Cambridge A Level Physics 9702 — 2018 Oct/Nov Paper 3 · Variant 1

1 In this experiment, you will investigate the motion of a wooden strip. (a) • Set up the apparatus as shown in Fig. 1.1. head of longer nail boss x wooden strip stand line head of shorter nail slotted mass bench Fig. 1.1 • The longer nail should be held in the boss and be placed through the top hole in the strip. • The shorter nail should be placed through the bottom hole in the strip to support the slotted mass. • The distance between the longer nail and the line on the strip is x, as shown in Fig. 1.1. Measure and record x. x = .......................................................... [1] (b) • Pull the bottom of the strip through a short distance, as shown in Fig. 1.2. Fig. 1.2 • Release the strip. The strip will oscillate. • Determine the period T of these oscillations. T = .......................................................... [1] (c) Vary x by placing the longer nail through different holes in the strip. Measure and record x and T. Repeat until you have six sets of values. Record your results in a table. Include values of T 2x and x2 in your table. [10] (d) (i) Plot a graph of T 2x 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 T and x are related by the equation T 2x = Ax2 + B where A and B are constants. Using your answers in (d)(iii), 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 with unit in the range 23.5–24.5 cm. 1 1(b) Value of T with unit in the range 1.0–1.5 s and to 0.1 s or better. 1 1(c) Six sets of readings of x (different values) and time without help from the Supervisor and showing the correct trend scores 5 marks, five sets scores 4 marks etc. 5 Range: Minimum value of x ˂ 10.5 cm. 1 Column headings: Each column heading must contain a quantity, a unit and a separating mark where appropriate. The presentation of the quantity and the unit must conform to accepted scientific convention e.g. T 2x / s2 m. 1 Consistency: All raw values of x must be given to the nearest mm only. 1 Significant figures: All values of x2 must be given to the same number of significant figures as (or one more than) the number of significant figures in raw values of x. 1 Calculation: Correct calculation of T 2x. 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 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. 1 Quality: General trend of points on graph must be positive. All points in the table (at least 5) must be plotted on the grid. It must be possible to draw a straight line that is within ±0.005 m2 on the x-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 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 by the candidate (i.e. circled or labelled). 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. The 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. Sign of gradient on answer line must match graph. 1 y-intercept: Correct read-off from a point on the line substituted into y = mx + c. 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. 1 1(e) Value of A = candidate’s gradient and value of B = candidate’s intercept. The values must not be fractions. 1 Unit for A correct (s2 m–1, s2 cm–1 or s2 mm–1) and unit for B correct (s2 m, s2 cm or s2 mm). 1

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2 In this experiment, you will investigate the movement of a chain of paper clips. (a) (i) You have been provided with a chain of paper clips. Measure and record the mass M of the chain. M = .......................................................... [1] (ii) Using your answer in (a)(i), calculate the mass m of one paper clip. m = .......................................................... [1] (iii) Justify the number of significant figures that you have given for your value of m. ........................................................................................................................................... ........................................................................................................................................... ...................................................................................................................................... [1] (b) (i) You have been provided with two identical spheres of modelling clay. Measure and record the mass S of one of the spheres. S = .......................................................... [1] (ii) Calculate c where S c = . m c = .......................................................... [1] (c) (i) • Place the wooden strip on the bench so that one end of the strip overhangs the bench, as shown in Fig. 2.1. SIDE VIEW wooden strip bench Fig. 2.1 • Place the chain on the wooden strip and place one of the spheres on the paper clip at the end of the chain, as shown in Fig. 2.2. The sphere must not touch the wooden strip. TOP VIEW chain of paper clips sphere of modelling clay wooden strip edge of bench Fig. 2.2 • Gradually move the paper clips off the end of the wooden strip so that they hang down, as shown in Fig. 2.3. wooden strip bench Fig. 2.3 • When the chain starts to slip, count and record the number p of paper clips hanging off the end of the wooden strip and the number q of paper clips remaining on the strip. p = ............................................................... q = ............................................................... (ii) Estimate the percentage uncertainty in your value of p. percentage uncertainty = .......................................................... [1] (d) • Replace the chain on the wooden strip and place both spheres on the paper clips at the end of the strip, as shown in Fig. 2.4. Fig. 2.4 • Determine p and q. p = ............................................................... q = ............................................................... [2]

Mark scheme: 2(a)(i) Value of M with unit and to the nearest 0.1 g or better. 1 2(a)(ii) Correct calculation of m dividing the value in (a)(i) by 25. 1 2(a)(iii) Justification for significant figures in m linked to the s.f. in M. 1 2(b)(i) Value of S in range 1.0 g ⩽ S ⩽ 2.0 g with consistent unit. 1 2(b)(ii) Correct calculation of c. 1 2(c)(i) Values p and q such that p + q = 25. 1 Evidence of repeated values of p. 1 2(c)(ii) Percentage uncertainty in p based on absolute uncertainty of 1 or 2. 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) Second values of p and q. 1 Quality: second value of q less than first value of q. 1 2(e)(i) Two values of k calculated correctly. 1 2(e)(ii) Valid comment consistent with calculated values of k, testing against a criterion stated by the candidate. 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 Difficulty linked to board during movement of clips e.g. paper clips flip over when moving affecting friction/clips move to the side/clips catch on end of board/board irregular and clips catch on edge/board moves on table as well as clips. C Difficulty linked to placing or keeping the spheres on the clips e.g. spheres fall off/clips too small to hold the sphere/ difficult to get two neighbouring paper clips level enough to take the two spheres/spheres touch table. D Difficulty linked to size of clips with a reason e.g. large increments of mass gives large uncertainty in the value of p or q/the exact force needed to cause movement may not be equal to a whole number of clips. E Masses of clips or spheres may be different. 1 mark for each point up to a maximum of 4. 4 2(f)(ii) A Take many readings (for different values of n) and plot a graph or take more values of k and compare. B Workable method e.g. provide a guide/over a pulley wheel/tape or clamp board to bench/sand the end of the board/sand out irregularities. C Workable method of adding/holding spheres e.g. use cuboid/disc shaped plasticine/tie paper clips together with thin cotton to keep flat. D Improved method to deal with large clips e.g. use more and smaller/lighter clips. E Check masses using a balance. 1 mark for each point up to a maximum of 4. 4

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