Cambridge A Level Physics 9702 — 2013 May/June Paper 3 · Variant 3

1 In this experiment, you will determine the resistivity of a metal in the form of a wire. Use (a) (i) Measure and record the diameter d of the short sample of wire that is attached to the card. You may remove the wire from the card. d = ..................................................[1] (ii) Calculate the cross-sectional area A of the wire, in m2, using the formula πd 2 A = . 4 A = ................................................. m2 (b) (i) Using the wire attached to the metre rule, set up the circuit shown in Fig. 1.1. – + A wire P Q l metre rule V Fig. 1.1 There are two crocodile clips labelled P and Q. P will remain in the same position throughout the experiment. Q can be moved to different positions along the wire. (ii) Position the slider approximately half-way along the rheostat (variable resistor). For Examiner’s (iii) Attach Q approximately half-way along the wire. Use (iv) Switch on the power supply. (v) Measure and record the length l of wire between P and Q. Record the voltmeter reading V. l = .................................................. m V = ................................................... V [1] (vi) Record the ammeter reading I. (1 mA = 0.001 A) I = ................................................... A (vii) Switch off the power supply. (c) (i) Reposition Q at a new distance l from P. (ii) Switch on the power supply. (iii) Adjust the slider on the rheostat until the ammeter reading is the same value as in (b)(vi). (iv) Measure and record the length l of wire between P and Q. Record the voltmeter reading V. l = .................................................. m V = ................................................... V (v) Switch off the power supply. (d) Repeat (c) until you have six sets of readings of l and V. For Examiner’s For each value of l, adjust the slider on the rheostat so that the ammeter reading Use I remains constant at the value in (b)(vi). You may find it helpful to copy your value from (b)(vi) here. I = ................................................... A V 1 Include values of and in your table. l l [10] V 1 (e) (i) Plot a graph of on the y-axis against on the x-axis. [3] l l (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 V and l are related by the equation For Examiner’s V M Use = – N l l where M and N are constants. (i) Use your answers in (e)(iii) to determine values for M and N. M = ................................................... V N = ............................................. V m–1 [1] (ii) The resistivity ρ of the material of the wire, in Ω m, can be found using the relationship NA ρ = . I Using your answers in (a)(ii), (b)(vi) and (f)(i), calculate a value for ρ. ρ = .......................................... Ω m [1] You may not need to use all of the materials provided. For Examiner’s

Mark scheme: 1 (a) (i) Value of raw d in the range 0.15 mm ≤ d ≤ 0.44 mm. [1] (b) (v) Value of l in range 0.1 m < l < 1 m. Value of V in range 0.1 V ≤ V ≤ 2.0 V. [1] (d) Six sets of readings of l and V scores 5 marks; five sets scores 4 marks etc. [5] Major help from Supervisor –2 (setting up apparatus). Minor help from Supervisor –1. Range of l :∆l ≥ 60 cm. [1] Column headings: [1] Each column heading must contain a quantity and a unit. The presentation of quantity and unit must conform to accepted scientific convention. e.g. 1/l /m–1, V/l / V m–1. Do not allow 1/l (m), V(V) / l (m). Consistency: [1] All values of raw l must be given to the nearest mm. Significant figures: [1] Significant figures for every row of values of 1/l same as or one greater than l as recorded in table. Calculation: [1] Values of V/l 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 points must be ≤ half a small square (no “blobs”). Check that the points are plotted correctly. Work to an accuracy of half a small square. Quality: [1] All points in the table must be plotted (at least 5) for this mark to be awarded. Scatter of points must be less than 0.1 m–1 from a straight line on the 1/l axis. (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 (i.e. circled or labelled) by the candidate. Line must not be kinked or thicker than half a small square. GCE AS/A LEVEL – May/June 2013 9702 33 (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: 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: Correct read-off of the intercept directly from the graph. (f) (i) Value of M = candidate’s gradient. Value of N = –(candidate’s intercept). [1] (ii) Answer in range ρ: 2.0 ≤ ρ ≤ 20.0 × 10–7 Ω m. Consistent with units. [1] [Total: 20]

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2 In this experiment, you will investigate how the loss of gravitational potential energy of a Use rolling ball depends on its initial height. (a) (i) Set up the two runways as shown in Fig. 2.1. stand boss and clamp runway H bench Fig. 2.1 One end of each runway should be resting on the bench. The other end should be clamped firmly at a height H approximately 15 cm above the bench. The runways should be lined up so that a ball rolling down one would roll up the other. (ii) Measure and record H. H = ..................................................[1] (b) (i) Place the ball close to the top of one of the runways as shown in Fig. 2.2. For Examiner’s ball Use h1 Fig. 2.2 (ii) Measure and record the height h1 of the bottom of the ball above the bench. h1 = ..................................................[1] (iii) Estimate the percentage uncertainty in your value of h1. percentage uncertainty = ..................................................[1] (c) (i) Place the ball on the runway at the height given in (b)(ii). (ii) Release the ball. (iii) The ball should roll down one runway and up the other one, as shown in Fig. 2.3. h2 Fig. 2.3 Measure and record the maximum height h2 of the bottom of the ball above the bench. h2 = ..................................................[2] (d) Calculate the fractional loss of energy F, where For (h1 – h2) Examiner’sUse F = . h1 F = ..................................................[1] (e) Place the ball at a lower starting position so that the height h1 is approximately half the value in (b)(ii). Repeat (b)(ii), (c)(ii), (c)(iii) and (d). h1 = ...................................................... h2 = ...................................................... F = ...................................................... [3]

Mark scheme: 2 (a) (ii) Measurement of raw H in range 10.0 cm < H < 20.0 cm consistent with unit. [1] (b) (ii) Measurement of raw h1 to nearest mm with unit. [1] (iii) Absolute uncertainty in h1 in the range 2–5 mm. If repeated readings have been taken, then the absolute uncertainty can be half the range. Correct method of calculation to get percentage uncertainty. [1] (c) (iii) Measurement of h2 less than h1. [1] Evidence of repeat readings here or in (e). [1] (d) Correct calculation of F with no units. [1] (e) Second value of h1. [1] Second value of h2. [1] Second value of h2 < first value of h2. [1] (f) (i) Two values of k calculated correctly. [1] (ii) Justification of s.f. in k linked to significant figures in h1 and (h1 – h2). [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 2013 9702 33 (g) (i) Limitations 4 max. (ii) Improvements 4 max. Do not credit A two readings not enough (to take many readings and plot a repeat readings draw a conclusion) graph/calculate more k values /few readings and compare /take more readings and (calculate) average k /only one reading B discontinuous movement at method of providing alignment bottom continuous ramp e.g. tape join /stick /fix C parallax error (or wtte) in h1 or ruler and set square with ruler perpendicular to bench h2 or heights detail e.g. set square from /parallax error in height ruler to track or ball D difficult to measure h1/h2 with measure to top of marble. H reason e.g. cannot see /measure diameter of marble /clear ramps bottom of marble/bottom of and subtract it from height to track not at bottom of top of marble marble/thickness of track not taken into account E difficult to release marble description of mechanical string method without applying a force method of releasing marble /use of helpers e.g. card gate F difficult to measure h2 with method of improved too fast/ball travelling too reason related to time e.g. measurement of h2 e.g. video quick, etc. short time interval/doesn’t with (clamped) rule/multiflash /high speed camera or slow stay still at h2 for long photography with (clamped) motion camera rule/trial and improvement method/position sensore at top of ramp/grid behind runway/scale on runway [Total: 20]

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