Cambridge A Level Physics 9702 — 2013 Oct/Nov Paper 5 · Variant 3

1 A student is investigating how the resistance R of nichrome in the form of a wire varies with For temperature θ. Examiner’s Use It is suggested that R = R0(1 + aθ) where R0 is the resistance at 0 °C, a is a constant and θ is the temperature measured in °C. Design a laboratory experiment to test the relationship between θ and R and determine the value of a. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to (a) the procedure to be followed, (b) the measurements to be taken, (c) the control of variables, (d) the analysis of the data, (e) the safety precautions to be taken. [15] Diagram For Examiner’s Use ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... For ......................................................................................................................................................... Examiner’s Use ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... Defining the Methods of Method of Safety Additional For problem data collection analysis considerations detail Examiner’s Use

Mark scheme: 1 Planning (15 marks) Defining the problem (3 marks) P θ is the independent variable or vary θ. [1] P R is the dependent variable or measure R. [1] P Keep length of wire constant. [1] Methods of data collection (5 marks) M Labelled diagram of apparatus: wire in oil/water bath or oven or beaker with water and source of heat. [1] M Circuit diagram to measure resistance. [1] M Use thermometer to measure the temperature of wire/water/oven. (Could be on diagram if labelled.) [1] M Method to determine resistance from circuit, e.g. read off ohmmeter/R = V/I [1] M Method to determine R0 e.g. use ice-water mixture. Do not allow ice (allow ice at 0 °C or melting ice). [1] Method of analysis (2 marks) Do NOT allow log-log graphs. A R against θ R/R0 against θ θ against R [1] A α = gradient/R0 α = gradient α = 1/ (R0 × gradient) [1] α = – 1/y–intercept Safety considerations (1 mark) S Reasoned method to prevent injury from hot water/hot wire e.g. gloves (to prevent injury) from hot water/wire; goggles to prevent splashes from hot water; do not touch hot wire/beaker. [1] Additional detail (4 marks) D Relevant points might include [4] 1 Use insulated wire 2 Use long/thin wire to increase resistance 3 Stir liquid 4 Wait for temperature to stabilise 5 Relationship is valid if straight line, provided plotted graph is correct 6 Relationship is valid if straight line not passing through origin, provided plotted graph is correct (any quoted expression must be correct, e.g. y-intercept = R0) 7 Use small current to minimise heating effect Do not allow vague computer methods. [Total 15] GCE AS/A LEVEL – October/November 2013 9702 53

More questions on Resistance and resistivity

2 A student is investigating the stopping distance for a motorcycle with high-performance For brakes. A motorcyclist riding and stopping a motorcycle on a test track is recorded on film. Examiner’s Use v Fig. 2.1 The stopping distance d is measured for different speeds v. Question 2 continues on the next page. It is suggested that v and d are related by the equation For 2 Examiner’s v Use d = + vt 2 a where a is the deceleration of the motorcycle and t is the thinking time of the rider. d(a) A graph is plotted of on the y-axis against v on the x-axis. Determine expressions for v the gradient and y-intercept in terms of a and t. gradient = ..................................................... y-intercept = ...................................................... [1] (b) Values of v and d are given in Fig. 2.2. v / m s–1 d / m 10 ± 1 13.0 ± 0.5 15 ± 1 24.5 ± 0.5 20 ± 1 39.5 ± 0.5 25 ± 1 57.5 ± 0.5 30 ± 1 79.0 ± 0.5 35 ± 1 103.0 ± 0.5 Fig. 2.2 d d Calculate and record values of / s in Fig. 2.2. Include the absolute uncertainties in . v v [3] d d(c) (i) Plot a graph of / s against v / m s–1. Include error bars for . Do not include v v horizontal error bars for 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 uncertainty in your answer. gradient = ................................................ [2] 3.2 For Examiner’s Use d / s v 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 5 10 15 20 25 30 35 40 v / m s–1

Mark scheme: 2 Analysis, conclusions and evaluation (15 marks) Mark Expected Answer Additional Guidance (a) A1 Gradient = 1/2a y-intercept = t (b) T1 d/v /s Column heading. Allow equivalent unit. T2 1.3 or 1.30 A mixture of 2 s.f. and 3 s.f. is allowed. 1.6 or 1.63 2.0 or 1.98 2.3 or 2.30 2.6 or 2.63 2.9 or 2.94 U1 ±0.2 / ±0.16 to ±0.09 / ±0.1 Uncertainties in d/v. (c) (i) G1 Six points plotted correctly Must be within half a small square. Ecf allowed from table. Penalise “blobs”. U2 All error bars in d/v plotted correctly Must be within half a small square. Ecf allowed from table. (ii) G2 Line of best fit If points are plotted correctly then lower end of line should pass between (9.5, 1.3) and (10.5, 1.3) and upper end of line should pass between (34.0, 2.9) and (35.5, 2.9). Allow ecf from points plotted incorrectly – examiner judgement. G3 Worst acceptable straight line. Line should be clearly labelled or Steepest or shallowest possible dashed. Should pass from top of top line that passes through all the error bar to bottom of bottom error bar or error bars. bottom of top error bar to top of bottom error bar. Mark scored only if error bars are plotted. (iii) C1 Gradient of best fit line The triangle used should be at least half the length of the drawn line. Check the read offs. Work to half a small square. Do not penalise POT. U3 Uncertainty in gradient Method of determining absolute uncertainty Difference in worst gradient and gradient. GCE AS/A LEVEL – October/November 2013 9702 53 (iv) C2 y-intercept of best fit line Check substitution in y = mx + c. Should be about 0.6 – 0.7. FOX does not score. U4 Uncertainty in y-intercept Check substitution in y = mx + c. Difference in worst y-intercept and y-intercept. FOX does not score. Allow ecf from (c)(iv). (d) (i) C3 a = 1/(2 × gradient) and in the Allow 7.3 to 7.7. range 7.25 to 7.74 and given to 2 s.f. or 3 s.f. C4 t = y-intercept and units for a [m s–2] and t [s] (ii) U5 Percentage uncertainties in a and t Percentage uncertainty in gradient. Percentage uncertainty in y-intercept. [Total 15] Uncertainties in Question 2 (c) (iii) Gradient [U3] Uncertainty = gradient of line of best fit – gradient of worst acceptable line Uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) (iv) [U4] Uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line Uncertainty = ½ (steepest worst line y-intercept – shallowest worst line y-intercept) (d) (ii) [U5] ∆ a ∆ m Percentage uncertainty in a = × 100 = × 100 a m ∆ t ∆ c Percentage uncertainty in t = × 100 = × 100 t c

More questions on Equations of motion