Cambridge A Level Physics 9702 — 2015 Oct/Nov Paper 3 · Variant 1

1 In this experiment, you will investigate the effect of air resistance on the motion of a circular card. (a) (i) Use the compasses to draw a circle of approximate diameter 20 cm on the card. (ii) Use the scissors to cut out the circle. (iii) Make a hole in the centre of the circle with the compasses. The hole should be big enough for the hook of the mass hanger to pass through. (iv) Measure and record the diameter d of the card as shown in Fig. 1.1. FDUG KROH G Fig. 1.1 d = ..................................................[1] (b) (i) Set up the apparatus as shown in Fig. 1.2. The rule should have a 0 cm mark at the bottom and a 100 cm mark at the top. boss clamp wooden rod stand boss stand springs rule card masses bench Fig. 1.2 (ii) Adjust the rule until the 5.0 cm mark is level with the card as shown in Fig. 1.3. 5.0 cm mark Fig. 1.3 (c) (i) Pull the masses down so that the card is level with the 0 cm mark as shown in Fig. 1.4. Release the masses and watch the movement of the masses and card. They will move up and down. When the card returns to its lowest point for the first time, it has completed one cycle as shown in Fig. 1.4. Gradually the card moves less and less and does not move down as far as the 0 cm mark. one complete cycle 5.0 cm mark 2.5 cm mark 0 cm mark Fig. 1.4 (ii) Pull the masses down so that the card is again level with the 0 cm mark. Release the masses and count the number N of cycles for the card to reach the 2.5 cm mark at its lowest point. N = ..................................................[1] (d) (i) Remove the card from the mass hanger. Use the compasses to draw a circle of approximate diameter 18 cm on the card. Use the scissors to cut out the circle. Measure and record the diameter d of the card. d = ...................................................... (ii) Repeat (b) and (c). N = ...................................................... (e) Cut smaller circles and repeat (b) and (c) until you have six sets of values of d and N. Include in your table the two sets of values already taken. 1 Also include values of and N in your table. d [10] 1(f) (i) Plot a graph of N on the y-axis against on the x-axis. [3] d (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ...................................................... y-intercept = ...................................................... [2] (g) It is suggested that the quantities N and d are related by the equation A N = + B d where A and B are constants. Using your answers in (f)(iii), 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 (a) (iv) Value of d in range 19.5 cm to 20.5 cm with unit. [1] (c) (ii) Value of N with evidence of repeat readings. [1] (e) Six sets of readings of d and N scores 5 marks, five sets scores 4 marks etc. [5] Incorrect trend –1. Help from Supervisor –1. Range: [1] Smallest value of d < 9.5 cm. Column headings: [1] 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. d –1 / m–1. Consistency: [1] All values of d must be given to the nearest mm. Significant figures: [1] Every value of 1 / d must be given to the same number of significant figures as (or one more than) the number of significant figures in the corresponding value of d. Calculation: [1] √N calculated correctly to the number of significant figures given by the candidate. (f) (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 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. Quality: [1] All points in the table must be plotted (at least 5) for this mark to be awarded. Scatter of points must be no more than ±0.5 in the √N direction from a straight line. (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 (i.e. circled or labelled) 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. Do not allow ∆x / ∆y. Sign of gradient must match graph drawn. 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 substituted into y = mx + c or an equivalent expression. Read-offs must be accurate to half a small square in both x and y directions. Or: Intercept read directly from the graph, with read-off accurate to half a small square. (g) Value of A = candidate’s gradient and value of B = candidate’s intercept. [1] Unit for A correct (e.g. m or cm or mm) and consistent with value. No unit given for B. [1]

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2 In this experiment, you will investigate the motion of a marble. (a) (i) Balance the wooden rod on the pivot as shown in Fig. 2.1. x wooden rod holes P Q pivot bench Fig. 2.1 (ii) Measure and record the distance x from the hole P to the pivot as shown in Fig. 2.1. Do not mark the wooden rod. x = ............................................. m [2] (b) (i) Calculate C using x 2 + h 2 C = x where h = 0.100 m. C = ............................................ m [1] (ii) Justify the number of significant figures that you have given for your value of C. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[1] (c) (i) Set up the apparatus with the nail through hole P, as shown in Fig. 2.2. boss nail clamp P wooden rod Q stand marble wooden cube container with sand bench Fig. 2.2 The nail should be held in the clamp. The bottom of the wooden rod should be just above the top of the wooden cube. The marble should be in contact with the wooden rod. (ii) Move the wooden rod to the left through a distance of 20 cm as shown in Fig. 2.3. Release the wooden rod. The wooden rod will move to the right and strike the marble. surface 20 cm of sand 5 Fig. 2.3 Measure and record the horizontal distance R moved by the marble through the air. R = ..................................................[2] (iii) Estimate the percentage uncertainty in your value of R. percentage uncertainty = ..................................................[1]

Mark scheme: 2 (a) (ii) Value for x to the nearest mm. [1] x in the range 0.155 m to 0.165 m. [1] (b) (i) Correct calculation of C in m (correct to 2 s.f.). [1] (ii) Justification for significant figures in C linked to significant figures in x and h. [1] (c) (ii) Value for R with unit. [1] Evidence of repeat readings. [1] (iii) Absolute uncertainty in R in range 5 mm to 20 mm and correct method of calculation to obtain percentage uncertainty. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. [1] (d) Second value of x. [1] Second value of R. [1] Second value of R < first value of R. [1] (e) (i) Two values of k calculated correctly. [1] (ii) Valid comment consistent with the calculated values of k, testing against a criterion specified by the candidate. [1] (f) (i) Limitations (4 max.) (ii) Improvements (4 max.) Do not credit A Not enough readings to draw a Take many readings for different Few readings/ conclusion holes and plot a graph/ only one reading/ obtain more k values and not enough readings for compare an accurate result/ “repeat readings” on its own/ take more readings and (calculate) average k B Ball rolls off block/ball does not Small groove in the wood to move along straight line from the place the marble wood/rod does not hit marble square on each time/rod hits marble at an angle C Difficult to measure distance rod is Use another stand or stop pulled back/difficult to hold rod still before release D Difficult to measure R with reason Improved method for measuring e.g. marble skids in sand leaving R e.g. video with scale/use elongated hole/can’t fit ruler in carbon paper/ink on marble/put sand tray/parallax error scale on the sand E Difficult to flatten sand/know when Use a straight edge/ sand is horizontal use a spirit level F Difficult to measure x with reason Method of measuring x/ e.g. wooden rod moves clamp rule close by/ draw scale on rod

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