Cambridge A Level Physics 9702 — 2015 May/June Paper 3 · Variant 3

1 In this experiment, you will investigate how the position of a suspended card varies with the distribution of masses attached to it. (a) (i) Use the nail to make two holes in the card as shown in Fig. 1.1 and Fig. 1.2. hole hole Fig. 1.1 1 cm card 1 cm Fig. 1.2 The holes should be approximately 1 cm from the edges of the card as shown in Fig. 1.2. Each hole should be big enough for the card to swing freely when the nail is inserted in the hole. (ii) Record the mass C of the card shown on the base of the stand. C = ................................................... g (b) (i) Set up the apparatus as shown in Fig. 1.3. Suspend the card from the nail through one of the holes. Hang the plumb-line from the nail. Mark the card at a point along the plumb-line as shown in Fig. 1.3. boss nail plumb-line mark bench Fig. 1.3 (ii) Remove the card. Draw a line on the card through the hole and the mark. This line should go just over half the length of the card as shown in Fig. 1.4. (iii) Repeat (b)(i) and (b)(ii) using the other hole in the card. (iv) Measure and record the distance y as shown in Fig. 1.4. hole card lines drawn on card y Fig. 1.4 y = ..................................................[1] (c) (i) Using some Blu-Tack, attach one of the 10 g slotted masses to the card. The position of the slotted mass should be half-way along the edge of the card and touching the edge as shown in Fig. 1.5. slotted mass Fig. 1.5 (ii) Repeat (b) using the card with the mass attached. y = ..................................................[1] (d) The mass attached to the card is m. Increase m by fixing another 10 g slotted mass on top of, or behind, the first mass. Record m and repeat (b) until you have six sets of readings of m and y. Include your results from (b) and (c). Include values of y (C + m) in your table. [10] (e) (i) Plot a graph of y (C + m) on the y-axis against m 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] (f) It is suggested that the quantities y, C and m are related by the equation AB y (C + m) = Am + 2 where A and B are constants. Use your answers in (e)(iii) to determine the values of A and B. Give appropriate units. A = ...................................................... B = ...................................................... [2] You may not need to use all of the materials provided.

Mark scheme: 1 (b) (iv) Value of y in the range 10.0 cm to 11.0 cm with unit. [1] (c) (ii) Value of y > value in (b)(iv). [1] (d) Six sets of readings of m and y scores 5 marks, five sets scores 4 marks etc. [5] Help from Supervisor –1. Range: [1] Range of m to include m = 0 g and m = 50 g or 60 g. Column headings: [1] Each column heading must contain a quantity and a unit where appropriate. The unit must conform to accepted scientific convention e.g. y(C + m) / cm g. Consistency: [1] All values of raw y must be given to the nearest mm. Significant figures: [1] Every value of value of y(C + m) must be given to the same number of s.f. as (or one more than) the least s.f. in the corresponding values of y, C and m as stated in the candidate’s table and (a)(ii). Calculation: [1] Values of y(C + m) calculated correctly to the number of s.f. given by the candidate. (e) (i) Axes: [1] Sensible scales must be used. Awkward scales (e.g. 3:10) are not allowed. 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. Plotting: [1] All observations must be plotted. Diameter of plotted points must be ≤ half a small square (no “blobs”). Plotted points must be accurate to within half a small square. Quality: [1] All points in the table (at least 5) must be plotted on the grid for this mark to be awarded. All points must be within ± 40 g cm of a straight line in the y(C + m) direction. (ii) Line of best fit: [1] 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. Lines must not be kinked or thicker than half a square. (iii) Gradient: [1] The hypotenuse of the triangle must be greater than half the length of the drawn line. The method of calculation must be correct. Both read-offs must be accurate to half a small square in both the x and y directions. y-intercept: [1] Either: Correct read-offs from a point on the line and substituted into y = mx + c. Read-offs must be accurate to half a small square in both x and y directions. Or: Check read-off of the intercept directly from the graph (accurate to half a small square). (f) Value of A = candidate’s gradient and value of B = 2 × candidate’s intercept / A. [1] Do not allow fractions or final answer to 1 s.f. Unit for A (m, cm or mm) and B (g or kg) correct and consistent with value, with correct power of ten. [1]

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2 In this experiment, you will investigate the motion of a small container in water. (a) You have been provided with three glass marbles and a small container with a separate lid. The dimensions of the glass marbles and the small container are shown in Fig. 2.1. D d h marble small container Fig. 2.1 (i) Measure and record the diameter d of the marble and the inner diameter D of the small container. d = ...................................................... D = ...................................................... [1] (ii) Measure and record the height h of the small container. h = ..................................................[1] (iii) Estimate the percentage uncertainty in your value of d. percentage uncertainty = ..................................................[1] (b) (i) Place the small container in the tray. Fill the small container with water from the beaker. (ii) Place two glass marbles in the small container. Wait until the water has stopped overflowing. Place the lid on the small container. (iii) The fraction x of glass in the small container is given by 2 n d 3 x = 2 3 D h where n is the number of marbles in the small container. Calculate x. x = ..................................................[1] (c) Justify the number of significant figures that you have given for your value of x. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[1] (d) (i) Place the small container in the cylinder as shown in Fig. 2.2. small container cylinder water tray bench Fig. 2.2 (ii) Release the small container and measure the time t taken for the small container to fall to the bottom of the cylinder. t = ..................................................[2]

Mark scheme: 2 (a) (i) Raw values of d and D to nearest 0.1 mm and with consistent SI unit, in ranges: 10.0 mm ≤=d ≤ 25.0 mm 20.0 mm ≤ D ≤ 40.0 mm. [1] (ii) Value of h with consistent unit in range 40.0 mm ≤ h ≤ 60.0 mm. [1] (iii) Percentage uncertainty in d based on absolute uncertainty of 0.1 or 0.2 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] (b) (iii) Correct calculation of x. Answer must be correct when rounded to 2 s.f. [1] (c) Correct justification of s.f. in x linked to s.f. in D, d and h. [1] (d) (ii) Value of average t ≥ 0.5 s with unit. [1] Evidence of repeated readings (here or in (e)). [1] (e) Second value of x. [1] Second value of t. [1] Second value of t < first value of t. [1] (f) (i) Two values of k calculated correctly. [1] (ii) Sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate. [1] (g) (i) Limitations (4 max.) (ii) Improvements (4 max.) Do not credit A Two readings not enough to draw Take many readings and plot “repeat readings”/ a valid conclusion a graph/ “too few readings” take more readings and compare k values. B Difficulty in release of cylinder Better method of holding and Clamps from same position every time releasing cylinder e.g. stop Force on release with reason, e.g. placing fingers in gate/ water, level of water surface use mark to ensure the water changing, difficult to judge start level is the same for each point release C Cylinder doesn’t always fall Method of attaching string Ignore string effects vertically (i.e. path at an angle or symmetrically/ Sand on its own cylinder tilted)/ method of symmetrical Narrow cylinder hits sides on descent distribution of mass e.g. use glass beads or sand/ modelling clay distributed evenly/ glue marbles in symmetrically D Times short/ Use longer tube/ Reaction time is short large uncertainty in time video with timer (or video and “too fast/quick” view frame by frame) High speed camera Light gate(s) Slow motion camera Terminal velocity E Difficulty in identifying end point Method to identify end point Flat bottomed cylinder with reason e.g. refraction, glass e.g. time to a mark on Sensors curvature, tray in the way, bottom cylinder/listening to impact of cylinder not flat F Limited number of marbles to fit in Use different shapes e.g. Sand on its own without container/ cubes/smaller spheres to explanation different diameter marbles/ occupy more space/ bubbles or air in container/ use sand/modelling clay to fill container deforms when more space/ measuring D measure and account for different diameter of marbles in equation for x

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