Cambridge A Level Physics 9702 — 2021 May/June Paper 3 · Variant 5

1 In this experiment, you will investigate the motion of a pendulum bob. (a) ● Set up the apparatus as shown in Fig. 1.1. clamp split cork bosses L wooden rod d string stand pendulum bob bench Fig. 1.1 ● The distance between the bottom of the cork and the centre of the bob is d. The distance between the bottom of the cork and the centre of the wooden rod is L. Adjust the height of the rod until the value of L is approximately 10 cm. Ensure the rod is horizontal and the string is just touching the rod. ● Measure and record L. L = ......................................................... [1] (b) ● Adjust the string in the cork until the value of d is approximately 30 cm. ● Measure and record d. d = ............................................................... ● Pull the bob towards you through a short distance at right angles to the rod. ● Release the bob. The bob will oscillate. ● Determine the period T of these oscillations. T = ............................................................ s [1] (c) ● Write down your value of L from (a). L = ............................................................... ● Keeping L constant, repeat (b) with different values of d until you have five sets of values of d and T. T (d – L) Record your results in a table. Include values of and in your table. d d [10] T (d – L)(d) (i) Plot a graph of on the y-axis against on the x-axis. [3] d d (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 d are related by the equation T (d – L) = P + Q d d where P and Q are constants. Using your answers in (d)(iii), determine the values of P and Q. Give appropriate units. P = ............................................................... Q = ............................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Final value of L with unit and in the range 9.5–10.5 cm. 1 1(b) Final value of T in the range 0.80–1.20 s. 1 1(c) Five sets of readings of d and time (different values) without help from the Supervisor and with the correct trend (d increases, T increases) scores 5 marks, four sets scores 4 marks etc. 5 Range: Includes d ⩽ 25.0 cm and d ⩾ 40.0 cm. 1 Column headings: Each column heading must contain a quantity and a unit where appropriate. The presentation of the quantity and the unit must conform to accepted scientific convention e.g. T / √d / s m–½. 1 Consistency: Raw values of d must all be given to the nearest mm. 1 Significant figures: All values of d L d − √ must be given to the same number of significant figures as, or one greater than, the least number of number of significant figures in either (d – L) or d. 1 Calculation: Correct calculation of T / √d and d L d − √ . 1 Question Answer Marks 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. Axes must be labelled with the quantity which 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. Points must be plotted to an accuracy of half a small square in both the x and y directions. 1 Quality: All points in the table (at least 4) must be plotted on the grid. Trend of points must be correct. It must be possible to draw a straight line that is within 0.01 on the d L d − √ axis of all plotted points. 1 1(d)(ii) Line of best fit: Judge by balance of all points on the grid about the candidate’s line (at least 4 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. There must be at least four points left after the anomalous point is disregarded. Lines 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. Method of calculation must be correct, i.e. Δy / Δx. Gradient sign on answer line matches graph drawn. Both read-offs must be accurate to half a small square in both the x and y directions. 1 y-intercept: Check correct read-off from a point on the line and 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 at x = 0, accurate to half a small square. 1 Question Answer Marks 1(e) Value of P = candidate’s gradient and value of Q = candidate’s intercept. Values must not be written as fractions. 1 Unit for P is correct (e.g. s m–½) and unit for Q is correct (s m–½). 1

More questions on Physical quantities

2 In this experiment, you will investigate the equilibrium of a wooden strip. (a) You have been provided with a wooden strip. There are three holes in the strip and string is attached to two of the holes. ● Press the modelling clay onto the end of the strip as shown in Fig. 2.1. modelling clay wooden strip string H Fig. 2.1 ● The distance between the centre of the modelling clay and the centre of the hole at the other end of the strip is H. Using the ruler, take measurements to determine H. H = .................................................... cm [1] (b) (i) ● Set up the apparatus as shown in Fig. 2.2. boss pulley string nail θ wooden strip x stand mass m stand bench Fig. 2.2 (not to scale) ● Hang a mass m of 100 g from the string. ● Adjust the heights of the boss and pulley until the string between the strip and the pulley is horizontal. ● The distance between the nail and the hole through which the string is attached is x. The angle between the strip and the horizontal string is θ. Measure and record x and θ. x = ......................................................... cm θ = ............................................................. ° [2] (ii) Estimate the percentage uncertainty in your value of θ. Show your working. percentage uncertainty = ......................................................... [1] (iii) Calculate x tan θ. x tan θ = .................................................... cm [1] (iv) Justify the number of significant figures that you have given for your value of x tan θ. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1]

Mark scheme: 2(a) Final value of H in the range 38.0–42.0 cm. 1 2(b)(i) Value of raw x to the nearest mm. 1 Value of rawθ to the nearest degree and in the range 60°–80°. 1 2(b)(ii) Percentage uncertainty in θ based on absolute uncertainty of 2°–5°. If repeat readings have been taken, then the absolute 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(b)(iii) Correct calculation of x tan θ. 1 2(b)(iv) Justification for significant figures in x tan θ linked to s.f. in x and θ. 1 2(c) Second value of x. 1 Second value of θ. 1 Second value of θ < first value of θ. 1 2(d)(i) Two values of k calculated correctly. Final values must not be written as fractions. 1 2(d)(ii) Valid comment consistent with calculated values of k, testing against a criterion stated by the candidate. 1 2(e) Correct calculation of M with consistent unit. 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 Difficult to measure H with a reason e.g. locating centre of modelling clay/parallax error/locating centre of the hole. C Difficult to measure H because the ruler is not long enough. D Difficult to determine if the string is horizontal or difficult to set up the string horizontally. E Difficulty measuring θ with reason e.g. parallax error/holding protractor in air/wooden strip moves when knocked by protractor. (Allow parallax error linked to H or θ only once.) F The modelling clay falls off. 1 mark for each point up to a maximum of 4. 4 2(f)(ii) A Take more readings and plot a graph or take more readings and compare k values (not “repeat readings” on its own). B Method of locating and marking the centre. C Use a half-metre rule or a metre rule. D Use a spirit level/metre rule and set square with detail. E Clamp protractor or take a photo and measure angle or attach protractor to wooden rod. F Use glue to stick a sphere of clay to end/use a regular shape of mass (instead of the modelling clay). 1 mark for each point up to a maximum of 4. 4

More questions on Physical quantities