Cambridge A Level Physics 9702 — 2019 Oct/Nov Paper 3 · Variant 4

1 In this experiment, you will investigate the motion of a wooden strip balanced on a curved surface. (a) • Assemble the apparatus as shown in Fig. 1.1. • Use pieces of modelling clay to ensure that the beaker is secure and that its axis is horizontal. • The centre of each mass should be the same distance x from the line at the midpoint of the wooden strip, where x is approximately 15 cm. 100 g mass 100 g mass wooden strip x x line beaker modelling clay bench Fig. 1.1 • Measure and record x. x = ................................................... cm [1] (b) • Push one end of the strip down by approximately 2 cm and release it so that it oscillates. • Take measurements to find the period T of the oscillations. T = ...................................................... s [1] (c) Change x and measure T. Repeat until you have six sets of values of x and T. Record your results in a table. Include values of x 2 and T 2 in your table. [9] (d) (i) Plot a graph of T 2 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 2 = ax 2 + 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] (f) • Take measurements to find the radius R of the beaker. R = ............................................................... • An approximate value for the acceleration of free fall g is given by 4π2 g = . Ra Calculate g. g = ............................................................... [1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Value of x in range 13.0–17.0 cm. 1 1(b) Evidence of repeat readings of nT with n ⩾ 5. 1 1(c) Six sets of readings of x and time with correct trend and without help from the Supervisor scores 4 marks, five sets scores 3 marks, etc. 4 Range: xmin ⩽ 5.0 cm and xmax⩾20.0 cm. 1 Column headings: Each column heading must contain a quantity, a unit and a separating mark. The presentation of quantity and unit must conform to accepted scientific convention. e.g. T2 / s2. 1 Consistency: All values of x must be given to the nearest 0.1 cm. 1 Significant figures: All values of x2 must be given to the same number of s.f. as, or one greater than, the number of s.f. of x as recorded in the table. 1 Calculation: Values of T2 calculated correctly. 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 points plotted on the grid 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. 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 must be plotted (at least 5). Trend of points on graph must be positive. Scatter of points must be no more than ±25 cm2 (to scale) from a straight line in the x2 direction. 1 Question Answer Marks 1(d)(ii) Line of best fit: Judge by the 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 its full length. One anomalous point is allowed 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. Line 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, e.g. not ∆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 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 the y direction. 1 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. s2 m–2) and unit for b is correct (s2). 1 1(f) Value for g calculated correctly. 1

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2 In this experiment, you will investigate the force needed to pull a cylinder up a step. (a) Measure the thickness h of the board, as shown in Fig. 2.1. board h Fig. 2.1 h = .................................................. mm [1] (b) • Suspend the two larger (100 g) slotted masses from the newton meter using the loop of thread, as shown in Fig. 2.2. newton meter loop of thread two slotted masses Fig. 2.2 • Record the total weight W of these masses. W = ..................................................... N [1] (c) (i) Take measurements to find the radius r of one of the larger slotted masses. r = .................................................. mm [1] (ii) The value of α is given by (r – h) sin α = . r Calculate α. α = ....................................................... ° [1] (iii) Justify the number of significant figures you have given for your value of α. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (d) • Place the board on the bench to make a step. Stand the two larger slotted masses on their edges next to the step with their slots at the top, as shown in Fig. 2.3. • Attach the loop of thread to the masses and the newton meter, as shown in Fig. 2.3. loop of thread handle hook bench step board Fig. 2.3 • Pull the handle of the newton meter horizontally and at right angles to the step. The force required to just start the slotted masses rolling up the step is F. Measure and record F. F = ......................................................... [2] (e) Estimate the percentage uncertainty in your value of F. percentage uncertainty = ......................................................... [1] (f) Repeat (b), (c)(i), (c)(ii) and (d) using the two smaller (50 g) slotted masses. W = ........................................................... N r = ........................................................ mm α = ............................................................ ° F = ............................................................... [2]

Mark scheme: 2(a) Value for h to nearest mm and in range 7–13 mm. 1 2(b) Value for W to nearest 0.1 N and in the range 1.0 N ⩽W ⩽ 5.0 N. 1 2(c)(i) Evidence that d has been measured to find r. 1 2(c)(ii) Correct calculation of α. 1 2(c)(iii) Justification based on s.f. in (r – h) and r. 1 2(d) Raw values for F to nearest 0.1 N with unit. 1 Evidence of repeat readings of F. 1 2(e) Percentage uncertainty based on an absolute uncertainty in F of 0.1–0.4 N. 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(f) Values for second W, r and F. 1 Quality: Second F less than first F. 1 2(g)(i) Two values of k calculated correctly. 1 2(g)(ii) Valid comment relating to the calculated values of k, testing against a criterion specified by the candidate. 1 Question Answer Marks 2(h)(i) A Too few readings/(only) two readings not enough to draw a (valid) conclusion (not ‘not enough for accurate results’, ‘few readings’). B Large percentage uncertainty in h or h is small so large uncertainty in h. C Difficult to measure diameter with reason, e.g. because diameter not clearly defined, edge is tapered. D Difficult to measure F/read newton meter with a reason, e.g. difficult to judge moment when cylinder starts to roll/cylinder moves suddenly/non-zero reading on newton meter when horizontal. E Force applied at different angles for each cylinder/difficult to pull newton meter horizontally. F Large percentage uncertainty in F or values of F small so large uncertainty in F. 1 mark for each point up to a maximum of 4. 4 2(h)(ii) A Take more readings and plot a graph or take more readings and compare k values (not ‘repeat readings’ on its own). B Use vernier/digital calipers or micrometer. C Improved method of measuring diameter, e.g. measure between set squares/put blocks either side and measure between blocks. D Use system of pulley and weights/sand or Pointer/marker that stays in maximum position on newton mete/use force sensor and data-logger or Video/film/record experiment with newton meter in view. E Method of applying force horizontally, e.g. use longer loop of thread/support newton meter with additional board. F Use e.g. 0–5 N newton meter (not ‘more accurate meter’). 1 mark for each point up to a maximum of 4. 4

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