Cambridge A Level Physics 9702 — 2011 May/June Paper 3 · Variant 2

1 In this experiment, you will investigate how the equilibrium position of a pivoted wooden strip Use changes when a horizontal force is applied. (a) Thread the string over the pulley and suspend the mass hanger from the end loop of the string, as shown in Fig. 1.1. nail wooden strip string H mass h hanger m bench Fig. 1.1 (b) Measure and record the height H of the nail above the bench. H = .......................................... cm [1] (c) Record the mass m that is suspended from the string. m = ...................................................... (d) (i) Adjust the height of the pulley until the string is parallel to the bench. Measure and record the height h of the string above the bench. h = .......................................... cm [1] (ii) Calculate the value of (H – h ). (H – h ) = ................................................ cm (e) By adding masses to the hanger, change the total suspended mass m. Repeat (c) and For (d) until you have six sets of values for m and h. Examiner’s Use 1 In your table of results include columns for the values of m2 and . (H – h)2 [10] 1(f) (i) Plot a graph of on the y-axis against m2 on the x-axis. [3] (H – h)2 (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 (g) It is suggested that the quantities h, H and m are related by the equation For Examiner’s Use 1 = abm2 + b (H – h)2 where a and b are constants. Using your answers from (f)(iii), determine the values of a and b. Give appropriate units. a = ...................................................... b = ...................................................... [2] You may not need to use all of the materials provided. For Examiner’s

Mark scheme: 1 (b) Raw reading for nail height H, to nearest mm. [1] (d) (i) Reading for string height h, less than H. [1] (e) No help from supervisor. [1] Six sets of readings scores 4 marks, five sets scores 3 marks etc. [4] Incorrect trend then –1. Range: m values must include 180 g or more. [1] 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. Consistency of presentation of raw readings: [1] All values of h must be given to the nearest mm. All values of m must be given to the nearest g. Significant figures: [1] S.f. for 1/(H–h)2 must be the same as, or one more than, the s.f. given for (H–h). Calculation: [1] 1/(H–h)2 calculated correctly. (f) (i) Axes: [1] Sensible scales must be used, no awkward scales (e.g. 3:10). Scales must be chosen so that the plotted points must occupy at least half the graph grid in both x and y directions. Scales must be labelled with the quantity which is being plotted. Ignore units. Scale markings must be no more than 3 large squares apart. Plotting of points: [1] All observations in the table 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] All points in the table must be plotted (at least 5) for this mark to be scored. Scatter of points must be less than ± 2000 g2 on the m2 axis from a straight line. (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. GCE A LEVEL – May/June 2011 9702 32 (f) (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. If incorrect, write in the correct value(s). Do not allow use of points from the table unless they are on the line. 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. Allow ecf of gradient value. Or: Check the read-off of the intercept directly from the graph. (g) Correct method used to find a and b. [1] Correct unit for a and correct unit for b. [1] [Total: 20]

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2 In this experiment you will investigate the deflection of a metre rule when two loads are Use placed on it. (a) (i) Position a metre rule on the two supports as shown in Fig. 2.1, with the supports 15.0 cm from each end of the rule. y h bench 15.0 cm 15.0 cm Fig. 2.1 (ii) Determine the distance y between the two supports. y = ..................................................[1] (iii) Measure the height h of the bottom edge of the mid-point of the rule above the bench. h = ..................................................[1] (b) (i) Position the two 500 g masses on top of the rule, with a mass 5.0 cm from each end of the rule, as shown in Fig. 2.2. x mass mass h1 bench 5.0 cm 5.0 cm Fig. 2.2 (ii) Determine the distance x of a mass from its nearest support. x = ..................................................[1] (iii) Measure the height h1 of the bottom edge of the mid-point of the rule above the bench. h1 = ..................................................[1] For (c) (i) Calculate the deflection d of the mid-point of the rule, where d = h1 – h. Examiner’s Use d = ..................................................[1] (ii) Estimate the percentage uncertainty in your value of d. percentage uncertainty = ..................................................[1] (d) (i) Remove the two 500 g masses and reposition the two supports 25.0 cm from each end of the rule. (ii) Repeat (a)(ii) and (a)(iii). y = ...................................................... h = ...................................................... (e) (i) Position the two 500 g masses on top of the rule, with a mass 15.0 cm from each end of the rule. (ii) Repeat (b)(ii), (b)(iii) and (c)(i). x = ...................................................... h1 = ...................................................... d = ...................................................... [4] Question 2 continues on the next page. (f) (i) It is suggested that the quantities d and y are related by the equation For Examiner’s d = ky2 Use 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 (a) (ii) y in range 65 to 75 cm. [1] (iii) Value for h to nearest mm and in range 1 to 20 cm, with unit. [1] (b) (ii) First value of x in range 8 to 11 cm. [1] (iii) First value of h1. [1] (c) (i) First value of d calculated correctly. [1] (ii) Percentage uncertainty in d calculated using correct method and using absolute uncertainty of 1 or 2 mm (or half the range if repeated readings have been taken). [1] (e) (ii) Second value of x. [1] Second value of h1. [1] Repeats: Any evidence of repeats for height values or x values. [1] Quality: Second value of d less than first value. [1] (f) (i) Two values of k calculated correctly. [1] (ii) Sensible comment relating to the calculated values of k, testing against a specified criterion. [1] GCE A LEVEL – May/June 2011 9702 32 (g) (i) Limitations 4 max (ii) Improvements 4 max Do not credit A Two readings are not enough Take more readings and plot a Few readings/take more (to draw a conclusion). graph/calculate more k values readings and calculate (and compare). average k/only one reading Allow ‘repeat readings and plot a graph’ B d is very small. 1. Use larger mass/use larger Parallax error. x value. 2. Use thinner rule. C Difficult to measure h Use vernier caliper/travelling (with reason). microscope/dial gauge/position sensor above rule. D Difficult to measure x Method of improving (with reason)/difficult to judge measurement of x (e.g. hang position of mass. masses below rule). X Other specific relevant Relevant solution. Apparatus slips. problem with apparatus. Do not accept ‘repeated readings’ or ‘light gates’. [Total: 20]

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