Cambridge A Level Physics 9702 — 2020 Oct/Nov Paper 5 · Variant 1

1 A student investigates a spring of width w made from a metal wire, as shown in Fig. 1.1. w metal wire Fig. 1.1 The student constructs several springs, each made from a metal wire of different cross-sectional area A. The student investigates how the extension x of each spring varies with A when a load of mass m is applied. It is suggested that the relationship between x and A is mgw3N An x = γρ where g is the acceleration of free fall, ρ is the density of the metal, N is the number of turns of wire in the spring and γ and n are constants. Design a laboratory experiment to test the relationship between x and A. Explain how your results could be used to determine values for γ and n. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to: ● the procedure to be followed ● the measurements to be taken ● the control of variables ● the analysis of the data ● any safety precautions to be taken. 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Mark scheme: 1 Defining the problem A is the independent variable and x is the dependent variable or vary A and measure x 1 keep m constant 1 Methods of data collection labelled diagram of workable experiment including: • spring fixed at one end (to a support) • load attached to the other end • labelled load/mass 1 clamped labelled ruler perpendicular by eye and ruler positioned close to the spring 1 method to determine x: record initial position, record final position and subtraction or record length of stretched spring, original length of spring and subtraction 1 use of a micrometer/calipers to determine diameter d of wire 1 Method of Analysis plots a graph of lg x against lg A or equivalent 1 n = gradient and relationship valid if a straight line 1 3 -intercept 10y mgw N γ ρ = × 1 Question Answer Marks 1 Additional detail including safety considerations 6 D1 use safety goggles/safety screen to prevent injury to eyes from (moving) spring/load or use cushion/sand box in case load falls D2 keep constant all of: • w • N • ρ (or use same material for wire) D3 measure mass of load/m with a balance or use newton meter to measure weight of load D4 use ruler/calipers to measure the width of the spring/w D5 use the equation ρ = mass of metal / volume to calculate ρ D6 method to measure w, e.g. w measured to the outside and subtract d or method to measure ρ, e.g. mass (balance) and volume (measuring cylinder) D7 repeat measurement of x (for the same A) and average D8 repeat measurements of either d or w made in different places/directions and average D9 use of A = πd2 / 4 to determine A of wire D10 use of set square to check that clamped ruler is vertical to bench or use of set square/pin as a fiducial mark to read positions (on the ruler)

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2 A student investigates the image of an object formed on a screen by a converging lens, as shown in Fig. 2.1. d ho object screen lens Fig. 2.1 The student measures the height ho of the object and the distance d from the lens to the screen. The height hi of the image is measured as shown in Fig. 2.2. screen hi Fig. 2.2 The experiment is repeated for different values of d. It is suggested that hi and d are related by the equation 1 t h i d + = + 1 f c 2 m h o where f is a property of the lens called the focal length and t is the thickness of the lens. hi (a) A graph is plotted of on the y-axis against d on the x-axis. ho Determine expressions for the gradient and y-intercept. gradient = ............................................................... y-intercept = ............................................................... [1] (b) The value of ho is (2.4 ± 0.1) cm. Values of d and hi are given in Table 2.1. Table 2.1 hi d / cm hi / cm ho 54.0 1.7 ± 0.1 57.5 1.9 ± 0.1 61.5 2.2 ± 0.1 67.0 2.6 ± 0.1 74.0 3.1 ± 0.1 80.5 3.6 ± 0.1 hi Calculate and record values of in Table 2.1. ho hi Include the absolute uncertainties in . [2] ho hi(c) (i) Plot a graph of against d / cm. ho hi Include error bars for . [2] ho (ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2] (iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer. gradient = ......................................................... [2]

Mark scheme: 2(a) gradient = 1 f y-intercept = 1 2 t f − 1 2(b) i o h h 0.71 or 0.708 0.79 or 0.792 0.92 or 0.917 1.1 or 1.08 1.3 or 1.29 1.5 or 1.50 1 Absolute uncertainties in i o h h from ± 0.07 to ± 0.1 (or ± 0.10 or ± 0.11). 1 2(c)(i) Six points plotted correctly. Must be accurate to nearest half a small square. Diameter of points must be less than half a small square. 1 Error bars in i o h h plotted correctly. All error bars must be plotted. Total length of bar must be accurate to less than half a small square and symmetrical. 1 Question Answer Marks 2(c)(ii) Line of best fit drawn. Points must be balanced. Do not accept line from top to bottom point. Line must pass between (55, 0.75) and (56, 0.75) and between (77, 1.40) and (78, 1.40). 1 Worst acceptable line drawn (steepest or shallowest possible line that passes through all the error bars). All error bars must be plotted. 1 2(c)(iii) Gradient determined with clear substitution of data points into Δy / Δx. Distance between data points must be at least half the length of the drawn line. 1 Gradient of worst acceptable line determined. uncertainty = (gradient of line of best fit – gradient of worst acceptable line) or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) 1 2(c)(iv) y-intercept determined from substitution into y = mx + c. 1 y-intercept determined using gradient from worst acceptable line. uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line or uncertainty = ½ (steepest worst line y-intercept – shallowest worst line y-intercept) No ECF from false origin method. 1 Question Answer Marks 2(d)(i) f determined using gradient with correct substitution shown. = = 1 1 gradient f (c)(iii) 1 f determined using gradient and given to two or three significant figures and correct SI unit shown with correct power of ten e.g. 33 cm or 0.33 m or 33.1 cm or 0.331 m 1 Absolute uncertainty in f determined. Δ = × gradient absolute uncertainty in gradient f f 1 2(d)(ii) t determined using y-intercept and given to two or three significant figures. Correct substitution of numbers required. ( ) 2 -intercept 1 t f y = × + or ( ) × + = 2 -intercept 1 gradient y t 1

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