Cambridge A Level Physics 9702 — 2022 Feb/March Paper 3 · Variant 3

1 In this experiment, you will investigate the density of a liquid. (a) (i) You have been provided with a U-tube containing coloured water. The U-tube has two sides, A and B, as shown in Fig. 1.1. The wooden strip is supported by a stand and clamp (not shown in Fig. 1.1). wooden strip A B U-tube coloured water weight bench tray Fig. 1.1 • You are provided with a beaker containing oil. Use the pipette to slowly put oil into A. Wait to allow the oil to reach the water surface. The final length of the oil column above the water in A is F. Continue adding oil until F is approximately 7 cm, as shown in Fig. 1.2. A B oil column F ≈ 7 cm Fig. 1.2 • Measure and record F. F = .................................................... cm [1] (ii) • Use the pipette to slowly put oil into B. Wait to allow the oil to reach the water surface. The final length of the oil column above the water in B is h. Continue adding oil until h is approximately 3 cm, as shown in Fig. 1.3. A B oil column h ≈ 3 cm a b Fig. 1.3 • Measure and record h. h = ........................................................ cm • The height of the water level in A is a, and the height of the water level in B is b, as shown in Fig. 1.3. Measure and record a and b. a = .............................................................. b = ............................................................... • Calculate y using y = b – a y = ............................................................... [2] (b) Repeat (a)(ii) with increasing amounts of oil in B until you have six sets of values of h, a, b and y. Record your results in a table. Some of your values of y may be negative. [7] (c) (i) Plot a graph of y on the y-axis against h 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 y and h are related by the equation y = P h + Q where P and Q are constants. Use your answers in (c)(iii) to determine the values of P and Q. Give appropriate units. P = ............................................................... Q = ............................................................... [2] (e) Calculate the density ρ of the oil using the relationship Q R = F ρ where R is a constant with value 1.0 g cm–3. Include an appropriate unit and give your answer to an appropriate number of significant figures. ρ = ......................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a)(i) Value of F to nearest mm and in range 6.5 to 8.5cm 1 1(a)(ii) a and b, with unit 1 Correct calculation of y 1 1(b) Six sets of readings of h and y with correct trend and without help scores 4 marks, five sets scores 3 marks etc. 4 Range: hmax ⩾ 18.0 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. h / cm. 1 Consistency: All values of h and a and b must be given to the nearest mm 1 1(c)(i) Axes: Sensible scales are used, no awkward scales (e.g. 3:10) Scales are chosen so that the plotted points occupy at least half the graph grid in both x and y directions Axes are labelled with the quantity which is being plotted. Scale markings are no more than 2 cm (one large square) apart. 1 Plotting of points: All observations in the table are plotted on the grid. Diameters of plotted points are less than half a small square (no blobs). Points are plotted to an accuracy of half a small square in both x and y directions. 1 Quality: All points in the table must be plotted (at least 5) for this mark to be awarded, and trend of points must have a negative gradient. It must be possible to draw a straight line that is within ± 0.5 cm on the y axis of all plotted points. 1 Question Answer Marks 1(c)(ii) Line of best fit: Judged by balance of all points on the grid (at least 5) about the candidate’s line. There must be an even distribution of points either side of the line along the full length. One anomalous point is allowed only if clearly indicated (i.e. circled or labelled) by the candidate. There must be at least 5 points left after the anomalous point is discarded. Lines must not be kinked or thicker than half a square. 1 1(c)(iii) Gradient: Sign of gradient matches graph. The hypotenuse of the triangle used is greater than half the length of the drawn line. Method of calculation is correct, not Δx / Δy. Both read-offs must be accurate to half a small square in both the x and y directions. 1 y-intercept: Either Correct read-off from a point on the line substituted into y = mx + c or an equivalent expression, with read-off accurate to half a small square in both x and y directions. Or Intercept read directly from the graph, with read-off at h = zero accurate to half a small square in y direction. 1 1(d) P equal to candidate’s gradient, and Q equal to candidate’s intercept. Values must not be written as fractions. 1 Units for P and Q correct and consistent with value (e.g. no unit for P, cm for Q) 1 1(e) Correct calculation of ρ, with correct unit 1 Value of ρ on answer line given to 2 or 3 s.f. 1

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2 In this experiment, you will investigate the oscillations of a spring system. (a) (i) • Assemble the apparatus as shown in Fig. 2.1. clamp boss chain of springs ≈ 55 cm stand boss clamp bench Fig. 2.1 • Adjust the apparatus so that the rods of the clamps are approximately 55 cm apart, as shown. • Roll the modelling clay into a sphere. • Measure and record the diameter d of the sphere. d = ................................................... cm [2] (ii) Estimate the percentage uncertainty in your value of d. Show your working. percentage uncertainty = ..................................................... % [1] (b) • Cut the sphere in half. • Reverse the two halves and then press them together firmly around the joint between the first and second springs, as shown in Fig. 2.2. modelling clay modelling clay Fig. 2.2 • Record the number n of springs above the modelling clay. n = ............................................................... • Pull the modelling clay down a short distance and release it so that it oscillates vertically. • Determine the period T of the oscillations. T = ............................................................... [3] (c) • Remove the modelling clay from the springs. • Cut away a quarter of the clay and roll the remaining modelling clay into a sphere. • Measure and record d. d = ........................................................ cm • Repeat (b) but this time press the modelling clay around the joint between the second and third springs. n = ............................................................... T = ............................................................... [3] (d) It is suggested that the relationship between d, n and T is d 3n (4 – n) = kT 2 where k is a constant. (i) Using your data, calculate two values of k. first value of k = ............................................................... second value of k = ............................................................... [1]

Mark scheme: 2(a)(i) All raw values of d to nearest mm. 1 Evidence of repeat readings for d. 1 2(a)(ii) Absolute uncertainty of 2 to 5 mm and correct method of calculation to obtain percentage uncertainty in d. If several readings have been taken, then the absolute uncertainty can be half the range (but not zero if values are equal) provided the working is clearly shown. 1 2(b) n = 1 1 Value for T in range 0.35 to 0.55 s, with unit. 1 At least two measurements of at least 5T. 1 2(c) (second d) ÷ (first d) in range 0.85 to 0.95 1 Second value for T. 1 Quality: second T longer than first T. 1 2(d)(i) Two values of k calculated correctly. 1 2(d)(ii) Justification for sig. fig. in k linked to sig. fig. in d and T 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 2(f)(i) Two k values are not enough to draw a valid conclusion Difficult to roll the clay into a sphere / diameter of sphere varies Parallax error when measuring d Clay covers some coils as well as the joint Difficult to judge the start and/or end of an oscillation Time period is short so it is difficult to count the oscillations Some horizontal oscillation as well as vertical 4 max 4 Question Answer Marks 2(f)(ii) Take more readings and plot a graph / calculate more k values and compare Improved method to make a perfect sphere Improved method of measuring d, e.g. use calipers / measure between blocks Method to prevent touching coils, e.g. denser material / improved shape / improved mounting method Put a fiducial mark at the centre of the oscillation Use video with timer in view / video and review frame by frame 4 max 4

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