A-LevelPhysicsOscillations9702/31 · May/June 2017 · Q220 Marks

In this experiment, you will investigate the motion of oscillating table tennis balls.

(a)Tape each ball to a length of string. Ensure the total length of the string and ball is 35.0 cm, as shown in [Figure 2.1].
(b)(i)Set up the apparatus as shown in [Figure 2.2].
(b)(ii)Pull one of the balls towards you through a short distance. Release the ball and determine the time for five complete oscillations. Repeat for the other ball. time = ..................................................... s time = ..................................................... s [1][1]
(b)(iii)Remove the balls and strings from the wooden rod.
(c)(i)Tape the shorter wooden block to one of the balls as shown in [Figure 2.3]. Tape should be used on opposite sides of the block and the ball.
(c)(ii)Measure and record x. x = ..................................................... [1][1]
(c)(iii)Estimate the percentage uncertainty in your value of x. percentage uncertainty = ..................................................... [1][1]
(d)(i)Set up the apparatus as shown in [Figure 2.4].
(d)(ii)Pull both balls towards you. Release the balls at the same time and watch the movement. The two balls will move backwards and forwards becoming out of phase. After a time they will be back in phase so that they move towards you together. The ball with the block attached completes n oscillations in this time.
(e)(i)Repeat (d)(ii) and record n. n = ..................................................... [2][2]
(e)(ii)Calculate (n + 1)²/n². (n + 1)²/n² = ..................................................... [1][1]
(f)Using the longer wooden block, repeat (c)(i), (c)(ii), (d) and (e). x = ..................................................... n = ..................................................... (n+1)²/n² = ..................................................... [3][3]
(g)(i)It is suggested that the relationship between n and x is (n + 1)²/n² = kx where k is a constant. Using your data, calculate two values of k. first value of k = ..................................................... second value of k = ..................................................... [1][1]
(g)(ii)Explain whether your results in (g)(i) support the suggested relationship. [1][1]
(h)The effective length of the pendulum formed by the ball and string is L. Use your second value of k to calculate L using the relationship k = 1/L. Give your answer to three significant figures. L = ..................................................... [1][1]
(i)(i)Describe four sources of uncertainty or limitations of the procedure for this experiment. 1. ................................................................................................................................................ 2. ................................................................................................................................................ 3. ................................................................................................................................................ 4. ................................................................................................................................................ [4][4]
(i)(ii)Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures. 1. ................................................................................................................................................ 2. ................................................................................................................................................ 3. ................................................................................................................................................ 4. ................................................................................................................................................ [4][4]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[1] Values of time in the range 3–7 s and within 0.4s of each other. All raw readings stated to same precision and to at least 0.1 s.
[1] x on the answer line in the range 35.0–40.0 cm and all value(s) of raw x to nearest mm with unit.
[1] Absolute uncertainty in x in range 2–5 mm. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. Correct method of calculation to obtain percentage uncertainty.
[1] Value of n on answer line in the range 10 to 20. No unit.
[1] Evidence of repeat readings.
[1] Correct calculation of (n + 1)²/n².
[1] Second value of x.
[1] Second value of n.
[1] Quality: second value of n < first value of n (if x2 < X₁ allow n₂ > n₁).
[1] Two values of k calculated correctly.
[1] Valid comment consistent with calculated values of k, testing against a criterion specified by the candidate.
[1] Correct calculation of L written to 3 s.f. and correctly rounded to 3 s.f.
[4] A Two readings are not enough to draw a valid conclusion (not “not enough for accurate results”, “few readings”). B Difficult to judge when the balls are back in phase. C Balls hit each other/blown by moving air/balls move sideways/irregular movement. D Difficult to ensure both lengths 35 cm or difficult to measure x with a reason e.g. string kinked/parallax error. E Damping/oscillations die out quickly. F Difficulty linked to fixing block/wood with reason e.g. longer block requires more tape (therefore an unfair test)/block comes unstuck/blocks attached at an angle (x not constant). G For two/both balls the release point is different or release instant is different. 1 mark for each point up to a maximum of 4.
[4] A Take more readings and plot a graph/take more readings and compare k values (not “repeat readings" on its own). B Video/film/record and perpendicular to plane of oscillation/from the side. C Turn off air conditioning/close windows/use windshield/use a longer rod. D Improved method of measuring 35 cm or x e.g. use clamps to fix loop and ball. F Improved method of attachment e.g. Blu-Tack/glue/Velcro/stickier tape/stronger adhesive on the tape. G Improved method of release e.g. bar to hold both balls then drop away like a gate. 1 mark for each point up to a maximum of 4.