Cambridge A Level Physics 9702 — 2020 Feb/March Paper 3 · Variant 3

1 In this experiment you will investigate the oscillations of a rod. (a) • Assemble the apparatus as shown in Fig. 1.1. • Adjust the apparatus until the two springs are approximately 15 cm apart. Each spring should be vertical and the same distance from the middle of the rod. The rod should be parallel to the bench. clamp boss spring rod x stand bench Fig. 1.1 • The distance between the two springs where they support the rod is x, as shown in Fig. 1.1. Measure and record x. x = .................................................... cm [1] (b) • Lift one end of the rod a short distance and push the other end of the rod down a short distance. Release the rod so that it oscillates with a rocking motion, as shown in Fig. 1.2. FRONT VIEW Fig. 1.2 • Take measurements to determine the period T of the oscillation. T = ....................................................... s [2] (c) • Change x by moving the stands. Adjust the apparatus until the springs are vertical and the rod is parallel to the bench. Measure x and T. • Repeat until you have six sets of values of x and T. 1 • Record your results in a table. Include values of in your table. x [9] 1(d) (i) Plot a graph of T on the y-axis against on the x-axis. [3] x (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ............................................................... y-intercept = ............................................................... [2] (e) It is suggested that the quantities T and x are related by the equation a T = + b x where a and b are constants. Use your answers in (d)(iii) to determine the values of a and b. Give appropriate units. a = ............................................................... b = ............................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Value of x in range 10.0 to 20.0 cm 1 1(b) Value of T in range 0.50 to 1.50 s 1 Evidence of repeat readings: at least two values of at least 5T 1 1(c) Six sets of readings of x and T with correct trend and without help scores 4 marks, five sets scores 3 marks etc. 4 Range: xmin ⩽ 12.0 cm and xmax ⩾ 25.0 cm 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. 1 / x (cm–1) 1 Consistency: All values of raw x must be given to the nearest mm 1 Significant figures: All values of 1 / x should be to the same s.f. as (or one more than) the s.f. in the corresponding x value 1 Calculation: Values of 1 / x calculated correctly 1 Question Answer Marks 1(d)(i) Axes: 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 which is being plotted. Scale markings should be no more than 3 large squares apart. 1 Plotting of points: All observations must be plotted on the grid. Diameter of plotted points must be ⩽ half a small square (no blobs). Plots must be accurate to within half a small square in both x and y directions. 1 Quality: All points in the table must be plotted (at least 5) for this mark to be awarded. Scatter of plots must be no more than ± 0.5 m–1 (± 0.005 cm–1) from a straight line in the x-direction. 1 1(d)(ii) Line of best fit: Judged by balance of all 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 One anomalous point is allowed only if clearly indicated (i.e. circled or labelled) by the candidate. Lines must not be kinked or thicker than half a square. 1 1(d)(iii) Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. Method of calculation must be correct. Both read-offs must be accurate to half a small square in both the x and y directions. 1 y-intercept: Either Correct read-off from a point on the line substituted into y = mx + c or an equivalent expression, with 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 x = zero accurate to half a small square in y direction. 1 Question Answer Marks 1(e) a equal to candidate’s gradient, and b equal to candidate’s intercept. a and b are not fractions. a has two or more significant figures. 1 1(e) Units for a and b correct (e.g. s cm or s m for a, and s for b). 1

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2 In this experiment you will investigate the magnetic field produced by an electrical current. (a) You are provided with a length of wire wrapped around a plastic channel to form a coil, as shown in Fig. 2.1. grooves plastic channel tape wire (wrapped through every other groove) Fig. 2.1 Count and record the number N of turns of wire in the coil. N = .......................................................... [1] (b) • Slide the compass into the plastic channel so that it is in the middle of the coil. • Connect the circuit as shown in Fig. 2.2. • Rotate the channel on the bench until the arrow of the compass is perpendicular to the channel, as shown. L compass inside crocodile crocodile plastic channel clip clip A Fig. 2.2 • The distance between the first and last turns of wire is L, as shown in Fig. 2.2. Measure and record L. L = ......................................................... [1] (c) • Close the switch. The compass arrow will rotate through an angle θ. • Measure and record θ. θ = ............................................................. ° • Record the ammeter reading I. I = ............................................................... • Open the switch. [2] (d) Estimate the percentage uncertainty in your value of θ. percentage uncertainty = ......................................................... [1] (e) Calculate the value of B using μ0(N−1) I B = L where μ0 = 1.26 × 10–6 N A–2. B = ......................................... N A–1 m–1 [1]

Mark scheme: 2(a) Value of N, with no unit, in range 10 to 14. 1 2(b) Value of L to nearest mm, with unit, in range 5.0 to 15.0 cm. 1 2(c) Value(s) of raw θ to nearest degree and < 90°. 1 Value of I to nearest mA or nearest 0.1 mA, with unit 1 2(d) Absolute uncertainty in θ value of 2 to 5° and correct method of calculation to obtain percentage uncertainty. If several readings have been taken, then the absolute uncertainty can be half the range (but not zero if values are equal) if the working is clearly shown. 1 2(e) Correct calculation of B 1 2(f) Second values of N and L 1 Second values of θ and I 1 Quality: second θ > first θ 1 2(g)(i) Two values of k calculated correctly. 1 2(g)(ii) Justification based on s.f. in θ, I and L. 1 2(g)(iii) Sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate. 1 Question Answer Marks 2(h)(i) Two readings are not enough to draw a valid conclusion 4 max Difficult to determine I as reading not steady Parallax error when measuring θ Large % uncertainty in θ Difficult to re-wind and fix the wire / wires may touch / wire is kinked Channel moves on bench 4 2(h)(ii) Take more readings and plot a graph / calculate more k values and compare 4 max Method of cleaning crocodile clips / contacts Method of overcoming parallax error, e.g. measure change of angle by turning channel on bench / measure θ on a photo / angle markings on compass / mark ‘before’ and ‘after’ positions on compass Use larger current / voltage Use two ready-wound channels / use new wire Method of fixing channel, e.g. tape channel to bench 4

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