A-LevelPhysicsForces, density and pressure9702/33 · May/June 2017 · Q220 Marks

In this experiment, you will investigate the equilibrium of a balanced metre rule and determine its mass.

(a)You have been provided with a metre rule with a hole close to each end as shown in Fig. 2.1. [Figure 2.1] The distance between the centres of the holes is A. Measure and record A. A =[1]
(b)(i)Set up the apparatus as shown in Fig. 2.2. [Figure 2.2] Adjust the position of the rule until it is balanced. The distance between the centre of the hole from which the 100 g mass hanger is supported and the position of the central string loop is x.
(b)(ii)Measure and record x. x =[1]
(c)(i)Add a 10 g slotted mass to each mass hanger.
(c)(ii)Adjust the position of the rule until it is balanced. The distance between the centre of the hole from which the 100 g mass hanger is supported and the position of the central string loop is now y as shown in Fig. 2.3.
(c)(iii)Measure and record y. y =[1]
(c)(iv)Calculate (y – x). (y - x) =[1]
(c)(v)Estimate the percentage uncertainty in your value of (y – x). percentage uncertainty =[1]
(d)(i)Calculate m(A – 2y) where m = 10.0 g. m(A-2y) =[1]
(d)(ii)Justify the number of significant figures that you have given for your value of m(A – 2y).[1]
(e)(i)Add another 10 g mass to each of the mass hangers and repeat (c)(ii), (c)(iii) and (c)(iv). y = (y - x) =[2]
(e)(ii)Calculate m(A – 2y) where m = 20.0 g. m(A – 2y) =
(f)(i)It is suggested that the relationship between y, x, m and A is (y – x) = km (A – 2y) where k is a constant. Using your data, calculate two values of k. first value of k = second value of k =[1]
(f)(ii)Explain whether your results in (f)(i) support the suggested relationship.[1]
(g)Using your second value of k, calculate the mass M of the metre rule using the relationship k = 1/(B+M) where B = 150 g. M =[1]
(h)(i)Describe four sources of uncertainty or limitations of the procedure for this experiment. 1. 2. 3. 4.[4]
(h)(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 (May/June 2017). The mark or mark type is shown in brackets.

[1] Value(s) of A with unit in the range 97.5–99.5 cm.
[1] Values of all raw x to nearest mm.
[1] Value of y > x.
[1] Correct calculation of (y – x).
[1] Percentage uncertainty in (y – x) based on absolute uncertainty of 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] Correct calculation of m(A – 2y).
[1] Justification for s.f. in m(A – 2y) linked to s.f. in A, y and m or (A – 2y) and m.
[1] Second value of y.
[1] Quality: second value of y > first value of y.
[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 M = 1/k-B.
[4] A Two readings are not enough to draw a (valid) conclusion (not "not enough for accurate results”, “few readings").
B Difficult to measure x or y with reason e.g. markings on rule obscured because of thickness of string/twist in string/ruler oscillating/ruler swinging/rule slides in loop/string not vertical.
C Large (%) uncertainty in (y – x) or (y – x) is small.
D Little difference in y values.
E Difficult to balance rule. 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 Use thinner string/tie a knot in loop/use two loops/use a hook/use longer loop/string.
C Heavier (added/slotted) masses (not heavier hangers).
D Use wider range of (added) masses.
E Suspend rule from its top edge/balance on fulcrum/use thicker string with reason such as to make easier to balance/prevent rule from slipping. 1 mark for each point up to a maximum of 4.