Cambridge A Level Physics 9702 — 2014 Oct/Nov Paper 3 · Variant 6

1 In this experiment, you will investigate a network of resistors. (a) (i) Assemble the circuit of Fig. 1.1. 3V d.c. supply resistance tape metre rule wire crocodile clip Mcrocodile V clip A B component holder Fig. 1.1 (ii) To check that your circuit is correct, close the switch and place the movable contact M on the resistance wire at the 50 cm mark. Record the voltmeter reading, which should be between 0.3 V and 0.7 V. voltmeter reading = ................................................. [1] (iii) Open the switch. (b) (i) Select one of the resistors labelled with a numerical value and connect it between the crocodile clips of the component holder. Record the resistance R of your selected resistor. R = ................................................. kΩ l M V A B component holder Fig. 1.2 (ii) Close the switch. Adjust the position of M on the resistance wire until the voltmeter reads zero. Measure and record the length l as shown in Fig. 1.2. l = ................................................. [1] (iii) Open the switch. (c) Repeat (b) using different labelled resistors in the component holder until you have six 1 1 sets of values of R and l. Include values of and in your table. R l [10] 1 1 (d) (i) Plot a graph of on the y-axis against on the x-axis. [3] l R (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ...................................................... y-intercept = ...................................................... [2] (e) The quantities l and R are related by the equation 1 a = + b l R where a and b are constants. Use your answers in (d)(iii) to determine the values of a and b. Give appropriate units. a = ...................................................... b = ...................................................... [2] You may not need to use all of the materials provided.

Mark scheme: 1 (a) (ii) Value of voltmeter reading with unit in range 0.30 V < V < 0.70 V. [1] (b) (ii) Value of l with unit in range 20 cm < l < 80 cm. [1] (c) Six sets of readings of R and l scores 5 marks, five sets (or use of R = 0) scores 4 marks etc. [5] Incorrect trend –1. Major help from Supervisor –2. Minor help from Supervisor –1. Range: [1] Values of R must include 0.22 kΩ or 0.33 kΩ, and 4.7 kΩ or 3.3 kΩ. Column headings: [1] Each column heading must contain a quantity and a unit. The presentation of quantity and unit must conform to accepted scientific convention e.g. 1 / R / kΩ–1 or 1 / R (kΩ)–1, 1 / l (m–1) or 1 / l (1 / m) but not 1 / R / k–1Ω–1, 1 / R(kΩ) or 1 / l (m). Consistency: [1] All values of raw l must be given to the nearest mm only. Significant figures: [1] Every value of 1 / l must given to the same s.f. as (or one greater than) the s.f. in raw l. Calculation: [1] Values of 1 / R calculated correctly to the number of significant figures given by the candidate. (d) (i) Axes: [1] Sensible scales must be used, no awkward scales (e.g. 3:10). Scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Scales must be labelled with the quantity that is being plotted. Scale markings should be no more than three large squares apart. Plotting: [1] All observations in the table must be plotted. Diameter of points must be ≤ half a small square (no “blobs”). Plotted points must be accurate to within half a small square. Quality: [1] All points in the table must be plotted (at least 5) for this mark to be awarded. Scatter of points must be less than ± 0.001 cm–1 of 1 / l from a straight line. (ii) Line of best fit: [1] Judge by balance of all points on the grid about the candidate’s line (at least 5 points). There must be an even distribution of points either side of the line along the full length. Allow one anomalous point only if clearly indicated (i.e. circled or labelled) by the candidate. Lines must not be kinked or thicker than half a small square. (iii) Gradient: [1] The hypotenuse of the triangle must be greater than half the length of the drawn line. Both read-offs must be accurate to half a small square in both the x and y directions. y-intercept: [1] Either: Correct read-off from a point on the line substituted into y = mx + c. Read-off must be accurate to half a small square in both x and y directions. Or: Correct read-off of the intercept directly from the graph. (e) a = the value of the gradient and b = the value of the y-intercept. [1] Unit for a and unit for b consistent with values given. [1] e.g. kΩ m–1 for a and m–1 for b. [Total: 20]

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2 In this experiment, you will investigate the motion of a partially-filled bottle. (a) (i) Place the stand in the tray and suspend the empty bottle from the nail, as shown in Fig. 2.1. Check that the bottle swings freely. stand nail boss clamp L bottle tray benchbench Fig. 2.1 (ii) Measure and record the distance L from the base of the bottle to the nail, as shown in Fig. 2.1. L = .......................................... mm [1] (b) (i) Pour water into the bottle until it is approximately half full, as shown in Fig. 2.2. d benchbench Fig. 2.2 (ii) With the bottle hanging vertically, measure and record the distance d from the base of the bottle to the water surface, as shown in Fig. 2.2. d = ........................................... mm [1] d (iii) Calculate the ratio c using the relationship c = . L c = ...................................................... (iv) Justify the number of significant figures that you have given for your value of c. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ............................................................................................................................. [1] (c) Calculate the value of q using the relationship c2 − c + 1 3 q = . c 1 − 2 q = ................................................. [1] (d) (i) Push the base of the bottle approximately 4 cm to one side and then release it so that it swings, as shown in Fig. 2.3. Ensure that the stand does not fall over when the bottle is swinging. one complete swing Fig. 2.3 (ii) Measure and record the total time t for 10 complete swings. t = ................................................. [2] (iii) Estimate the percentage uncertainty in your value of t.

Mark scheme: 2 (a) (ii) Value of L in range 150 mm < L < 250 mm and to nearest mm only. [1] (b) (ii) Value of d = 0.5L ± 20 mm. [1] (iv) Correct justification of significant figures in c linked to significant figures in L and d. [1] (c) Correct calculation of q. [1] (d) (ii) Value of raw t to 0.1 s or better, with unit, in range 6 s < t < 20 s. [1] Evidence of repeat measurements of t. [1] (iii) Absolute uncertainty in t in range 0.2 s to 0.5 s. If repeated readings have been taken, uncertainty can be half the range (but not zero) if the working is shown. Method of calculation to obtain percentage uncertainty must be correct. [1] (e) (ii) Second value of d. [1] Second value of t. [1] Quality: Correct trend for t with respect to d (t decreases as d increases). [1] (f) (i) Two values of k calculated correctly. [1] (ii) Valid comment consistent with calculated values of k, testing against a stated criterion e.g. “The calculated percentage difference between k values is less than the percentage uncertainty found in (d)(iii), so the relationship is valid”. [1] (g) (i) Limitations (4 max.) (ii) Improvements (4 max.) Do not credit A Two readings not enough to Take more readings (for Not enough readings / draw a conclusion different d) and plot a graph / repeat readings / take more readings and few readings / compare k values too few readings / ‘two readings’ (on its own) B Difficult to measure L or d Improved method to Marks on bottle / finding with reason e.g. parallax / measure L or d e.g. detailed centre of nail / meniscus transparent liquid / use of set square on bench / problem hanging above bench / colour water / add scale to bottle not vertical / bottle / place bottle on bench bottle not uniform and use rule C Difficult to judge the end of Improved method of timing Release height / amplitude oscillation e.g. video with timer / varies / human reaction video and view frame by time / video and play back / frame / put marker at the high speed camera / centre of oscillation / slow motion camera / motion sensor with correct use of motion sensor / position i.e. placed so the use of light gates / bottle moves towards and away from it. D d varies as bottle swings Use sand (or named material that can be poured) E Difference in t values is Use larger change in depths Use longer bottle / small t is small F Stand (or nail) moves while Method to stabilise clamp (or Glue stand to bench bottle oscillates nail) e.g. G-clamp / add weight to stand / clamp nail between wooden blocks Do not credit: damping / release force / friction / hitting stand / fans / problems with counting / use computer / just “use data logger” on its own. [Total: 20]

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