fig. 2.1. wooden block tube wooden block b a sand tray bench Fig. 2.1 (b) (i) Ensure that the lower end of the tube is horizontal and approximately 30 cm above the bench, and that the upper end of the tube is vertical and about 50 cm above the bench. (ii) Measure and record the height a above the bench of the lower end of the tube, as shown in Fig. 2.1. a = ...................................................... (iii) Measure and record the height b above the bench of the higher end of the tube. b = ...................................................... [2] (c) (i) Drop the steel ball into the top of the tube and note its landing position in the tray of For sand. The range R is the horizontal distance of the landing position from the end of Examiner’s the tube, as shown in Fig. 2.2. Use R Fig. 2.2 (ii) Measure and record R. R = ..............................................m [2] (d) Estimate the percentage uncertainty in R. percentage uncertainty = ................................................. [1] g(e) Calculate the horizontal velocity v of the steel ball using the relationship v = R , where g = 9.81 ms–2. 2a v = ................................................. [1] (f) (i) Adjust the height of the upper end of the tube to about 30 cm above the bench, and For adjust the height of the lower end to about 20 cm above the bench. Ensure that the Examiner’s lower end of the tube is horizontal. Use (ii) Repeat (b)(ii), (b)(iii), (c) and (e). a = ...................................................... b = ...................................................... [1] R = ..............................................m [2] v = ..................................................[1] (g) (i) It is suggested that the relationship between v, b and a is v 2 = k(b – a) where k is a constant. Using your data, calculate two values of k. first value of k = ...................................................... second value of k = ...................................................... [1] (ii) Explain whether your results support the suggested relationship. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[1]

Mark scheme: 2 (b) 0.250 m ≤ a ≤ 0.350 m and 0.450 m ≤ b ≤ 0.550 m, both with a correct and consistent [1] unit. Values of a and b given to nearest mm e.g. 0.350 m or 35.0 cm. [1] (c) (ii) Value of R in range 0.05 m to 0.50 m (5 cm to 50 cm). [1] Evidence of repeats (credit evidence here or in (f)). [1] (d) Percentage uncertainty in R based on absolute uncertainty in range 0.002 m to 0.01 m [1] (2 mm to 10 mm). (If repeated readings have been done then the absolute uncertainty could be half the range, unless this is zero.) Correct method to get % uncertainty. (e) Correct calculation of v with consistent unit. [1] (f) (ii) Second values of a and b. [1] Second value of R. [1] Second R less than first R. [1] Correct calculation of second v. [1] (g) (i) Two values of k calculated correctly. [1] (ii) Valid conclusion based on the variation in k being within (or outside) a stated [1] criterion. GCE AS/A LEVEL – October/November 2011 9702 36 (h) (i) Limitations 4 max. (ii) Improvements 4 max. Do not credit A Two readings are not enough Take more readings and plot Few readings/only one (to draw a conclusion) a graph/calculate more k reading/take more readings values (and compare). and calculate average k /‘repeat readings’ B Difficult to locate start position Method to locate start point ‘Parallax error’/parallax error /measure R owing to parallax e.g. plumb line/clamped linked to a or b vertical rule using set square to bench C Difficult to locate end point Method to locate end point of Vague video methods/ball /measure R owing to ball R e.g. vertical clamped moves/smooth sand/change bouncing/skipping/sinking/rule pointer/tray without lip (so rule depth of sand displaced from ball can be placed on sand)/sand on bench/carbon paper /painted ball/video with playback plus scale in shot/ detailed hot spot D Difficult to release ball from Method of improving release Use a release mechanism rest/without exerting a force e.g. use an electromagnet E (Vertical) distance fallen is Method of measuring a to less than a surface of sand/correcting the value of a by measuring depth of sand F Difficult to make tube Method to ensure tube is horizontal (as not flexible horizontal e.g. use reference enough)/judge horizontal/ line (window sill)/spirit level clamp blocks horizontally /measure several heights from bench. G Ball sticks in tube/slows down Method to overcome sticking Lubricate/clean tube due to e.g. sand in tube/bend e.g. use new ball each time in tube/kink in tube/too much /clean ball with cloth before friction putting back in tube/use wider tube/smaller ball/open track Do not allow ‘rule is not perpendicular to bench’. Do not allow unspecified computer methods. [Total: 20]

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