Cambridge A Level Physics 9702 — 2012 Oct/Nov Paper 3 · Variant 6

1 In this experiment, you will investigate how the light intensity incident on a light sensor varies Use with distance from the light source. (a) You are provided with a lamp mounted inside one end of a black paper tube, together with a light sensor in the form of a light-dependent resistor (LDR) mounted on a half- metre rule, as shown in Fig. 1.1. resistance meter 6 V d.c. supply (ohmmeter) Ÿ LDR l half-metre paper tube lamp inside rule tube x Fig. 1.1 (b) (i) Measure and record the distance l from the lamp to the open end of the tube, as shown in Fig. 1.1. l = ...................................................... (ii) Measure and record the distance x from the front of the LDR to the end of the half-metre rule, as shown in Fig. 1.1. x = ..................................................[1] (c) (i) Push the rule into the tube until the LDR is approximately half way along the tube, For as shown in Fig. 1.2. Examiner’s Use p d l Fig. 1.2 (ii) Record the length p of the half-metre rule inside the tube. p = ...................................................... (iii) Calculate the distance d of the LDR from the lamp using d = l – (x + p). d = ...................................................... (iv) Switch on the lamp and record the resistance reading R on the resistance meter. R = ............................................ kΩ [1] (d) Repeat (c) using different values of p until you have six sets of values of p and R for For p 20 cm. Examiner’s In your table of results include values for d and d 1.5 (d 1.5 = d 3). Use [10] (e) (i) Plot a graph of R on the y-axis against d 1.5 on the x-axis. [3] (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ...................................................... y-intercept = ...................................................... [2] For Examiner’s Use (f) The quantities R and d are related by the equation For Examiner’s R = a d 1.5 + b Use where a and b are constants. Using your answers from (e)(iii), determine the values of a and b. Give appropriate units. a = ...................................................... b = ...................................................... [2] You may not need to use all of the materials provided. For Examiner’s

Mark scheme: 1 (b) (ii) Value of raw x in range 2 mm ≤ x ≤ 15 mm. Consistent with unit. [1] (c) (iv) Value of R in range 1 kΩ to 200 kΩ [1] (d) Six sets of readings of p and R scores 5 marks, five sets scores 4 marks etc. [5] Minor help from supervisor –1, major help –2. Incorrect trend / no p values / no R values then –1. Range of p: pmax – pmin ≥ 15 cm [1] Column headings: [1] Each column heading must contain a quantity and a unit. The unit must conform to accepted scientific convention e.g. d / cm, d1.5 /m1.5, d1.5 (m1.5) or d1.5 in m1.5, √d3 /√m3, R / kΩ Consistency of presentation of raw readings: [1] All raw values of p must be given to the nearest mm. Significant figures: [1] All values of d1.5 must be given to the same s.f. as (or one more than) the s.f. in d. Calculation: [1] Values of d1.5 calculated correctly. (e) (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 which is being plotted. Scale markings must be no more than 3 large squares apart. Plotting of points: [1] All observations in the table must be plotted on the graph grid. Diameter of plots must be ≤ half a small square (no “blobs”). Points must be plotted correctly to an accuracy of half a small square in both x and y directions. Quality: [1] All points in the table must be plotted (at least 5) for this mark to be scored. Judge by the scatter of all points about a straight line. All points must be within 0.005 m1.5 = 5 cm1.5 = 160 mm1.5 of a straight line, in the d1.5 direction. (ii) Line of best fit: [1] Judged by balance of all points on the grid (at least 5 points) about the candidate’s line. There must be an even distribution of points either side of the line along the full length. One anomalous point is allowed only if clearly indicated (i.e. circled or labelled) by the candidate. Line must not be kinked or thicker than half a small square. (e) (iii) Gradient: GCE AS/A LEVEL – October/November 2012 9702 36 Sign of gradient must match graph. [1] The hypotenuse of the triangle should be greater than half the length of the drawn line. Both read-offs must be accurate to half a small square in both x and y directions. The method of calculation must be correct. y-intercept: [1] Either: Check correct read-offs from a point on the line and substituted into y = mx + c. Read off must be accurate to half a small square in both x and y directions. Or: Check read-off of the intercept directly from the graph. (f) Value of a = candidate’s gradient. Value of b = candidate’s intercept. [1] Do not allow a value presented as a fraction. Unit for a (e.g. kΩ cm –1.5). [1] [Total: 20]

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2 In this experiment, you will investigate the speed of a cylindrical piston moving through water. Use (a) (i) You are provided with a container of water and a piece of modelling clay which can be moulded into a cylindrical piston. You are also provided with a card on which is written the internal diameter d0 of the container, together with two other values A and B. Mould the piece of modelling clay into a cylinder with a diameter approximately equal to value A. Measure and record the diameter d of this cylinder. d = ..................................................[1] (ii) Estimate the percentage uncertainty in your value of d. percentage uncertainty = ..................................................[1] (iii) You are also provided with a string running over a pulley. The string has a mass X attached to one end and a paperclip at the other end. Push the paperclip into the centre of your clay cylinder and lower it into the container of water, as shown in Fig. 2.1, with the clay cylinder axis vertical. pulley paper clip pushed into string modelling clay modelling clay cylinder marks on container container X bench Fig. 2.1 (iv) Measure and record the distance h between the marks on the container of water. For Examiner’s Use h = ..................................................[1] (b) (i) Raise X until the clay cylinder reaches the bottom of the container of water. Release X and take measurements to determine the time t taken for the clay cylinder to rise from the lower mark to the higher mark. t = ..................................................[2] h (ii) Calculate the average speed v of the clay cylinder between the marks using v = . t v = ..................................................[1] (iii) Justify the number of significant figures that you have given for your value of v. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[1] (c) (i) Remove the modelling clay from its paperclip and re-mould it into a cylinder with a diameter approximately equal to value B from the card. Measure and record the diameter d of the cylinder. d = ..................................................[1] (ii) Push the paperclip into the centre of your clay cylinder again and lower it into the For container of water. Repeat (b)(i) and (b)(ii). Examiner’s Use t = ...................................................... v = ...................................................... [2] (d) (i) It is suggested that the relationship between v and d is v = k (d0 – d ) where k is a constant and d0 is given on your card. Using your data, calculate two values of k. first value of k = ...................................................... second value of k = ...................................................... [1] (ii) Explain whether your results support the suggested relationship. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[1]

Mark scheme: 2 (a) (i) Value of raw d to nearest mm only, with unit. [1] (ii) Absolute uncertainty between 2 mm and 5 mm. [1] If repeated readings have been taken, then the absolute uncertainty can be half the range. Correct method used to calculate the percentage uncertainty. (iv) Value(s) of raw h in range 13.0 cm ≤ h ≤ 17.0 cm, with unit. [1] (b) (i) Value(s) of raw t in range 1.0 s to 10.0 s, with unit, to at least 0.1 s. [1] Evidence of repeat readings of t. [1] (ii) Correct calculation of v, with consistent unit. [1] (iii) Valid justification for s.f. in v based on s.f. in t and h. [1] Not just ‘raw readings’. (c) (i) Second value of d. [1] (ii) Second value of t. [1] Quality: Correct trend. When d decreases (i.e. second d value is less than first d value) t also decreases (i.e. second t value is less than first t value) or vice versa. [1] GCE AS/A LEVEL – October/November 2012 9702 36 (d) (i) Correct calculation of two values of k. [1] (ii) Sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate. [1] (e) (i) Limitations 4 max. (ii) Improvements 4 max. Do not credit A two results not enough take more readings and plot a ‘repeat readings’ on its graph / own / calculate more k values and ‘few readings’ / compare ‘take more readings and (calculate) average k’ / ‘only one reading’ B difficult to form a perfect cylinder method to make uniform cylinder pre-sized cylinders / / diameter of cylinder varied e.g. moulds / pastry cutter idea pastry cutter idea placing all plasticine inside removing off-cuts (mass must stay constant) / repeat diameter and average / no change of material C cylinder does not rise steadily / method to overcome sticking use wider tube oscillates as rises/hits sides / pulley e.g. lubricant problem linked to sticking pulley D difficult to start/stop the watch at method to improve time video to take reading / the instant when cylinder passes measurement e.g. light gates parallax linked to marks mark(s) / reaction time error with timer / video with timer or or h / reaction time error linked to start/stop of stopwatch frame by frame / motion sensor on its own / timer gates / below X video and playback knowing / judging when to start/stop stopwatch E difficult to time as the time is method to increase time larger tube small / large uncertainty in time / e.g. increase h / longer tube / cylinder moves too fast linked more plasticine / decrease mass to time of X F difficult to measure diameter of improved method for parallax error in d / cylinder due to curved shape of measurement e.g. (vernier) calipers linked to h sides calipers / set squares with detail Do not allow: repeated readings / human error using stopwatch / helpers / use a computer /use of micrometer screw gauge [Total: 20]

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