Cambridge A Level Physics 9702 — 2017 Oct/Nov Paper 5 · Variant 1

1 A student is investigating the resistance of a light-dependent resistor (LDR) separated from a source of light by different depths of water as shown in Fig. 1.1. light water LDR Fig. 1.1 It is suggested that the relationship between the resistance R of the LDR and the depth d of the LDR in the water is 4πd 2 R = K where K is a constant. Design a laboratory experiment to test the relationship between R and d. Explain how your results could be used to determine a value for K. 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 d is the independent variable and R is the dependent variable or vary d and measure R 1 keep intensity/power of light source constant 1 Methods of data collection labelled diagram showing a light source fixed above container of water with the labelled LDR positioned in the beaker 1 correct circuit diagram to measure R, e.g. V and I methods or ohmmeter 1 method to determine R, e.g. = R p.d. across LDR current or read off ohmmeter 1 method to determine d, e.g. use a ruler or drawn labelled vertical ruler adjacent to container with d indicated 1 Method of analysis plots a graph of R against d2 1 relationship valid if a straight line produced passing through the origin 1 π = K 4 gradient 1 Question Answer Marks 1 Additional detail including safety considerations Max. 6 D1 dark glasses to prevent damage to eyes due to light source or do not look directly at light source or do not touch hot lamp/use gloves to position hot lamp/heat-proof gloves to position lamp D2 dark room or shielding LDR (so as to avoid light from other sources) D3 use high intensity lamp or collimated beam or laser D4 method described to check that current in light source is constant, e.g. use an ammeter and variable resistor / variable power supply D5 keep position of light source constant or distance between light source and LDR constant D6 light source is placed close to water surface to increase intensity/reduce reflections or light source is placed further away to make it more directional D7 use tall container to give a wide range of d or R or to reduce uncertainties or use a wide container to reduce reflections D8 method to position ruler vertically to measure d described e.g. use a set square/spirit level D9 use of horizontal fiducial mark from ruler to meniscus or middle of LDR, e.g. pin or d = reading on rule at surface – reading at top of LDR D10 ensure that the electrical connections/wire to the LDR are waterproof

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2 A student is investigating how the forces acting on a bridge vary as the position of a load on the bridge is changed. The bridge is modelled as shown in Fig. 2.1 with two newton-meters providing the support forces. s T1 T2 newton-meter newton-meter x A m Fig. 2.1 A load of mass m is placed at a distance x from support A. The readings of the newton-meters T1 and T2 are recorded for different values of x. It is suggested that T1, T2 and x are related by the equation mg(s − x) − mgx T1 − T2 = s where s is the separation of the newton-meters and g is the acceleration of free fall. (a) A graph is plotted of (T1 − T2) on the y-axis against x on the x-axis. Determine expressions for the gradient and the y-intercept. gradient = ........................................................ y-intercept = ........................................................ [1] (b) Values of x, T1 and T2 are given in Fig. 2.2. x / m T1 / N T2 / N 0.100 6.9 ± 0.1 1.4 ± 0.1 0.160 6.4 ± 0.1 1.8 ± 0.1 0.220 5.9 ± 0.1 2.3 ± 0.1 0.280 5.5 ± 0.1 2.7 ± 0.1 0.340 5.0 ± 0.1 3.1 ± 0.1 0.400 4.6 ± 0.1 3.3 ± 0.1 Fig. 2.2 Calculate and record values of (T1 − T2) / N in Fig. 2.2. Include the absolute uncertainties in (T1 − T2). [2] (c) (i) Plot a graph of (T1 − T2) / N against x / m. Include error bars for (T1 − T2). [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 = −2mg s y-intercept = mg 1 2(b) (T1 –T2) / N 5.5 ± 0.2 4.6 ± 0.2 3.6 ± 0.2 2.8 ± 0.2 1.9 ± 0.2 1.3 ± 0.2 First mark for column heading and values of (T1 –T2) / N. Second mark for all uncertainties = ±0.2. 2 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 P plotted correctly. All error bars to be plotted. 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. Must not be drawn from top point to bottom point. If points are plotted correctly then upper end of line should pass between (0.125, 5.0) and (0.140, 5.0) and lower end of line should pass between (0.360, 1.5) and (0.380, 1.5). 1 Worst acceptable line drawn correctly (steepest or shallowest possible line). All error bars must be plotted. 1 2(c)(iii) Gradient determined with a triangle that is at least half the length of the drawn line. 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 determined from substitution into y = mx + c. 1 y-intercept determined using gradient of 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) m determined using candidate’s y-intercept and correct units for m and s. y y m g -intercept -intercept = = 9.81 1 s determined using candidate’s gradient and m and s given to 2 or 3 significant figures. Correct substitution of numbers must be seen. − −× = = 2mg y s 2 -intercept gradient gradient 1 2(d)(ii) percentage uncertainty in m = percentage uncertainty in y-intercept 1 percentage uncertainty in s = percentage uncertainty in gradient + percentage uncertainty in y-intercept or percentage uncertainty in s = percentage uncertainty in gradient + percentage uncertainty m Maximum/minimum methods: −× − × = y g m s 2 max -intercept 2 max max min gradient min gradient or −× − × = y g m s 2 min -intercept 2 min min max gradient max gradient or Correct substitution of numbers must be seen. 1

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