Cambridge A Level Physics 9702 — 2015 Oct/Nov Paper 3 · Variant 5

1 In this experiment, you will investigate how the potential difference across a resistor changes as the resistance of the circuit is changed. (a) (i) Set up the circuit shown in Fig. 1.1. power supply + – a b nail wire wooden strip A V wooden strip B Fig. 1.1 The two crocodile clips attached to the wires on the wooden strips should be approximately half-way along each of the wires. (ii) Measure and record the lengths a and b. a = ...................................................... b = ...................................................... (iii) Calculate the value of C where C = a + b. C = ...................................................... (iv) Close the switch. (v) Record the voltmeter reading V. V = ...................................................... (vi) Open the switch. (b) (i) Change the value of a. Measure and record this value of a. a = ..................................................[1] (ii) Calculate the new value of b using b = C – a. b = ...................................................... (iii) Change b to the value shown in (b)(ii). (iv) Close the switch. (v) Record the voltmeter reading V. V = ..................................................[1] (vi) Open the switch. (c) Repeat (b) until you have six sets of readings of a, b and V. 1 Include values of in your table. V [10] 1(d) (i) Plot a graph of on the y-axis against b on the x-axis. [3] V (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ...................................................... y-intercept = ...................................................... [2] (e) The quantities V and b are related by the equation 1 = Pb + Q V where P and Q are constants. Using your answers in (d)(iii), determine values for P and Q. Give appropriate units. P = ...................................................... Q = ...................................................... [2] You may not need to use all of the materials provided.

Mark scheme: 1 (b) (i) Value of a with consistent unit and in the range 0 to 50.0 cm. [1] (v) Value of V with unit to nearest 0.001 V and in range 0 to 2 V. [1] (c) Six sets of readings of a, b and V scores 5 marks, five sets scores 4 marks etc. [5] Incorrect trend –1. Minor help from Supervisor –1. Major help from Supervisor –2. Range: [1] amax – amin ⩾ 30.0 cm. 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. a / m or a (m), 1/V / V–1. Consistency: [1] All values of a and b must be given to the nearest mm. Significant figures: [1] Every value of 1 / V must be given to the same number of significant figures as (or one more than) the number of significant figures in the corresponding value of V. Calculation: [1] Values of 1 / V calculated correctly to the number of significant figures given by the candidate. (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 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: [1] All observations in the table must be plotted on the grid. Diameter of plotted points must be ⩽ half a small square (no “blobs”). Points must be plotted 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 no more than ± 0.050 m (5.0 cm) to scale in the b direction from 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 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. Lines must not be kinked or thicker than half a square. (iii) Gradient: [1] The hypotenuse of the triangle must be greater than half the length of the drawn line. Do not allow ∆x / ∆y. Sign of gradient must match graph drawn. Both read-offs must be accurate to half a small square in both the x and y directions. y-intercept: [1] Either: Correct read-off from a point on the line substituted into y = mx + c or an equivalent expression. Read-offs must be accurate to half a small square in both x and y directions. Or: Intercept read directly from the graph, with read-off accurate to half a small square. (e) Value of P = candidate’s gradient and value of Q = candidate’s intercept. [1] Unit for P is correct (e.g. m–1 V–1) and unit for Q is correct (e.g. V–1). [1]

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2 In this experiment, you will investigate the motion of a magnetised object in a magnetic field. (a) You have been provided with a nail and two magnets. Hold the head of the nail. Move one of the magnets as shown by the dotted path in Fig. 2.1. S head of nail Fig. 2.1 The S pole of the magnet should remain in contact with the nail until it reaches the end of the nail. At the end of the nail, lift the magnet above the nail and back to the head. Repeat 10 times. The nail should not touch a magnet during the remainder of the experiment. If it does, you should re-magnetise the nail by repeating (a). (b) (i) Place the sheet of paper flat on the bench as shown in Fig. 2.2. sheet of paper spot ≈ 20 cm edge of bench Fig. 2.2 (ii) Set up the apparatus as shown in Fig. 2.3. stand wooden rod clamp nail in loop boss sheet of paper protractor Fig. 2.3 Place the protractor on the line with its centre over the spot. Align the rod so that the rod is directly above and parallel to the line on the sheet of paper. Place the nail in the paper loop. Suspend the loop from the rod. The nail will be perpendicular to the line on the sheet of paper. The nail should be just above the protractor with the mark on the loop above the spot on the line. The loop should be free to rotate. (iii) With the apparatus set up as shown in Fig. 2.3, position the magnets on the sheet of paper as shown in Fig. 2.4. N S x x N S Fig. 2.4 Move the magnets along the line until the nail rotates through approximately 45°. The magnets should each be the same distance x from the spot and should remain in these positions throughout the experiment. (iv) Measure and record x. x = ..................................................[1] (c) (i) Without removing the loop and nail, move the wooden rod so that the rod makes an angle θ of approximately 30° to the line on the sheet of paper as shown in Fig. 2.5. N S wooden rod θ N S Fig. 2.5 The mark on the loop should be above the spot. Measure and record θ. θ = ................................................° [1] (ii) Estimate the percentage uncertainty in your value of θ. percentage uncertainty = ..................................................[1]

Mark scheme: 2 (b) (iv) All values of x with unit to nearest mm. Average x ⩽ 20.0 cm. [1] (c) (i) Value of θ to the nearest degree in the range 25° to 35°. [1] (ii) Absolute uncertainty in θ in range 2° to 5° and correct method of calculation to obtain percentage uncertainty. If repeated readings have been taken, then the absolute uncertainty can be half the range (but not zero) if working is clearly shown. [1] (iii) Correct calculation of cos2(θ / 2). No unit. [1] (iv) Justification for significant figures in cos2(θ / 2) linked to significant figures in θ. [1] (d) (ii) T in range 0.5 s to 2.5 s, with unit. [1] Evidence of repeat readings of T. [1] (f) Second value of θ. [1] Second values of T1 and T2. [1] Second value of T1 / T2 < first value of T1 / T2 when rounded to 2 s.f. [1] (g) (i) Two values of k calculated correctly. [1] (ii) Valid comment consistent with the calculated values of k, testing against a criterion specified by the candidate. [1] (h) (i) Limitations (4 max.) (ii) Improvements (4 max.) Do not credit A Not enough readings to draw a Take more readings and plot a Few readings/ conclusion graph/ only one reading/ obtain more k values and not enough readings compare for an accurate result/ “repeat readings” on its own/ take more readings and (calculate) average k B Difficult to measure θ or read Improved method of measuring Just “difficult to protractor with reason e.g. rod is θ e.g. shadow projection with measure θ”/ above protractor/rod obscures view light above/thinner rod/rod with smaller rod/ smaller diameter/plumb-lines “protractor reads to hung from rod/larger 1°” protractor/360° protractor C Oscillations or T affected by... Improved method of release e.g. Release by e.g. air movement card gate electromagnet/ force on release or cutting string/ different forces switch off air conditioning/close damping/ angle of release windows/closed room air resistance/ unwanted modes of oscillation friction D Large percentage uncertainty in Valid method to improve timing Oscillations too fast/ time/period T is short e.g. use video with timer/frame high/low speed by frame/motion sensor and camera/ position at side of cradle video on its own/ or human reaction time/ Increase T by... e.g. heavier just “difficult to nail/longer nail/string determine time”/ fiducial marker E Valid problem linked to magnetism Valid method to overcome Nail loses magnetism e.g. nail weakly magnetised/metal problem linked with magnetism stand attracts nail/interference by e.g. stroke nail more times/use Earth’s magnetic field. of coil F Method of fixing Just “stick paper” paper/protractor/magnets e.g. without method tape/Blu-tack/draw protractor on paper

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