Cambridge A Level Physics 9702 — 2020 May/June Paper 5 · Variant 3

1 A student investigates springs made of metal wire, as shown in Fig. 1.1. cross-sectional area A metal wire Fig. 1.1 The student constructs several springs from wire of thickness t. Each spring has a different cross-sectional area A. The student investigates how the spring constant k varies with A. It is suggested that the relationship between k and A is βρt 4 k = 3 A 2N where ρ is the density of the metal, N is the number of turns of wire on the spring and β is a constant. Design a laboratory experiment to test the relationship between k and A. Explain how your results could be used to determine a value for β. 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. Diagram .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .................................................................................................................................................................. .......................................................................................................................................................... [15]

Mark scheme: 1 Defining the problem A is the independent variable and k is the dependent variable or vary A and measure k 1 keep N 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 of the spring • labelled load 1 method to measure mass or weight of load: use top-pan balance to measure mass or newton meter to measure weight 1 use of a micrometer/calipers to determine t and rule/calipers to measure the diameter of the spring 1 method to measure extension, e.g. labelled ruler drawn parallel to spring, equilibrium position and displaced position indicated and x indicated or description of use of ruler to measure equilibrium position and displaced position and difference determined 1 Method of analysis plot a graph of k against 1 / A3/2 (or A–3/2) or equivalent e.g. lg k against lg A 1 relationship valid if a straight line passing through the origin is produced (for lg k against lg A, relationship valid if a straight line with gradient –3/2) 1 4 gradient N t β ρ × = [for lg k against lg A, β = 10y-intercept × N / (ρt4) ] 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 t constant D3 or mg F k x x = D4 use of set square when taking measurements to determine extension of spring D5 repeat measurement of t along wire/spring and average D6 repeat measurement of diameter D of spring (to determine A) in different directions and average D7 use of 2 4 D A π = D8 method to ensure clamped rule to measure extension is vertical, e.g. correctly positioned set square indicated at right angles between the rule and the horizontal surface or plumb line shown in appropriate position D9 method to determine the density of the wire or additional detail on construction of coil D10 method to determine the mean diameter of the spring, e.g. subtract t from external diameter of spring Question Answer Marks

More questions on Physical quantities

2 A student investigates the discharge of a capacitor through a resistor using the circuit shown in Fig. 2.1. C V R Fig. 2.1 The student initially closes the switch and charges the capacitor. The switch is then opened and a stop-watch is started. The capacitor discharges through the resistor. At time t the potential difference V across the capacitor is measured. It is suggested that V and t are related by the equation t 0 c RC m e - V = o e QC where Q0 is the charge of the fully charged capacitor, C is the capacitance of the capacitor and R is the resistance of the resistor. (a) A graph is plotted of ln V on the y-axis against t on the x-axis. Determine expressions for the gradient and y-intercept. gradient = ............................................................... y-intercept = ............................................................... [1] (b) Values of t and V are given in Table 2.1. Table 2.1 t / s V / V ln (V / V) 0 6.2 ± 0.2 6 4.6 ± 0.2 12 3.4 ± 0.2 18 2.6 ± 0.2 24 2.0 ± 0.2 30 1.4 ± 0.2 Calculate and record values of ln (V / V) in Table 2.1. Include the absolute uncertainties in ln (V / V). [2] (c) (i) Plot a graph of ln (V / V) against t / s. Include error bars for ln (V / V). [2] (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 CR − y-intercept = ln 0 Q C 1 2(b) ln (V / V) 1.82 or 1.825 1.53 or 1.526 1.22 or 1.224 0.96 or 0.956 0.69 or 0.693 0.34 or 0.336 1 Absolute uncertainties in ln V from ± 0.03 or ± 0.04 to ± 0.13 or ± 0.14 or ± 0.15. 1 2(c)(i) Six points plotted correctly. Must be within half a small square. Diameter of points must be less than half a small square. 1 Error bars in ln V plotted correctly. All error bars to be plotted. Length of bar must be accurate to less than half a small square and symmetrical. 1 2(c)(ii) Line of best fit drawn. Points must be balanced. Do not accept top point to bottom point. Line must pass between (4.0, 1.6) and (5.0, 1.6) and between (26.5, 0.5) and (28.0, 0.5) 1 Worst acceptable line drawn (steepest or shallowest possible line that passes through all the error bars). All error bars must be plotted. 1 Question Answer Marks 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. Gradient must be negative. 1 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 read from y-axis to less than half a small square or y-intercept determined from substitution into y = mx + c. 1 2(d)(i) C determined using gradient and C and Q0 given to two or three significant figures. Correct substitution of numbers required. 3 3 1 1 39 10 gradient 39 10 C − − = = × × × × (c)(iii) 1 Q0 determined using y-intercept. -intercept 0 y Q C e C e = × = × (c)(iv) 1 C determined using gradient and Q0 determined using y-intercept and dimensionally correct units for C (F or s Ω–1) and Q0 (C or V s Ω–1 or A s). 1 2(d)(ii) Absolute uncertainty in C. gradient 0.05 gradient C C   Δ Δ = + ×     1 Question Answer Marks 2(e) V determined from (d)(i) (or (c)(iii) and (c)(iv)) with correct substitution shown and correct power of ten. ( ) 60 gradient 60 -intercept 0 y CR Q V e e e C − × = × = × or ln V = – (t / RC) + ln (Q0 / C) = – (60 / 39 000) × (d)(i) + ln (Q0 / C) ln V = 60 × gradient + y-intercept ln V = 60 × (c)(iii) + (c)(iv) 1

More questions on Errors and uncertainties