Cambridge A Level Physics 9702 — 2014 Oct/Nov Paper 3 · Variant 4

1 In this experiment, you will investigate the refraction of light by a transparent block. (a) You are provided with a sheet of paper with lines marked as shown in Fig. 1.1. The sheet is attached to a board. Stick a pin vertically into the board on the line AB approximately 3 cm to the right of A. Stick another pin vertically into the board at C. approx. 3 cm A B pins board C D E Fig. 1.1 (not to scale) (b) (i) View the two pins horizontally from the direction shown in Fig. 1.2. Stick the third pin into the board on the curved line so that it is in line with the first two pins. A B C D third pin S E view pins from this direction Fig. 1.2 (not to scale) (ii) Measure and record the perpendicular distance p from the third pin to the line DE, as shown in Fig. 1.2. p = ................................................... cm [1] (iii) Remove the third pin from the board. (c) (i) Place the semicircular block on the board with its centre mark next to the pin at C, as shown in Fig. 1.3. (ii) View the first two pins horizontally from the direction shown in Fig. 1.3. Look at the bottom of the first pin through the block. Stick the third pin in the board on the curved line so that it appears to be in line with the first two pins. A B block centre mark C D curved line third pin T E view pins from this direction Fig. 1.3 (not to scale) (iii) Measure and record the perpendicular distance q from the third pin to the line DE, as shown in Fig. 1.3. q = ................................................... cm [1] (iv) Remove the third pin and the block from the board. (d) Move the first pin to a different position on the line AB. Repeat (b) and (c) until you have six sets of values of p and q. q 1 Include values for and in your table. p p [10] q 1 (e) (i) Plot a graph of on the y-axis against on the x-axis. [2] p p (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ............................................................... y-intercept = ............................................................... [2] (f) The quantities q and p are related by the equation q a(1 – b) = + b p p where a and b are constants. Using your answers from (e)(iii), determine the values of a and b. Give units where appropriate. a = ................................................................ b = ................................................................ [3] You may not need to use all of the materials provided.

Mark scheme: 1 (b) (ii) Value for p in range 4.0 to 5.0 cm. [1] (c) (iii) Value for q greater than p. [1] (d) Six sets of values for p and q scores 5 marks, five sets scores 4 marks etc. [5] Incorrect trend –1. Help from Supervisor –1. Range: [1] p values must include 3.0 cm or less and 5.0 cm or more. Column headings: [1] Each column heading must contain a quantity and a unit where appropriate. Units should be shown using accepted scientific convention e.g. 1 / p / cm–1 or 1 / p (1 / cm), and q / p must have no unit. Consistency: [1] All values of p and q must be given to the nearest mm. Significant figures: [1] Every value of 1 / p must be given to the same s.f. as (or one more than) the s.f. in the corresponding p. Calculation: [1] 1 / p 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 that is being plotted. Scale markings must be no more than three large squares apart. Plotting: [1] All observations in the table must be plotted on the grid. Diameter of plotted points must be ≤ half a small square (no “blobs”). Plotted points must be accurate to within half a small square. (ii) Line of best fit: [1] Judge by the 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 plot only if clearly indicated by the candidate (i.e. circled or labelled). Line must not be kinked or thicker than half a small square. (iii) Gradient: [1] The hypotenuse must 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. y-intercept: [1] Either: 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. (f) a = gradient / (1 – intercept) and b = intercept. [1] Correct and consistent units for a (e.g. cm) and no unit for b. [1] Quality: Value for b in range 1.40 to 1.55. [1] [Total: 20]

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2 In this experiment, you will investigate the relationship between surface area and friction as a rod is hammered into a container of rice. (a) You are provided with two pencils labelled P and Q. (i) Measure and record the distance d between the opposite flat faces of pencil P, as shown in Fig. 2.1. d pencil P Fig. 2.1 d = ................................................... cm [1] (ii) Measure and record the length x between the two marks on pencil P, as shown in Fig. 2.2. first second mark mark P l x Fig. 2.2 x = ................................................... cm [1] (iii) Measure and record the length l along the flat section of the pencil to the first mark, as shown in Fig. 2.2. l = ................................................... cm [1] (b) Estimate the percentage uncertainty in your value of l. percentage uncertainty = ......................................................... [1] (c) Calculate the surface area A of the pencil up to the first mark, using the relationship A = 2 3d l . A = ......................................................... [1] (d) (i) Push the sharp end of the pencil vertically into the centre of the container of rice until the first mark is about 1 cm above the surface of the rice, as shown in Fig. 2.3. hinged wooden strip boss pencil nail first mark 1 cm rice stand container bench Fig. 2.3 (ii) Position the stand and wooden strip so that the free end of the wooden strip rests on top of the pencil. Adjust the height of the nail so that the wooden strip is horizontal, as shown in Fig. 2.3. (iii) Raise the free end of the wooden strip by 3 cm and drop it onto the pencil. Repeat until the first mark on the pencil is level with the surface of the rice. (iv) Adjust the height of the nail so that the wooden strip is horizontal again. (v) Raise the free end of the wooden strip by 3 cm and drop it onto the pencil. Repeat until the second mark on the pencil is level with the surface of the rice, counting the number n of times the wooden strip is dropped. n = .......................................................... [2] (e) Repeat (a), (c) and (d) using pencil Q. d = ............................................................... x = ............................................................... l = ............................................................... A = ............................................................... n = ............................................................... [2] (f) It is suggested that the relationship between n and A is n = k Ax where k is a constant. (i) Using your data, calculate two values of k. first value of k = ............................................................... second value of k = ............................................................... [1] (ii) Justify the number of significant figures that you have given for your values of k. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[1]

Mark scheme: 2 (a) (i) Raw value(s) for d to nearest 0.01 cm or 0.001 cm and in range 0.5 to 1.5 cm. [1] (ii) Value for x in range 2.2 to 2.8 cm. [1] (iii) Raw value(s) of l to nearest mm or better. [1] (b) Estimate of percentage uncertainty based on an absolute uncertainty of 2 to 5 mm and method of calculation correct. [1] If repeated readings have been taken, then uncertainty can be half the range (but not zero) if the working is clearly shown. (c) Correct calculation of A with consistent unit. [1] (d) (v) Value for n. [1] Evidence of repeat measurements of n. [1] (e) Second values of x and l. [1] Quality: n increases as l increases. [1] (f) (i) Correct calculation of two values of k. [1] (ii) Justification based on the s.f. in x, d and l. Ignore any reference to n or A. [1] (iii) Valid comment consistent with the calculated values of k, testing against a stated criterion e.g. “The calculated percentage difference between k values is less than the percentage uncertainty in (b), so the relationship is valid”. [1] (g) Limitations (4 max.) Improvements (4 max.) Do not credit A Two readings are not enough to draw Take many A values and plot a Repeat / too few a valid conclusion graph / take more readings and readings compare k values / repeat readings and plot graph B Difficult to measure because hard to Use a flat-ended rod judge where parallel section of pencil starts / to judge where to measure from C Pencil not vertical Use guides D Difficult to keep drop height Use a stop with detail / use a Difficult to release constant / drop height not constant fixed ruler behind strip / use strip without a pointer with detail e.g. pointer force / use fiducial mounted in a stand marker E Difficult to judge when mark reaches Use ring of card resting on rice Rice spills out of surface because rice surface uneven around pencil / measure change container during in height of pencil experiment F Difficult to judge if strip is Measure (or compare) height at horizontal / strip may not be each end / use spirit level horizontal / strip is not horizontal G Conical section of pencil not taken into account [Total: 20]

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