Cambridge A Level Physics 9702 — 2023 Oct/Nov Paper 5 · Variant 2

1 Two identical beakers, each of mass M, are attached to each other using string and suspended from a pulley, as shown in Fig. 1.1. pulley string surface beakers h Fig. 1.1 (not to scale) The beakers are held at rest at a height h above a surface. Cooking oil of volume V is added to one of the beakers. The beakers are released so that the beaker with the oil begins to fall. The speed of the beaker as it reaches the surface is z. It is suggested that z is related to V by the relationship 2h 2M 1 = + z2 abV b where a and b are constants. Plan a laboratory experiment to test the relationship between z and V. Draw a diagram showing the arrangement of your equipment. Explain how the results could be used to determine values for a and b. In your plan you should include: ● 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: Question Answer Marks 1 Defining the problem V is the independent variable and z is the dependent variable or vary V and measure z 1 keep h constant 1 Methods of data collection labelled diagram of workable experiment including: 1 • pulley supported by stand • stand placed on surface/bench/floor • minimum of two labels from stand, beaker, oil, surface/bench/floor, pulley, string use (metre) rule to measure h or (metre) rule correctly positioned with h marked on diagram 1 use measuring cylinder to measure V 1 timing method to measure time t of fall of beaker to determine z 1 e.g. use timer/stopwatch or use light gate(s) connected to a timer/data logger 1 Method of Analysis 1 1 1 1 1 plot a graph of against or equivalent (e.g. against ) z 2 V V z 2 Do not accept logarithms. 1 1 b = 2h  y -intercept 1 1 M  gradient gradient (for against : b = or b = − ) V z 2 ah 2h  y -intercept M 2M  y -intercept 1 a = or a = bh gradient gradient 1 1 (for against : a = −2M  y -intercept ) V z 2 1 Additional detail including safety considerations 6 D1 precaution linked to oil spillage, e.g. use of cushion/sand box/tray for falling beaker to land or use of bungs/lids on beakers or use foam on bench/floor or use foam to prevent rising beaker hitting pulley D2 precaution linked to oil contact with skin e.g. use gloves to avoid contact with oil D3 keep M constant D4 use a (top-pan) balance to measure M D5 method to keep h constant e.g. use a fiducial mark to release the beaker from the same position or release from the same position on the clamped rule each time D6 equation to determine z for method used, e.g. for timing h, z = 2h / t or for one light gate, z = L / t where L is the length of the interrupted beam or for two light gates, z = distance between light gates / t Do not accept h / t. D7 additional detail on diagram to measure h, e.g. clamp (metre) rule with stand on surface or use of set squares positioned on the surface to side of rule or spirit level positioned to side of rule D8 use large value of h to increase time of fall of beaker D9 repeat measurements of z for the same V and average z  1  D10 relationship valid if a straight line is produced (passing through   )  2bh  Do not accept line passing through the origin.

More questions on Momentum and Newton’s laws of motion

2 A student investigates the discharge of capacitors in the circuit shown in Fig. 2.1. CA CB V R Fig. 2.1 The capacitors have capacitances CA and CB. The student closes the switch to charge the capacitors. The switch is opened and a stop-watch is started. The capacitors discharge through the resistor of resistance R. At a fixed time t the voltmeter reading V is recorded. The experiment is repeated for different values of CA and CB. For each combination of CA and CB, the combined capacitance C is calculated. It is suggested that C and V are related by the equation _ t V = I0Re CR where I0 is the initial current in the resistor. 1 (a) A graph is plotted of lnV on the y-axis against on the x-axis. C Determine expressions for the gradient and y-intercept. gradient = ............................................................... y-intercept = ............................................................... [1] (b) Values of CA, CB and V are given in Table 2.1. Table 2.1 1 CA / 10– 4 F CB / 10– 4 F / 104 F–1 V / V ln (V / V) C 2.2 2.2 2.45 ± 0.05 2.2 3.3 2.75 ± 0.05 2.2 5.6 3.05 ± 0.05 3.3 3.3 3.10 ± 0.05 3.3 5.6 3.50 ± 0.05 5.6 5.6 3.85 ± 0.05 The relationship between C, CA and CB is 1 CA + CB = . C CACB 1 Calculate and record values of / 104 F–1 and ln (V / V) in Table 2.1. C Include the absolute uncertainties in ln (V / V). [2] 1 (c) (i) Plot a graph of ln (V / V) against / 104 F–1. C 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. Label both lines. [2] (iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer. gradient = ......................................................... [2]

Mark scheme: 2(a) 1 gradient = −t R y-intercept = ln I0R 2(b) 1 1 / C / 104 F–1 ln (V / V) 0.91 or 0.909 0.896 or 0.8961 0.76 or 0.758 1.012 or 1.0116 0.63 or 0.633 1.115 or 1.1151 0.61 or 0.606 1.131 or 1.1314 0.48 or 0.482 1.253 or 1.2528 0.36 or 0.357 1.348 or 1.3481 Values correct as shown above. Uncertainties in ln (V / V) from ± 0.021 or ± 0.020 to ± 0.010 or ± 0.013 1 2(c)(i) Six points from (b) plotted correctly. 1 Must be within half a small square. Diameter of points must be less than half a small square. Error bars in ln (V / V) plotted correctly. 1 All error bars to be plotted. Total length of bar must be accurate to less than half a small square and symmetrical. 2(c)(ii) Straight line of best fit drawn. 1 Do not accept line from top point to bottom point. Points must be balanced. Line must pass between (0.820, 0.95) and (0.845, 0.95) and between (0.400, 1.30) and (0.425, 1.30) Worst acceptable line drawn (steepest or shallowest possible line that passes through all the error bars). 1 All error bars must be plotted. 2(c)(iii) Gradient determined with clear substitution of data points into y / x. 1 Distance between data points must be greater than half the length of the drawn line. Gradient must be negative. Gradient determined of worst acceptable line. 1 uncertainty = (gradient of line of best fit – gradient of worst acceptable line) or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) 2(c)(iv) y-intercept determined by substitution of correct point with consistent power of ten in m and x into y = mx + c. 1 2(d)(i) R determined using gradient. 1 30.0 30.0 R = − = gradient (c)(iii) I0 determined using y-intercept with method shown. 1 e y -intercept e (c)(iv) I0 = = R (d)(i) R and I0 determined correctly using gradient and y-intercept 1 and R and I0 given to 2 or 3 significant figures and R and I0 given with SI units with appropriate powers of ten. Units: R:  or s F-1 I0: A or V F s–1 or V  –1 2(d)(ii) Percentage uncertainty in R with method shown. 1  t gradient  percentage uncertainty in R =  +   100  t gradient  or Correct substitution for max/min methods. 2(e) C determined to a minimum of 2 significant figures from (c)(iii) and (c)(iv) or (d)(i) with correct substitutions. 1 gradient gradient C = or C = − ln V − y -intercept y -intercept − ln V or t t C = − or C = R ( ln V − ln I0 R ) R ( ln I0 R − ln V )

More questions on Discharging a capacitor