A-LevelPhysicsOscillations9702/32 · May/June 2017 · Q220 Marks

In this experiment, you will investigate the rotational oscillation of a combination of springs.

(a)(i)You are provided with two joined springs and three joined springs. Using the two joined springs, set up the apparatus as shown in Fig. 2.1.
(a)(ii)Measure and record the height h₁ of the bottom of the mass hanger above the bench, as shown in Fig. 2.1.[1]
(a)(iii)Add the 100g mass to the mass hanger. Measure and record the height h₂ of the bottom of the mass hanger above the bench.[1]
(a)(iv)Estimate the percentage uncertainty in your value of h2.[1]
(b)(i)Calculate the spring constant k for the combination, using the expression k = mg / (h₁-h₂) where m = 0.100 kg and g = 9.81 N kg⁻¹.[1]
(b)(ii)Justify the number of significant figures you have given for your value of k.[1]
(c)(i)Use small pieces of adhesive tape to reduce movement at the joints between components, as shown in Fig. 2.2.
(c)(ii)Rotate the mass hanger and mass through one turn and release them. The masses make rotational oscillations, as shown in Fig. 2.3.
(c)(iii)Take measurements to find the period T of the rotational oscillations.[2]
(d)Repeat (a)(ii), (a)(iii), (b)(i) and (c) using the three joined springs.[3]
(e)(i)It is suggested that the relationship between T and k is T³ = C/k² where C is a constant. Using your data, calculate two values of C.[1]
(e)(ii)Explain whether your results in (e)(i) support the suggested relationship.[1]
(f)(i)Describe four sources of uncertainty or limitations of the procedure for this experiment.[4]
(f)(ii)Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures.[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.

Value of h₁ to nearest 0.1 cm.
h₂ < h₁.
Absolute uncertainty in h₂ of 2–5 mm and correct method of calculation to obtain percentage uncertainty. If repeated readings have been taken, then the absolute uncertainty can be half the range (but not zero) if the working is clearly shown.
Correct calculation of k.
Justification for s.f. in k linked to s.f. in m, g and (h₁-h₂) or m, g, h₁ and h₂.
Value of T in range 1.00–3.00 s.
Evidence of repeat readings of nT with n ≥ 5.
Second values of h₁ and h₂.
Second value of T.
Quality: T for three springs > T for two springs.
Two values of C calculated correctly.
Valid comment consistent with the calculated values of C, testing against a criterion specified by the candidate.
A Two readings are not enough to draw a (valid) conclusion (not "not enough for accurate results”, “few readings").
B (Difficulty) measuring h because of parallax/metre rule not vertical.
C Oscillation dies away quickly/oscillation damped.
D Difficult to judge/tell end of oscillation/decide when to operate stopwatch.
E Other modes of oscillation occur.
F Some movement at joints still occurs.
1 mark for each point up to a maximum of 4.
A Take more readings and plot a graph/take more readings and compare C values (not “repeat readings" on its own).
B Use set square against rule (with detail)/use pointer attached to bottom of mass/use set square from rule to bottom of mass.
C Twist through larger angle to get more rotations.
D View (video) recording/film of motion with timer in view or put mark on mass to make it easier to see motion.
E Workable method of restricting vertical/swinging movement (e.g. enclose in transparent tube).
F Better method of fixing joints/use two complete springs.
1 mark for each point up to a maximum of 4.