Cambridge A Level Physics 9702 — 2023 May/June Paper 3 · Variant 4

1 In this experiment, you will investigate the oscillations of a pendulum. (a) ● Assemble the apparatus as shown in Fig. 1.1 with the nail held securely in the cork. Check that the wooden rod can swing freely. top hole cork clamp nail boss wooden rod lower mass stand bench Fig. 1.1 ● You have been provided with one 50 g and four 10 g slotted masses. Use the bolt and nut to attach some of the 10 g slotted masses to the top hole. ● Record the total mass M of the slotted masses that are attached to the top hole. M = ............................................................... ● Push the bottom of the wooden rod a small distance to one side. ● Release the wooden rod so that it oscillates. ● Take measurements to determine the period T of the oscillations. T = ............................................................... [3] (b) Change M and determine T. Repeat until you have six sets of values of M and T. Do not change the lower mass. Record your results in a table. Include values of M 2 and T 2 in your table. [9] (c) (i) Plot a graph of T 2 on the y-axis against M 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] (d) It is suggested that the quantities T and M are related by the equation T 2 = aM 2 + 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] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Value of M with unit and in range 10–100 g. 1 Value of T with unit and in range 0.950–2.00s. 1 Repeats: At least two measurements of at least 5T. 1 1(b) Six sets of readings of M (different values, may include 0 g) and T (or time) with correct trend (as M increases T increases) and without help from the Supervisor scores 4 marks, five sets scores 3 marks etc. 4 Range: Mmin ⩽10 g and Mmax ⩾ 70 g. 1 Column headings: Each column heading must contain a quantity and a unit where appropriate. The presentation of quantity and unit conforms to accepted scientific convention e.g. M 2 / g2. 1 Consistency: All values of raw time must be given to the nearest 0.01s or all to the nearest 0.1 s. 1 Significant figures: Values of T2 must be given to the same number of s.f. as (or one more than) the number of s.f. in the corresponding T. 1 Calculation: Values of T2 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 positive. All points in the table must be plotted on the grid. It must be possible to draw a straight line that is within  500 g2 (to scale) on the M 2 axis of all plotted points. 1 1(c)(ii) Line of best fit: ‘Best fit’ is judged by 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 small 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 M2 = 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 Correct units for a and b (e.g. s2g–2 for a and s2 for b). 1

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2 In this experiment, you will investigate the thermal expansion of plastic. (a) You have been provided with two plastic pipes. Each pipe has a string loop attached at each end, as shown in Fig. 2.1. pipe string loop string loop L Fig. 2.1 ● Measure and record the length L of the longer pipe, as shown in Fig. 2.1. L = ............................................................... ● Place the thermometer on the bench. Record the room temperature T0. T0 = ............................................................... [2] (b) (i) You have been provided with a wooden rod supported by a pin. ● Using the longer pipe, assemble the apparatus as shown in Fig. 2.2. clamp cork hook rod string loop boss holding clamp measuring pin through rod cylinder x1 pipe stand string loop bench mass and mass hanger Fig. 2.2 ● Adjust the apparatus so that the rod is parallel to the bench and the mass hanger rests on the bottom of the measuring cylinder. ● Measure and record the height x1 of the end of the rod above the bench, as shown in Fig. 2.2. x1 = ......................................................... [1] (ii) ● Slowly pour boiling water into the measuring cylinder until it covers the pipe. ● Place the thermometer in the water. Record the temperature T. T = ............................................................... ● Remove the thermometer from the water. ● The expansion of the pipe causes the end of the rod to move down. Measure the new height x2 of the end of the rod above the bench. x2 = ............................................................... ● Carefully remove the pipe and mass hanger (the masses will be very hot) and pour the hot water into the sink. [2] (iii) Calculate (x1 – x2). (x1 – x2) = ......................................................... [1] (iv) Estimate the percentage uncertainty in your value of (x1 – x2). Show your working. percentage uncertainty = ..................................................... % [1] (c) ● Measure and record the length L of the shorter pipe. L = ............................................................... ● Repeat (b)(i), (b)(ii) and (b)(iii) using the shorter pipe. x1 = ............................................................... T = ............................................................... x2 = ............................................................... (x1 – x2) = ............................................................... [2]

Mark scheme: 2(a) Value for L with unit, to nearest mm and in range 11.7–12.7cm. 1 Value for T0 with unit and to nearest degree. 1 2(b)(i) Value for x1 with unit and to nearest mm. 1 2(b)(ii) Value for T greater than T0. 1 Value of x2 different from x1. 1 2(b)(iii) Correct calculation of (x1 – x2). 1 2(b)(iv) Percentage uncertainty in (x1 – x2) based on absolute uncertainty in the range 0.2–0.5 cm. Correct method of calculation to obtain percentage uncertainty e.g. (absolute uncertainty / value from (b)(iii))  100. If several readings have been taken, then the absolute uncertainty can be half the range (but not zero) provided the working is shown clearly. 1 2(c) Second values of L, x1, T and x2. 1 Second L less than first L. 1 2(d)(i) Two values of k calculated correctly. The final k values must not be written as fractions. 1 2(d)(ii) Justification for significant figures in k linked to significant figures in (x1 – x2), L and (T – T0). 1 2(e) Calculation of percentage difference between candidate’s two k values. Comparison of percentage difference with 20% leading to a consistent conclusion. 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 x or height with a reason e.g. rod moves/rule not vertical/ruler moves. C (x1 – x2) is small so large uncertainty or large % uncertainty in (x1 – x2). D Difficult to measure T or water temperature with a reason e.g. T varies with position in measuring cylinder/thermometer touches sides of cylinder/cannot measure x and T at the same time/T decreases rapidly. E T0 or room temperature may change during the experiment. F Difficulty with pipe e.g. difficult to measure L because pipe is curved/pipe does not expand as expected/L is not the distance between the holes. G Difficulty with string e.g. string changes length when wet. 1 mark for each point up to a maximum of 4. 4 2(f)(ii) A Take more readings (for different values of x) and plot a graph or take more readings and compare k values (not “repeat readings” on its own). B Clamp rule/use a plumb line. C Increase length of rod/pipe. D Use a stirrer for the water/clamp thermometer/thermostatically controlled water bath. E Measure T0 just before water is added. F Use tape measure/string and ruler or make L the distance between the holes. G Use named waterproof material e.g. nylon string/plastic/metal wire. 1 mark for each point up to a maximum of 4. 4

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