Cambridge A Level Physics 9702 — 2017 May/June Paper 3 · Variant 5

1 In this experiment, you will investigate the motion of a supported copper wire. (a) You have been provided with a copper wire and two spheres of modelling clay. (i) Bend the wire about its midpoint so that the two lengths are perpendicular to each other, as shown in Fig. 1.1. § 25 cm § 25 cm 90° wire Fig. 1.1 (ii) Push each end of the wire through the centre of a sphere of modelling clay. Place the spheres approximately half-way along each length of the wire as shown in Fig. 1.2. x x sphere of modelling clay Fig. 1.2 The centres of the spheres should each be the same distance from the midpoint of the wire. Gently press the modelling clay onto the wire to ensure the spheres stay in position. (iii) Measure and record the distance x from the midpoint of the wire to the centre of a sphere. x = ..................................................[1] (b) (i) Set up the apparatus as shown in Fig. 1.3. wooden rod boss wire stand bench Fig. 1.3 (ii) Move one end of the wire down through a short distance. Release the wire. The wire will oscillate. Determine the period T of these oscillations. T = ..................................................[1] (c) Vary x and repeat (a)(iii) and (b) until you have six sets of values of x and T. Record your results in a table. Include values of x 2 in your table. [9] (d) (i) Plot a graph of T on the y-axis against x 2 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 T and x are related by the equation T = Px 2 + Q where P and Q are constants. Using your answers in (d)(iii), determine the values of P and Q. Give appropriate units. P = ...................................................... Q = ...................................................... [2] (f) (i) Remove the spheres from the wire. (ii) Repeat (b)(ii). T = ...................................................... (iii) Calculate the value of x that corresponds to the value of T in (f)(ii). x = ..................................................[1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a)(iii) Value of x with unit to the nearest mm in the range 10.0–15.0 cm. 1 1(b)(ii) Evidence of repeated timings. Must see nT repeated where n ⩾ 5. 1 1(c) Six sets of readings of x (different values) and time with correct trend and without help from Supervisor scores 5 marks, five sets scores 4 marks etc. 5 Range: xmin ⩽ 5.0 cm and xmax ⩾ 20.0 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. x2 / m2. 1 Consistency: All values of raw x must be given to the nearest mm. 1 Significant figures: All values of x2 must be given to the same number of s.f. as (or one more than) the s.f. in raw x. 1 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 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. 1 Quality: All points in the table must be plotted for this mark to be awarded. It must be possible to draw a straight line that is within ± 0.025 s on the T axis of all plotted points. 1 Question Answer Marks 1(d)(ii) Line of best fit: Judge by balance of all points on the grid about the candidate’s line (at least 5). 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 five points left after the anomalous point is disregarded. Lines 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. Gradient sign must match graph. Method of calculation must be correct. Do not allow ∆x / ∆y. Both read-offs must be accurate to half a small square in both the x and y directions. 1 y-intercept: Correct read-off from a point on the line substituted correctly 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 x2 = 0, accurate to half a small square in the y direction. 1 1(e) Value of P = candidate’s gradient and value of Q = candidate’s intercept. The values must not be fractions. 1 Unit for P dimensionally correct (e.g. s m–2 or s cm–2 or s mm–2). Unit for Q correct (s). 1 1(f)(iii) Correct calculation of x. 1

More questions on Physical quantities

2 In this experiment, you will investigate the equilibrium of a system of three identical springs. (a) Measure the length L of the unstretched coiled section of one of the springs as shown in Fig. 2.1. L spring Fig. 2.1 L = ..................................................[1] (b) Set up the apparatus as shown in Fig. 2.2. spring A spring B tape d § 5 cm spring C G-clamp stand bench Fig. 2.2 (not to scale) The springs are identical. Hold spring A as shown in Fig. 2.2. The distance d between the loops of springs B and C on the stand should be approximately 5 cm as shown in Fig. 2.2. Do not mark the tape. (c) (i) Pull spring A until the length of its coiled section is 15 cm as shown in Fig. 2.3. y 15 cm θ Fig. 2.3 (not to scale) The length of the coiled section of spring B is y. The angle between springs B and C is θ. (ii) Measure and record y. y = ..................................................[1] (iii) Measure and record θ. θ = ............................................... ° [1] (d) Estimate the percentage uncertainty in your value of θ. percentage uncertainty = ................................................. [1] (e) (i) Calculate (y – L). (y – L) = ..................................................[1] (ii) Calculate cos (θ2). cos (θ2) = ..................................................[1] (iii) Justify the number of significant figures that you have given for your value of cos (θ2). ................................................................................................................................. ................................................................................................................................. ............................................................................................................................. [1] (f) Increase d to approximately 10 cm and repeat (c), (e)(i) and (e)(ii). y = ...................................................... θ = .................................................... ° (y – L) = ...................................................... cos (θ2) = ...................................................... [3]

Mark scheme: 2(a) Value of raw L with unit in range 1.5–2.5 cm. 1 2(c)(ii) Value of y ⩾ L and to the nearest mm. 1 2(c)(iii) Value of raw θ to the nearest degree. 1 2(d) Percentage uncertainty in θ based on absolute uncertainty of 2–10°. 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(e)(i) Correct calculation of (y – L). 1 2(e)(ii) Correct calculation of cos (θ / 2). 1 2(e)(iii) Justification for s.f. in cos (θ / 2) linked to s.f. in θ. 1 2(f) Second value of y. 1 Second value of θ. 1 Quality: second value of θ > first value of θ. 1 2(g)(i) Two values of k calculated correctly. 1 2(g)(ii) Valid comment consistent with calculated values of k, testing against a criterion specified by the candidate. 1 Question Answer Marks 2(h)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Moving hands affecting keeping 15 cm the same or measuring y or θ. C Parallax error affecting the measurement of y or θ. D Reason for d not remaining constant e.g. loops slip on stand. E Difficult to know where to measure from for the angle or y. 1 mark for each point up to a maximum of 4. 4 2(h)(ii) A Take more readings and plot a graph/take more readings and compare k values (not “repeat readings” on its own). B Use another stand for valid purpose (e.g. instead of hand to hold spring). C Photo or still from video to measure θ or including scale in frame to measure y. D Improved method of fixing springs onto stand e.g. use Blu-Tack/tape/vertically clamped hacksaw blade/bulldog clips or use sandpaper to make stand rough. E Use a grid behind the springs/markers on spring. 1 mark for each point up to a maximum of 4. 4

More questions on Errors and uncertainties