Cambridge A Level Physics 9702 — 2022 May/June Paper 3 · Variant 5

1 In this experiment, you will investigate the oscillations of a wooden strip. You have been provided with a wooden strip with two string loops attached. (a) ● Set up the apparatus as shown in Fig. 1.1. boss rod of clamp spring wooden strip string loop longest string loop shortest string loop 50 g mass hanger stand mass m ≈ 4 cm bench Fig. 1.1 ● Add a 100 g mass to the 100 g mass hanger to make a total mass m of 200 g. ● Suspend mass m from the longest string loop. ● Record m. m = ............................................................ g ● Suspend the 50 g mass hanger from the shortest string loop. ● Adjust the position of the wooden strip in the string loop attached to the spring until the strip balances. Use some of the adhesive putty to fix this string loop to the strip. ● Pull mass m down to the bench and secure it to the bench using adhesive putty. ● With mass m stuck to the bench, adjust the height of the boss until the wooden strip is parallel to the bench, as shown in Fig. 1.2. adhesive putty adhesive putty Fig. 1.2 ● Pull the 50 g mass hanger down through a short distance. ● Release the 50 g mass hanger. The hanger will oscillate. ● Determine the period T of these oscillations. T = ............................................................... ● Carefully remove all the adhesive putty from mass m and the strip. [2] (b) Vary m and repeat (a) with different values of m until you have six sets of readings of m and T. T 1 Record your results in a table. Include values of and in your table. m m [10] T 1(c) (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] (d) It is suggested that the quantities T and m are related by the equation T P = + Q m m where P and Q are constants. Using your answers in (c)(iii), determine values for P and Q. Give appropriate units. P = ............................................................... Q = ............................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Value of T with unit and in the range 1.0–1.5 s. 1 nT measured at least twice with n ⩾ 5. 1 1(b) Six sets of readings of m and time with correct trend (T increases as m increases) and without help from the Supervisor scores 5 marks, five sets scores 4 marks etc. 5 Range: Values of m include m ⩾ 400 g and m ⩽ 150 g. 1 Column headings: Each column heading must contain a quantity and a unit where appropriate. The presentation of quantity and unit must conform to accepted scientific convention e.g. T / m / s kg–1 and 1 / m / kg–1. 1 Consistency: All raw values of time given to the nearest 0.1 s or all given to the nearest 0.01 s. 1 Significant figures: All values of T / m must be given to the same number of significant figures as (or one more than) the least number of s.f. in the raw time and m. 1 Calculation: Correct calculation of T / m. 1 Question Answer Marks 1(c)(i) Axes: Sensible scales must be used, no awkward scales (e.g. 3:10 or fractions). Scales must be chosen so that the plotted points occupy at least half the graph grid in both the x and y directions. Axes must be labelled with the quantity that is being plotted. Scale markings are no more than 2 cm (one large square) apart. 1 Plotting of points: All observations in the table must be plotted on the grid. Diameter of plotted points must be ⩽ half a small square. Points must be plotted to an accuracy of half a small square in both x and y directions. 1 Quality: All points in the table (at least 5) must be plotted on the grid for this mark to be awarded. Trend of the points must be positive. It must be possible to draw a straight line that is within  0.2 kg–1 on the 1 / m axis of all plotted points. 1 1(c)(ii) Line of best fit: Judge by the 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. There must be at least 5 points left after the anomalous point is disregarded. Lines must not be kinked or thicker than half a small square. 1 1(c)(iii) The hypotenuse of the triangle used must be greater than 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. Method of calculation must be correct (not x / y). Gradient sign on answer line matches graph drawn. 1 y-intercept: Correct read-off from a point on the line and substituted into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both x and y directions. or Intercept read directly from the graph, with read-off at 1 / m = 0, accurate to half a small square. 1 Question Answer Marks 1(d) Value of P = candidate’s gradient and value of Q = candidate’s intercept. The values must not be fractions. 1 Unit for P: s and unit for Q: s kg–1. 1

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2 In this experiment, you will investigate the effect of temperature on an electric circuit. You have been provided with two copper wires of the same length. You have also been provided with two constantan wires of different lengths. (a) (i) Measure and record the diameter d of the longer constantan wire. d = ......................................................... [1] (ii) ● Using the two copper wires and the longer constantan wire, twist the ends together to form junctions as shown in Fig. 2.1. L junction junction longer constantan wire copper wire copper wire Fig. 2.1 ● Ensure the junctions are tight so that the wires cannot be separated by pulling. ● The distance between the junctions along the constantan wire is L, as shown in Fig. 2.1. Measure and record L. L = ................................................... cm [1] (iii) Estimate the percentage uncertainty in your value of L. Show your working. percentage uncertainty = ..................................................... % [1] (iv) Calculate C where d2 C = . L C = ......................................................... [1] (v) Justify the number of significant figures that you have given for your value of C. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (b) ● Measure and record the temperature θR of the room. θR = .......................................................... °C ● Connect the copper wires to the ammeter as shown in Fig. 2.2. A copper wire copper wire Fig. 2.2 ● Pour boiling water into the beaker so that the beaker is half-full. ● Place one of the junctions deep in the water. The other junction should be at room temperature. ● Record the ammeter reading I when the temperature θ of the water passes 75 °C. I = ............................................................... ● Record θ. θ = .......................................................... °C ● Calculate Δθ where Δθ = (θ ─ θR). Δθ = .......................................................... °C ● Pour the hot water into the sink. [2]

Mark scheme: 2(a)(i) Value(s) of raw d to the nearest 0.01 mm or 0.001 mm with unit and final value in the range 0.43–0.49 mm. 1 2(a)(ii) Value of raw L to the nearest mm and final value in the range 43.0–49.0 cm. 1 2(a)(iii) Percentage uncertainty in L based on absolute uncertainty of 2–6 mm. If several readings have been taken, then the absolute uncertainty can be half the range (but not zero) provided the working is clearly shown. Correct method of calculation to obtain percentage uncertainty. 1 2(a)(iv) Correct calculation of C. 1 2(a)(v) Justification for significant figures in C linked to significant figures in d and L. 1 2(b) Value of  to the nearest 1° or 0.5° and 80 °C ⩾  ⩾ 70 °C. 1 Correct calculation of . 1 2(c)(i) Second value of d < first value of d. 1 Second value of L. 1 2(c)(ii) Second value of I with unit. 1 2(d) Two values of k calculated correctly. The final k values must not be written as fractions. 1 2(e) Calculation of percentage difference between candidate’s two k values. Comparison of percentage difference with 30% leading to a consistent conclusion. 1 Question Answer Marks 2(f)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficult to measure L with a reason e.g. unclear where the junction starts/wire not straight. C Difficulty in reading  or temperature with a reason e.g. temperature not the same throughout/time lag of thermometer/reading thermometer and ammeter simultaneously. D Difficulty in reading I with reason e.g. readings fluctuate/(variable contact) resistance of wires and clips. E Problem identified with setup e.g. wires came apart at the junctions/wires short-circuiting/keeping second junction away from hot beaker. 1 mark for each point up to a maximum of 4. 4 2(f)(ii) A Take more readings and plot a graph or take more readings and compare k values (not “repeat readings” on its own). B Method to improve measurement of L e.g. tape/glue wire onto ruler. C Use a stirrer to ensure the water temperature is constant throughout/use water bath to control temperature or use a digital thermometer (with a lower response time) or use video with thermometer and ammeter in view. D Improved method of joining wires e.g. solder. E Method to limit movement of wires e.g. clamp the wires or use insulated wire to prevent short circuit. 1 mark for each point up to a maximum of 4. 4

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