A-LevelPhysicsPhysical quantities and units9702/31 · Oct/Nov 2019 · Q220 Marks

In this experiment, you will investigate the motion of two pendulums.

(a)(i)You have been provided with two pendulums. • Set up the apparatus using the pendulum that has a loop of string at the end, as shown in Fig. 2.1. [Figure 2.1] • The distance between the bottom of the lower wooden rod and the centre of the bob is x. The distance between the bottom of the upper wooden rod and the centre of the bob is L₀. Adjust the position of the lower wooden rod until x is approximately 10cm. • Measure and record x and L₀. x = L₀ =[1]
(a)(ii)Estimate the percentage uncertainty in your value of x.[1]
(b)(i)• Set up a second pendulum as shown in Fig. 2.2. [Figure 2.2] • The distance between the bottom of the split cork and the centre of the bob is L. Adjust the string in the split cork until L is approximately 30 cm. • Pull both bobs towards you through a short distance. • Release the bobs at the same time. The oscillations of the bobs will be out of phase. • Adjust L so that the oscillations of the bobs remain in phase for several cycles after release. • Measure and record L. L =[1]
(b)(ii)Calculate √L.[1]
(b)(iii)Justify the number of significant figures that you have given for your value of √L.[1]
(c)• Adjust the position of the lower wooden rod until x is approximately 35 cm. • Measure and record x. • Repeat (b)(i) and (b)(ii). x = L = √L =[3]
(d)(i)It is suggested that the relationship between L and x is 2√L = k + √x where k is a constant. Using your data, calculate two values of k. first value of k = second value of k =[1]
(d)(ii)Explain whether your results support the suggested relationship.[1]
(e)(i)• Remove the lower wooden rod. • Take measurements to determine the period T of the oscillations of the pendulum of length L₀. T=...s[1]
(e)(ii)Theory suggests that T = 2πk/√g where g is the acceleration of free fall. Use your second value of k to determine a value for g. Give appropriate units. g =[1]
(f)(i)Describe four sources of uncertainty or limitations of the procedure for this experiment. 1. 2. 3. 4.[4]
(f)(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]

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 (Oct/Nov 2019). The mark or mark type is shown in brackets.

[1] Value of x to the nearest mm with unit in the range 9.0–11.0 cm.
[1] Percentage uncertainty in x based on absolute uncertainty of 2–4 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 raw L to the nearest mm with unit and in the range 20.0-30.0 cm.
[1] Correct calculation of √L.
[1] Justification for s.f. in √L linked to s.f. in L.
[1] Second value of x.
[1] Second value of L.
[1] Quality: Second value of L > first value of L.
[1] Two values of k calculated correctly.
[1] Valid comment consistent with calculated values of k, testing against a criterion stated by the candidate.
[1] Value of T in the range 1.0–2.0 s.
[1] Correct calculation of g with correct consistent unit using second value of k.
[1] Too few readings/(only) two readings not enough to draw a (valid) conclusion (not 'not enough for accurate results', 'few readings').
[1] Difficult to determine x or L₀ or L with reason e.g. parallax error/locating centre of bob/lower curved edge of wooden rod/holding ruler by hand.
[1] Difficult to release two bobs at same instant/time.
[1] Pendulums have different amplitudes/displacements or Two oscillations have different motions so difficult to compare.
[1] Difficult to judge when the two pendulums are exactly in phase/difficult to adjust to the exact length so that the pendulums are in phase/trial and error process needed to identify when length gives same phase.
[1] Difficult to judge start of/end of/complete oscillation.
[1] Take more readings and plot a graph or take more readings and compare k values (not 'repeat readings' on its own).
[1] Measure to top and bottom of ball and take average or Take string off and measure on table or Clamp a ruler (vertically).
[1] Improved method of release e.g. card gate release.
[1] Use stop-watch and test for same period for each pendulum.
[1] Video/record/film and view with timer/frame-by-frame.