Cambridge A Level Physics 9702 — 2023 May/June Paper 3 · Variant 2

1 In this experiment, you will investigate the equilibrium position of a metre rule. (a) ● Assemble the apparatus as shown in Fig. 1.1. stand clamp boss spring string loop metre rule string loop spring protractor string plumb-line weight W bench Fig. 1.1 ● Adjust the height of the boss and the position of the weight W on the bench so that the metre rule is parallel to the bench and both springs are vertical. ● Slide the rubber band and slotted mass onto the rule so that the rubber band is approximately 30 cm from the end of the rule. The rule will tilt down, as shown in Fig. 1.2. ● Adjust the position of W so that both springs are vertical. rubber band x θ slotted mass W bench Fig. 1.2 ● The distance between the rubber band and the end of the rule is x, as shown in Fig. 1.2. Measure and record x. x = ............................................................... ● The angle indicated by the plumb‑line on the protractor scale is θ, as shown in Fig. 1.2. Measure and record θ. θ = ............................................................. ° [2] (b) Vary x by moving the rubber band along the metre rule. Adjust the position of W so that both springs are vertical. Measure x and θ. Repeat until you have six sets of values of x and θ. Record your results in a table. Include values of cos θ in your table. [9] (c) (i) Plot a graph of cos θ on the y‑axis against x 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] (d) It is suggested that the quantities θ and x are related by the equation cos θ = ax + b where a and b are constants. Using your answers in (c)(iii), determine the values of a and b. Give appropriate units. a = ............................................................... b = ............................................................... [2] (e) For this experiment, the constant a is related to the spring constant S of each spring by p a = – S where p = 13.15 N m–2. Determine the value of S. Give an appropriate unit. S = ......................................................... [1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Final value of x with unit in range 29.0–31.0 cm. 1 Value of  to nearest degree and in the range 60–80°. 1 1(b) Six sets of readings of x (different values) and  with correct trend (as x increases  increases) and without help from the Supervisor scores 4 marks, five sets scores 3 marks, etc. 4 Range: xmin ⩽ 10.0 cm and xmax ⩾ 55.0 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.  / , x / cm. cos must not have a unit. 1 Consistency: All values of x must be given to the nearest millimetre. 1 Significant figures: Values of cos  given to 2 or 3 significant figures. 1 Calculation: Values of cos  calculated correctly. 1 Question Answer Marks 1(c)(i) Axes: Axes must be labelled with the correct quantities. Scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Scale markings are no more than 2 cm apart (one large square). Sensible scales must be used. Scale must not be awkward (e.g. 3:10 or fractions). 1 Plotting of points: All observations in the table must be plotted on the grid. Diameter of plotted points must be less than half a small square. Points must be plotted to an accuracy of half a small square in both x and y directions. 1 Quality: Trend of points must be negative. All points in the table must be plotted on the grid. It must be possible to draw a straight line that is within  4.0 cm (to scale) on the x-axis of all plotted points. 1 1(c)(ii) Line of best fit: ‘Best fit’ is judged by the balance of all points on the grid (at least 5 points) about the candidate’s line. There must be an even distribution of points either side of the line along the full length. Lines must not be kinked or thicker than half a square. Some candidates may choose to identify an anomalous point. If they identify one point as anomalous (e.g. by circling or labelling) then this point is to be disregarded when judging the line of best fit. There must be at least 5 points left after the anomalous point is disregarded. 1 1(c)(iii) Gradient: The hypotenuse of the triangle used should be greater than half the length of the drawn line. Both read-offs must be accurate to half a small square in both x and y directions. The method of calculation must be correct, not x / y. The gradient sign on the answer line must be consistent with the graph drawn. 1 y-intercept: Intercept read directly from the graph, with read-off at x = 0, accurate to half a small square in y direction. or Correct read-off from a point on the line and substituted correctly into y = mx + c or an equivalent expression. Read-off is accurate to half a small square in both x and y directions. 1 Question Answer Marks 1(d) Value of a = candidate’s gradient and value of b = candidate’s intercept. Values must not be written as fractions or given to only one significant figure. 1 Units for a and b correct and consistent with readings (e.g. cm–1 for a and no unit for b). 1 1(e) Correct calculation of S with unit (e.g. N m–1 or N cm–1). 1

More questions on Physical quantities

2 In this experiment, you will investigate the properties of a flywheel. (a) (i) You are provided with a slotted mass fixed to a length of plastic tube, as shown in Fig. 2.1. slot slotted mass tube D1 Fig. 2.1 ● Measure and record the diameter D1 of the slotted mass. D1 = .......................................................... cm ● Calculate C using C = M1D12 where M1 = 0.100 kg. C = ............................................................... [2] (ii) Justify the number of significant figures that you have given for your value of C. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (iii) ● Assemble the apparatus as shown in Fig. 2.2. slotted mass stand tube boss bamboo rod clamp gripping rod string bench mass hanger floor Fig. 2.2 ● Pass the string through the slot of the slotted mass and tie it to the tube, as shown in Fig. 2.2. ● Hook the mass hanger onto the other end of the string and then adjust the height of the boss until the mass hanger is just touching the floor. ● Rotate the slotted mass and tube 16 times so that the string is wound around the tube, as shown in Fig. 2.3. floor Fig. 2.3 ● Release the slotted mass and take measurements to determine the time T for the mass hanger to reach the floor. T = ......................................................... [2]

Mark scheme: 2(a)(i) Correct calculation of C. 1 2(a)(ii) Justification for significant figures in C linked to significant figures in M1 and D1. 1 2(a)(iii) All values of T to nearest 0.01 s or all to the nearest 0.1 s, with unit. 1 Evidence of repeat readings of T. 1 2(b)(i) Value for D2 that is greater than D1. 1 2(b)(ii) Absolute uncertainty in D2 in the range 0.2–0.5 cm. Correct method of calculation to find percentage uncertainty in D2, e.g. (absolute uncertainty / value from 2(b)(i))  100. If repeated readings have been taken, then the absolute uncertainty can be half the range (but not zero) provided the working is clearly shown. 1 2(b)(iii) Correct calculation of new value of C. 1 2(b)(iv) Value for T. 1 New value of T greater than first T. 1 2(c) Two values of k calculated correctly. The final k values must not be written as fractions or given to only one significant figure. 1 2(d) Calculation of percentage difference between candidate’s two k values. Comparison of percentage difference with 15% leading to a consistent conclusion. 1 Question Answer Marks 2(e)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficult to measure T or time with a reason e.g. difficult to judge when mass hanger reaches the floor/difficult to judge start of descent of mass hanger. C Time or T is short so uncertainty in T is large or percentage uncertainty in T is large. D Difficult to measure D1 or D2 or diameter with a reason e.g. plastic tube gets in way of ruler/parallax error. E Difficulty with D2 with a reason e.g. inconsistent thickness of clay layer, thickness of clay layer varies. F Difficult to exactly judge 16 turns of the flywheel/difficult to exactly judge number of turns of the flywheel. G Mass hanger does not fall smoothly/consistently/hanger stops and starts. 1 mark for each point up to a maximum of 4. 4 2(e)(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 video/record/film (descent of mass hanger in view) and timer in view/view frame-by-frame. C Method to increase T or time e.g. use longer drop/decrease mass of mass hanger/increase number of turns. D Use (vernier) calipers. E Hold a roller on the modelling clay while flywheel is turned/use a preformed ring of clay/use a mould/flatten clay between boards. F Use height change (preset height) instead of turns or use fiducial mark and line up with slot on mass/mark on mass. G Improved method to allow hanger to fall smoothly e.g. support bamboo rod at both ends/use tube with circular cross- section. 1 mark for each point up to a maximum of 4. 4

More questions on Errors and uncertainties