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

1 In this experiment, you will investigate how the extension of an arrangement of springs Use depends on the loads applied to it. (a) (i) Set up the apparatus as shown in Fig. 1.1. stands rod of clamp A boss two rod of clamp B springs single spring wooden rod 65 cm h0 strings with loops bench Fig. 1.1 Place the rod of clamp A, supporting the two springs, approximately 65 cm above the bench. Once fixed do not change the position of the rod of clamp A throughout the experiment. Suspend the wooden rod, with strings attached, using the springs as shown. Adjust the position of the rod of clamp B until the wooden rod is horizontal. Ensure the springs hang vertically. (ii) Measure and record the distance h0 between the centre of the rod of clamp B (supporting the single spring) and the bench. h0 = ..............................................m [1] (b) (i) Add masses to the wooden rod as shown in Fig. 1.2. The 100 g mass hanger should For be attached to the longer, central string. Examiner’s Use wooden rod total mass 100 g mass hanger m = 150 g Fig. 1.2 (ii) Adjust the height of the rod of clamp B until the wooden rod is horizontal. (iii) Measure and record the distance h between the centre of the rod of clamp B and the bench, as shown in Fig. 1.3. h Fig. 1.3 h = ..................................................[1] (iv) Calculate the value of (h0 – h). For Examiner’s Use (h0 – h) = ...................................................... (c) By increasing the mass m, repeat (b)(ii), (b)(iii) and (b)(iv) until you have five sets of values of m and h. Do not change the mass attached to the longer, central string. (h0 – h) 1 Include values of and in your table. m m [10] (h0 – h) 1(d) (i) Plot a graph of on the y-axis against on the x-axis. [3] m 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 (e) The quantities h and m are related by the equation For (h0 – h) P Examiner’sUse = + Q m m where P and Q are constants. Use your answers in (d)(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

Mark scheme: 1 (a) (ii) Value of h0 in range 0.70 m > h0 > 0.50 m. Consistent with unit. [1] (b) (iii) Value of h, less than h0 in (a)(ii), with unit. [1] (c) Five sets of readings of h and m scores 5 marks, four sets scores 4 marks etc. Major help from Supervisor –2 (setting up apparatus). Minor help from Supervisor –1. [5] Range of m: [1] To include 0.350 kg. Column headings: [1] Each column heading must contain a quantity and a unit. The unit must conform to accepted scientific convention e.g. m / kg, m(kg) or m in kg, (h0 – h)/m / m kg–1, 1/m / kg–1 Consistency: [1] All values of h must be given to the nearest mm. Significant figures: [1] Significant figures for every row of values of 1/m same as or one greater than m as recorded in the table. Calculation: [1] Values of (h0 – h) /m calculated correctly. (d) (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 must be no more than 3 large squares apart. Plotting of points: [1] All observations in the table must be plotted. Diameter of plots 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 (at least 4) for this mark to be awarded. Scatter of points must be less than 0.5 kg–1 (0.0005 g–1) of 1/m of a straight line. (ii) Line of best fit: [1] Judge by balance of all points on the grid about the candidate’s line (at least 4 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. (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 x and y directions. Do not allow ∆x / ∆y. GCE AS/A LEVEL – May/June 2012 9702 33 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. (e) Value of P = candidate’s gradient. Value of Q = candidate’s intercept. [1] Unit for P (e.g. m) consistent with value, and Q (m kg–1) [1] [Total: 20]

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2 In this experiment, you will investigate how the cooling rate of a hot liquid depends on the Use surface area of the liquid exposed to air. (a) (i) Pour cold water into the beaker up to the 200 ml mark. (ii) Pour the water into the cup and use the pen to place a mark on the inside surface of the cup, level with the water surface. (iii) Empty out the cold water. (iv) Repeat (a)(i), (a)(ii) and (a)(iii) for the bowl. (b) (i) Pour boiling water into the cup up to the mark. (ii) When the temperature of the water falls to approximately 75 °C, start the stopwatch. Record this starting temperature θ0. θ0 = ..................................................[1] (iii) After two minutes, measure and record the temperature θ. θ = ..................................................[1] (iv) Calculate the change in temperature Δθ = (θ0 – θ). Δθ = ................................................. [1] (c) (i) Measure and record the diameter d of the water surface. d = ..................................................[1] (ii) Estimate the percentage uncertainty in your value of d. For Examiner’s Use percentage uncertainty = ..................................................[1] (d) Repeat (b) and (c)(i) for the bowl. θ0 = ...................................................... θ = ...................................................... Δθ = (θ0 – θ) = ...................................................... d = ...................................................... [4] (e) It is suggested that the relationship between Δθ and d is For Examiner’s Δθ = k d 2 Use where k is a constant. (i) Using your data, calculate two values of k. first value of k = ...................................................... second value of k = ...................................................... [1] (ii) Justify the number of significant figures that you have given for your values of k. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[1] (iii) Explain whether your results in (e)(i) support the suggested relationship. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[1]

Mark scheme: 2 (b) (ii) Value of θ0 to the nearest degree or 0.5° in range 70° # θ # 80° [1] (iii) Value of θ with unit, θ < θ0 [1] (iv) Correct calculation of (θ0 – θ) [1] (c) (i) Value of raw d with unit to nearest mm. [1] (ii) Absolute uncertainty in 2 mm < d < 5 mm. [1] If repeated readings have been taken, then the absolute uncertainty can be half the range. Correct method shown to find the percentage uncertainty. (d) Second value of θ0 within 1 ºC of first value of θ0. [1] Second value of θ. [1] Second value of ∆θ > first value of ∆θ (check second value of d > first value of d). [1] Evidence of repeat readings of d here or in (c)(i). [1] (e) (i) Two values of k calculated correctly. [1] (ii) Justification of s.f. in k linked to significant figures in d and ∆θ. [1] (iii) Sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate. [1] GCE AS/A LEVEL – May/June 2012 9702 33 (f) (i) Limitations 4 max. (ii) Improvements 4 max. No credit/not enough A two results not enough take more readings and plot a ‘repeat readings’ on its own/ graph/ few readings/ calculate more k values and take more readings and compare (calculate) average k/ only one reading B heat lost through sides and /or method to reduce heat loss/ use of lid/ bottom lag/ heat loss in warming bowl/cup/ insulate/ draughts/ polystyrene container heat loss to surroundings C temperature change is small/ time for longer/ ∆θ values too close higher starting temperature/ greater range of surface areas D large (percentage) uncertainty use thermometer with greater use more accurate in ∆θ sensitivity or precision/ thermometer/ use thermometer that can read thermometer not precise to 0.1 ºC enough/ not just ‘digital thermometer’ E water in bowl barely covers use larger volume of water/ not just ‘digital thermometer’ (bulb of) thermometer use of thermocouple/ any reference to stirrer/ other small temperature sensor non-uniform temperature/ (e.g. probe) thermometer touching base F parallax error in measuring d / use dividers/calipers string measurements to reason for difficulty in access measure d in measuring d G difficult to mark level with method of making mark stay reason e.g. depth gauge/ calibrated marks/ marker on outside Do not allow: use of coloured ink/reaction time/fans/draughts/water left behind/beakers not accurate/ helpers. [Total: 20]

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