Cambridge A Level Physics 9702 — 2016 Oct/Nov Paper 3 · Variant 4

1 In this experiment, you will investigate the oscillations of a wooden strip. (a) Set up the apparatus as shown in Fig. 1.1, with the distance x approximately equal to 25 cm. boss rod of clamp stand string spring loop nail wooden strip boss x bench Fig. 1.1 (b) (i) Ensure that the spring is vertical and the wooden strip is parallel to the bench. (ii) Measure and record the distance x between the string loop and the end of the wooden strip, as shown in Fig. 1.1. x = ............................................... [1] (iii) Push down the free end of the wooden strip by approximately 2 cm. Release it so that it oscillates. (iv) Take measurements to find the period T of the oscillations. Record T. T = .............................................. s [2] (c) Vary x by moving the string loop along the wooden strip and repeat (b) until you have six sets of values for x and T. Do not use values of x less than 15 cm. 1 Include values for 2 in your table. T [9] 1 (d) (i) Plot a graph of 2 on the y-axis against x on the x-axis. [3] T (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 x and T are related by the equation 1 = px + q T 2 where p and q are constants. Use your answers from (d)(iii) to determine the values of p and q. Give appropriate units. p = .................................................... q = ..................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1 (b) (ii) Value for x in range 24.0 cm to 26.0 cm, with unit. [1] (iv) Value for T in range 0.30 s to 1.00 s. [1] Evidence of repeat readings (at least two recordings of nT where n ⩾ 5). [1] (c) Six sets of values for x and T (with correct trend and without help from Supervisor) scores 4 marks, five sets scores 3 marks etc. [4] Range: [1] xmin ⩽ 20.0 cm and xmax ⩾ 30.0 cm. Column headings: [1] Each column heading must contain a quantity and an appropriate unit. The presentation of the quantity and unit must conform to accepted scientific convention e.g. 1 / T2 (s–2) or 1 / T2 / 1 / s2. Consistency: [1] All values of x must be given to the nearest mm. Significant figures: [1] Every value of 1/T2 must be given to the same number of s.f. as (or one greater than) the number of s.f. in the corresponding times. Calculation: [1] Values of 1/T 2 calculated correctly to the number of s.f. given by the candidate. (d) (i) Axes: [1] Sensible scales must be used. Awkward scales (e.g. 3:10, fractions or non- linear) are not allowed. 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 of points: [1] All observations in the table must be plotted on the grid. Diameter of plotted points must be ⩽ half a small square (no “blobs”). Points must be plotted to an accuracy of half a small square. Quality: [1] All points in the table must be plotted (at least 5) for this mark to be awarded. All points must be within ± 1.0 cm (to scale) of a straight line in the x direction. (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 plot if clearly indicated (i.e. circled or labelled) by the candidate. There must be at least five points left after the anomalous point is disregarded. Line 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. The method of calculation must be correct. Do not allow ∆x / ∆y. Both read-offs must be accurate to half a small square in both the x and y directions. y-intercept: [1] Either: Check correct read-off 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 (accurate to half a small square. (e) Value of p = candidate’s gradient and value of q = candidate’s intercept. Do not allow fractions. [1] Units for p (e.g. cm–1 s–2) and q (e.g. s–2) correct. [1]

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2 In this experiment, you will investigate the movement of a metre rule on two sliding supports. (a) Set up the apparatus with the metre rule resting on the rods of the clamps, as shown in Fig. 2.1. The metre rule should be parallel to the bench. clamps metre rule FRONT VIEW bosses stands bench TOP VIEW base of base of bosses stand stand metre rule rod of rod of clamp clamp Fig. 2.1 (not to scale) (b) Measure and record the length L of the wooden strip labelled A. L = ............................................... [1] (c) (i) Position the stands so that the rod of one of the clamps is supporting the metre rule at the 10 cm mark, and the rod of the other clamp is supporting the metre rule at the 90 cm mark. (ii) Using Blu-Tack, fix the wooden strip labelled A to the metre rule at the 0 cm end, as shown in Fig. 2.2. wooden FRONT VIEW strip 0 cm end bench TOP VIEW wooden strip Fig. 2.2 (not to scale) (iii) Without touching the metre rule, slowly slide the stands towards each other until their bases touch each other, as shown in Fig. 2.3. base base x1 x2 Fig. 2.3 (not to scale) (iv) Measure and record the distances x1 and x2 of the points of contact from the end of the rule, as shown in Fig. 2.3. x1 = ............................................... cm x2 = ............................................... cm [2] (x1 + x2) (v) Calculate the value of X, where X = . 2 X = ............................................... cm [1] (d) Estimate the percentage uncertainty in your value of X. percentage uncertainty = ............................................... [1]

Mark scheme: 2 (b) L in range 19.0 cm to 21.0 cm, with unit. [1] (c) (iv) Values for x1 and x2 to nearest mm and x2 > x1. [1] Evidence of repeat readings of x1 and x2. [1] (v) Correct calculation of X. [1] (d) Absolute uncertainty in X in range 2 mm to 10 mm. If repeated readings have been taken, then absolute uncertainty can be half the range (but not zero) if working is clearly shown. Correct method of calculation to obtain percentage uncertainty. [1] (e) Second value for L. [1] Second values for x1 and x2. [1] Quality: X smaller for larger L. [1] (f) (i) Two values of k calculated correctly. [1] (ii) Justification of s.f. in k based on the s.f. in L, x1 and x2. [1] (iii) Valid comment consistent with the calculated values of k, testing against a stated numerical criterion. [1] (g) Value for X = 50 cm. [1] (h) (i) Limitations [4] (ii) Improvements [4] Do not credit A Two readings not enough to draw Take more readings and plot Two readings not a conclusion graph/ enough for accurate obtain more k values and results compare Repeat readings Few readings Take more readings and calculate average k B Metre rule is not parallel to Use a second rule and measure bench/horizontal at both ends/ use a (spirit) level C Difficult to move stands with Guide for stands (fixed to Use a smooth(er) bench reason e.g. friction/ bench)/ bench is rough/ mount stands on rollers/ Use lubricant stands tend to stick put wheels on stands/ method to reduce friction e.g. sand bench with sandpaper D Difficulty with rule Use V-shaped rods/ Falls off e.g. rule skewed/ groove in rods/ moves sideways guide for ruler with some details E Difficult to measure x with reason Scale on vertical edge of rule/ Large contact area e.g parallax error/ draw a line on the rod/ difficult to tell point where rod use a thinner rod/ touches ruler replace rods with sharp edges e.g. prisms Do not allow ‘use a computer to improve the experiment’.

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