Cambridge A Level Physics 9702 — 2019 Oct/Nov Paper 3 · Variant 6

1 In this experiment, you will investigate the equilibrium of a loaded wooden strip. (a) (i) • Balance the wooden strip on the prism. • Use the pencil to make a small line on the side of the wooden strip where it touches the prism, as shown in Fig. 1.1. wooden strip line prism bench Fig. 1.1 • Roll the piece of modelling clay into a uniform cylinder of approximate length 20 cm and place it on the wooden strip with one end above the line, as shown in Fig. 1.2. • Place the mass on the wooden strip and adjust the position of the mass until the strip balances, as shown in Fig. 1.2. x modelling clay L mass Fig. 1.2 (not to scale) • The length of the cylinder of modelling clay is x, as shown in Fig. 1.2. Measure and record x. x = .................................................... cm [1] (ii) The distance between the centre of the mass and the end of the wooden strip is L, as shown in Fig. 1.2. Measure and record L. L = .................................................... cm [1] (b) • Reduce x by cutting off and removing approximately 1 cm of the cylinder of modelling clay at the end furthest from the line, as shown in Fig. 1.3. Adjust the position of the mass until the wooden strip is balanced. x L Fig. 1.3 (not to scale) • Measure and record the new values of x and L. x = ..........................................................cm L = ..........................................................cm [1] (c) Continue to reduce x until you have six sets of values of x and L. You may include your previous results. Record your results in a table. Include values of x2 in the table. [9] (d) (i) Plot a graph of L on the y-axis against x2 on the x-axis. [3] (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 L and x are related by the equation L = ax2 + b 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)(i) Value of x in range 17.0–23.0 cm. 1 1(a)(ii) Value of L to nearest mm. 1 1(b) Value of L greater than value in (a)(ii). 1 1(c) Six sets of readings of x and L with correct trend and without help from the Supervisor scores four marks, five sets scores three marks, etc. 4 Range: xmin ⩽ 10.0 cm. 1 Column headings: Each column heading must contain a quantity and a unit. The presentation of quantity and unit must conform to accepted scientific convention, e.g. x2 / cm2. 1 Consistency: All values of x and L must be given to the nearest mm. 1 Significant figures: Number of significant figures for every value of x2 same as, or one greater than, the number of s.f. of raw x as recorded in table. 1 Calculation: Values of x2 calculated correctly. 1 Question Answer Marks 1(d)(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 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. 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 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 five). Scatter of plots must be no more than ±1 cm (to scale) from a straight line in the L direction. Trend of points on graph must be negative. 1 1(d)(ii) Line of best fit: Judge by balance of all points on the grid (at least five) 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. There must be at least five points left after disregarding the anomalous point. Line must not be kinked or thicker than half a small 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, e.g. not ∆x / ∆y. Both read-offs must be accurate to half a small square in both the x and y directions. Sign of gradient on answer line must match graph drawn. 1 y-intercept: Correct read-off from a point on the line substituted into y = mx + c or an equivalent expression. Read-off must be accurate to half a small square in both x and y directions. or Intercept read directly from the graph, with read-off at x = 0 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. The values must not be fractions. 1 Unit for a is correct (e.g. cm–1) and unit for b is correct (e.g. cm). 1

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2 In this experiment, you will investigate the expansion of a wire heated by an electric current. (a) • The apparatus is partly assembled as shown in Fig. 2.1. boss wooden rod insulation crocodile clip wire stand crocodile clip wooden strip nail held in boss bench Fig. 2.1 Assemble the circuit shown in Fig. 2.2 with the switch open and the power supply set to its minimum voltage. power supply V A h0 Fig. 2.2 • The height of the end of the wooden strip above the bench is h0, as shown in Fig. 2.2. Measure and record h0. h0 = ...................................................mm [1] (b) (i) • When the switch is closed, the wire will get hot. Do not touch the wire. • Close the switch and adjust the power supply until the ammeter reading I is between 0.40 A and 0.50 A. • Measure and record I and the voltmeter reading V. I = ............................................................ A V = ............................................................ V [2] (ii) The wire expands and this causes the wooden strip to move. • The height of the end of the wooden strip above the bench is now h. Measure and record h. h = .........................................................mm • Open the switch. [1] (iii) Calculate the change in height Δh, where Δh = h0 – h. Δh = ...................................................mm [1] (c) Estimate the percentage uncertainty in your value of Δh. percentage uncertainty = ......................................................... [1] (d) • Write down the value, in kelvin, of the room temperature T0 given on the card. T0 = ............................................................ K • Calculate the temperature T of the wire using the relationship T = T0 + αΔh where α = 11.8 K mm–1. T = ...................................................... K [1] (e) Repeat (b) and (d) with the ammeter reading between 0.90 A and 1.00 A. I = ............................................................ A V = ............................................................ V h = .........................................................mm Δh = .........................................................mm T = ............................................................ K [2]

Mark scheme: 2(a) Value for h0 to nearest mm and in range 20–200 mm. 1 2(b)(i) Value for I in range 0.20–0.70 A and obtained without help from the Supervisor. 1 Value for V in range 0.5–3.5 V. 1 2(b)(ii) Value for h < h0. 1 2(b)(iii) Correct calculation of ∆h. 1 2(c) Percentage uncertainty based on an absolute uncertainty in ∆h value of 1 or 2 mm. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. Correct method of calculation to obtain percentage uncertainty. 1 2(d) Correct calculation of T and value given to nearest K. 1 2(e) Second values of I, V and h. 1 Quality: Second ∆h greater than first ∆h. 1 2(f)(i) Two values of β calculated correctly. 1 2(f)(ii) Justification based on significant figures in I, V and T4–T04. 1 2(f)(iii) Valid comment relating to the calculated values of β, testing against a criterion specified by the candidate. 1 Question Answer Marks 2(g)(i) A Too few readings/(only) two readings not enough to draw a (valid) conclusion (not ‘not enough for accurate results’, ‘few readings’). B Difficulty measuring h/h0/height because rule not vertical/not steady. C Large percentage uncertainty in ∆h/large uncertainty in ∆h because ∆h small. D T0 may vary from stated value (during the experiment). E Meter readings fluctuate. F Expansion may be permanent/doesn’t return to h0. 1 mark for each point up to a maximum of 4. 4 2(g)(ii) A Take more readings and plot a graph or take more readings and compare β values (not ‘repeat readings’ on its own). B Hold rule (vertically) in clamp. C1 Use longer wooden strip/attach wire closer to pivot. C2 Use larger current/voltage. C3 Use vernier calipers/digital calipers/travelling microscope. D Use a thermometer to measure T0 at the time the h readings are taken/during experiment. E Clean crocodile clips/contacts with method. F Re-measure h0 between tests. 1 mark for each point up to a maximum of 4. 4

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