Cambridge A Level Physics 9702 — 2012 May/June Paper 3 · Variant 1

1 In this experiment, you will investigate how the motion of a pendulum whose swing is interrupted depends on its length. (a) (i) Lay the pendulum next to the rule and use the pen to make a mark on the string so that the distance L is 0.180 m, as shown in Fig. 1.1. mark bob string L = 0.180 m metre rule Fig. 1.1 (ii) Set up the apparatus, fixing the string in the split bung so that the string is just For touching the wooden rod at the mark you have made. Examiner’s Use Fig. 1.2 shows a side view and a front view of the apparatus. split bung in clamp stand string x wooden rod x mark L L bob 5 cm bench side view front view Fig. 1.2 The centre of the bob should be approximately 5 cm above the bench. The distance x between the bottom of the bung and the centre of the bob should be approximately 55 cm. The mark on the string should be level with the centre of the rod. (iii) Measure and record the distance x. x = ............................................. m [1] (b) (i) Move the bob sideways through a distance of approximately 5 cm, as shown in For Fig. 1.3. Examiner’s Use wooden rod 5 cm Fig. 1.3 (ii) Release the bob and watch its movement. The bob will move to the right and then to the left again completing a swing, as shown in Fig. 1.4. Let the pendulum swing to and fro, counting the number of swings. one complete swing Fig. 1.4 Measure and record the time for at least 10 consecutive swings. Record enough readings to determine an accurate value for the time T taken for one complete swing. T = .................................................. [2] (c) Reduce the distance x. Keep L constant, by adjusting the height of the wooden rod if For necessary. Repeat (a)(iii) and (b) until you have six sets of values of x and T. Examiner’s Use Include values of x in your table. [9] (d) (i) Plot a graph of T on the y-axis against x on the x-axis. [3] (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 (e) The quantities T and x are related by the equation For Examiner’s T = P x + Q Use where P and Q are constants. Using your answers from (d)(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 Use

Mark scheme: 1 (a) (iii) Value of x in the range 0.50 – 0.60 m. [1] (b) (ii) Value of T with unit: 0.9 s < T < 1.3 s. [1] Evidence of repeats. [1] (c) Six sets of readings of x and T scores 4 marks, five sets scores 3 marks etc. Incorrect trend –1. Minor help from Supervisor –1; major help –2. [4] Range of x at least 25 cm. [1] Column headings: Each column heading must contain a quantity and a unit where appropriate. [1] The unit must conform to accepted scientific convention e.g. x/m or x(m) or x in m. Consistency of presentation of raw readings: [1] All values of x must be given to the nearest mm. Significant figures: [1] Significant figures for √x should be the same as, or one more than, s.f. for x. Calculation: √x calculated correctly. [1] (d) (i) Axes: [1] Sensible scales must be used. Awkward scales (e.g. 3:10) are not allowed. Scales must be chosen so that the plotted points on the grid 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 not be greater than three large squares apart. Plotting of points: [1] All the observations in the table must be plotted. Check the points are plotted correctly. 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. Judge by the scatter of all the points about a straight line. All points must be within 0.04 m½ (0.4 cm½) on the √x axis from a straight line. (ii) Line of best fit: [1] Judge by the balance of all the 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. Allow one anomalous point if clearly indicated (e.g. circled or labelled) by the candidate. Line must not be kinked or thicker than half a small square. GCE AS/A LEVEL – May/June 2012 9702 31 (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. Do not allow ∆x/∆y. 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 in both the x and y directions. Allow ecf of gradient value. Or: Check the read-off of the intercept directly from the graph. (e) Value of P = candidate’s gradient and Q = value of candidate’s intercept. Do not allow fractions. [1] Unit for P (s m–½ or s cm–½ or s mm–½) consistent with value, and Q (s). [1] [Total: 20]

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2 In this experiment, you will investigate how the force required to pull a block up an inclined plane depends on the angle between the inclined plane and the bench. (a) (i) Place the board on the bench. (ii) Place the block with attached masses on the board, and attach the newton-meter as shown in Fig. 2.1. masses newton-meter block board bench Fig. 2.1 (iii) Gently pull the newton-meter until the block just starts to move. Measure and record the reading F0 on the newton-meter, at the instant the block just starts to move. F0 = ................................................. [2] (iv) Estimate the percentage uncertainty in your value of F0. percentage uncertainty = ................................................. [1] F0 (v) Calculate μ where μ = . W W is the value of the weight of the block and masses written on the card. μ = ................................................. [1] (b) (i) Place the board and supporting block as shown in Fig. 2.2. The longer edge of the For supporting block should be vertical. Examiner’s Use board longer edge of supporting block e Fig. 2.2 (ii) Using the protractor, measure and record the angle θ between the board and the bench. θ = ................................................ [1] (iii) Using your values from (a)(v) and (b)(ii), calculate (sin θ + μcos θ). (sin θ + μcos θ) = ................................................. [1] (c) (i) Place the block with masses on the board and attach it to the newton-meter, as shown in Fig. 2.3. Fig. 2.3 (ii) Pull the newton-meter until the block just starts to move. Measure and record the reading F on the newton-meter. F = ................................................. [1] (d) Place the supporting block as shown in Fig. 2.4 with a shorter edge vertical. For Examiner’s Repeat (b)(ii), (b)(iii) and (c). Use Fig. 2.4 θ = ...................................................... (sin θ + μcos θ) = ...................................................... F = ...................................................... [3] (e) It is suggested that the relationship between F and θ is F = k (sin θ + μcos θ) where k is a constant and μ is the value calculated in (a)(v). (i) 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) (iii) Value of F0 with unit. [1] Evidence of repeats. [1] (iv) Absolute uncertainty in F0 in range 0.4 – 1 N. If repeated readings have been taken, then the uncertainty can be half the range. Correct method of calculation of percentage uncertainty. [1] (v) Value of µ given to 2 or 3 s.f. [1] (b) (ii) Value of θ with unit to the nearest degree. [1] (iii) Correct calculation of (sin θ + µ cos θ). [1] (c) (ii) Value of F. [1] (d) Second value of θ. [1] Second value of θ < first value of θ. [1] Second value of F < first value of F. [1] Allow F2 > F1 if θ2 > θ1. (e) (i) Correct calculation of two values of k. [1] (ii) Sensible comment relating to the calculated values of k, testing against a specified criterion. [1] GCE AS/A LEVEL – May/June 2012 9702 31 (f) (i) Limitations 4 max. (ii) Improvements 4 max. No credit/not enough A two readings are not enough take more readings and plot few readings/ (to draw a conclusion) a graph/ take more readings and calculate more k values and calculate average k/ compare only one reading B some parts of board rougher method to ensure same board is rough/ than others/ section of board used in each there is friction between the surface of board is uneven/ experiment (e.g. mark one block and the board/ board not flat section) use a smoother surface/ references to oil/lubricants C large (percentage) uncertainty use larger/heavier masses values of F very similar in F D difficulty in arranging newton- use (long) piece of string to newton-meter touching board meter parallel to board/pulling connect the newton-meter to when attached in line with board the block E block moves suddenly/without use system of pulley and warning (so difficult to read weights/ sand to measure F/ newton-meter at the instant use a newton-meter with a the block starts to move) max hold facility/ use video and playback/ value of F changes when use force sensor and block moves datalogger/computer F board tends to slip/ method described to secure board not stable/ board/block/support e.g. supporting block can topple clamp the board, fix the supporting block to the bench with tape/blu-tack G cannot zero newton-meter use system of pulley and zero error in newton-meter when used horizontally weights/ sand to measure F/ use force sensor and datalogger/computer Ignore ‘parallax problems’, ‘use assistant’ or references to draughts, fans, a.c. [Total: 20]

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