A-LevelPhysicsForces, density and pressure9702/31 · May/June 2020 · Q220 Marks

In this experiment, you will investigate the equilibrium of a metre rule.

(a)(i)You have been provided with a metre rule with two springs attached. The distance between one end of the metre rule and the string is L, as shown in Fig. 2.1. Measure and record L. L = [1][1]
(a)(ii)Calculate L/n where n = 3. L/n = [1][1]
(b)(i)• Set up the apparatus as shown in Fig. 2.2. • Adjust the apparatus until the horizontal distance between the centres of the rods of the clamps is equal to your value of L/n. • Adjust the heights of the bosses so that the rule is horizontal and the springs are vertical and unstretched when the rule is held in position. • Gradually release the rule by lowering your hand. The rule will tilt. • The angle between the rule and the horizontal is θ, as shown in Fig. 2.3. Measure and record θ. θ = ° [2][2]
(b)(ii)Estimate the percentage uncertainty in your value of θ. Show your working. percentage uncertainty = [1][1]
(b)(iii)Calculate sin θ. sin θ = [1][1]
(b)(iv)Justify the number of significant figures that you have given for your value of sin θ. [1][1]
(c)• Calculate L/n where n = 4. • Repeat (b)(i) and (b)(iii) using this value of L/n. L/n = θ = sin θ = [2][2]
(d)(i)It is suggested that the relationship between θ and n is sin θ = C(n²/2 – n) where C is a constant. Using your data, calculate two values of C. first value of C = second value of C = [1][1]
(d)(ii)Explain whether your results support the suggested relationship. [1][1]
(e)Theory suggests that C = Mg/kL where • M is the mass of the metre rule given on the card • k is the spring constant of the spring system • g = 9.81 ms⁻². Use your second value of C to determine a value for k. Give appropriate units. k = [1][1]
(f)(i)Describe four sources of uncertainty or limitations of the procedure for this experiment. 1. 2. 3. 4. [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][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 2020). The mark or mark type is shown in brackets.

[1] Value of L to the nearest mm in the range 98.5–99.5 cm with unit.
[1] Correct calculation of L/3.
[1] Measurement of θ to the nearest degree.
[1] Value of θ in the range 0°–20°.
[1] Percentage uncertainty in θ based on absolute uncertainty in the range 2°–5°. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown.
[1] Correct method of calculation to obtain percentage uncertainty.
[1] Correct calculation of sin θ.
[1] Justification for s.f. in sin θ linked to s.f. in θ.
[1] Second value of θ.
[1] Quality: Second value of θ > first value of θ.
[1] Two values of C calculated correctly.
[1] Valid comment consistent with calculated values of C, testing against a criterion stated by the candidate.
[1] Value of k correctly calculated and in the range 10–20 N m⁻¹ and with consistent unit.
[4] A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings"). B Difficult to measure θ with reason e.g. holding protractor and hand moves. C Rule slips on clamp. D Difficult to know when rule is horizontal. E Difficulty linked to setting L /n with a reason e.g. stands move suddenly/friction between bench and stands. F Difficult to hold one end of the rule and adjust the other end at the same time. 1 mark for each point up to a maximum of 4.
[4] A Take more readings and plot a graph or take more readings and compare k values (not "repeat readings" on its own). B Mount protractor on block/use another ruler and use trigonometry to determine angle. C Use adhesive putty/tape on rod. D Use spirit level/another rule to ensure horizontal. E Method to ensure smooth movement of stands e.g. mount stands on wheels/rollers. F Use a third stand and clamp to hold the free end of the rule. 1 mark for each point up to a maximum of 4.