A-LevelPhysicsForces, density and pressure9702/33 · Oct/Nov 2018 · Q220 Marks

In this experiment, you will investigate the equilibrium of a system of three identical springs.

(a)You have been provided with three springs attached to a ring. Measure and record the unstretched length S of the coiled section of one of the springs, as [Figure 2.1]. S =[1]
(b)(i)• Set up the apparatus as [Figure 2.2]. • The total mass m of the mass hanger and the slotted masses should be 0.300 kg. • Adjust the position of the bosses so that the centres of the rods of the clamps are at the same height above the bench. • Change the separation of the stands until the angle between the springs is 90°. • The lengths S₁ and S₂ of the coiled sections of the two springs attached to the ring are shown in [Figure 2.3]. The angle between the single spring and the vertical is θ. Measure and record m, S₁, S2 and θ. m = kg S₁ = S2 = θ= °[2]
(b)(ii)Estimate the percentage uncertainty in your value of θ. percentage uncertainty =[1]
(b)(iii)Calculate e₁ cos θ and e₂ sin θ where e₁ = S₁ - S and e₂ = S₂ – S. e₁ cos θ = e₂ sin θ =[1]
(b)(iv)Justify the number of significant figures that you have given for your value of e₁ cos θ.[1]
(c)Change m to 0.600 kg and repeat (b)(i) and (b)(iii). m = kg S₁ = S2 = θ= ° e₁ cos θ = e₂ sin θ =[3]
(d)(i)It is suggested that the relationship between e₁, e₂, θ and m is e₁ cos θ + e₂ sin θ = βm where β is a constant. Using your data, calculate two values of β. first value of β = second value of β =[1]
(d)(ii)Explain whether your results support the suggested relationship.[1]
(e)Theory suggests that β = g k where the acceleration of free fall g is 9.81 m s⁻² and k is the spring constant of a spring. Using your second value of β, calculate k. Give an appropriate unit. k =[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 2018). The mark or mark type is shown in brackets.

[1] Value of S with unit in the range 0.5cm < S ≤ 2.5cm and to the nearest mm.
[1] Values of S₁ and S₂ and S₁ > S₂.
[1] Value of raw θ to the nearest degree and value of θ < 45° on answer line.
[1] Percentage uncertainty in θ based on an absolute uncertainty of 3–10°. 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] Correct calculation of e₁ cos θ and e₂ sin θ.
[1] Justification for significant figures in e₁ cos θ linked to s.f. in: (S₁ - S) and θ or e₁ and θ or S, S₁ and θ.
[1] Second values of S₁ and S₂.
[1] Quality: Second values of S₁ and S₂ greater than first values of S₁ and S₂.
[1] Second value of θ.
[1] Two values of β calculated correctly.
[1] Valid comment consistent with the calculated values of β, testing against a criterion stated by the candidate.
[1] Correct calculation of k using second value of β with a correct unit.
[1] A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results", "few readings").
[1] B Difficult to judge the vertical.
[1] C Difficult to determine angle because of parallax error or cannot see the lines defining the angle.
[1] D Difficult to determine angle because cannot hold the protractor steady.
[1] E Difficult to measure S₁ or S₂ with reason e.g. springs move or mass moves.
[1] F The stands tilt/topple/slide or the bosses twist on loading.
[1] A Take many readings (for different values of m) and plot a graph or take more values of β and compare (not "repeat readings" on its own).
[1] B Method to get vertical reference e.g. plumb line/use of set square on bench with metre rule/use spirit level vertically.
[1] C Use a larger protractor/have a protractor drawn on card at the back/use projection ideas/take a photograph and measure angle.
[1] D Clamp protractor (valid method).
[1] E Clamp ruler/take photograph with scale or ruler in the frame.
[1] F Use G-clamps/clamp the stands/use heavy weights/lower the bosses.