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Date	May 2019	Marks available	2	Reference code	19M.3.SL.TZ1.1
Level	Standard level	Paper	Paper 3	Time zone	1
Command term	State and Explain	Question number	1	Adapted from	N/A

Question

In an experiment to measure the acceleration of free fall a student ties two different blocks of masses m₁ and m₂ to the ends of a string that passes over a frictionless pulley.

The student calculates the acceleration a of the blocks by measuring the time taken by the heavier mass to fall through a given distance. Their theory predicts that $a = g\frac{{{m_1} - {m_2}}}{{{m_1} + {m_2}}}$ and this can be re-arranged to give $g = a\frac{{{m_1} + {m_2}}}{{{m_1} - {m_2}}}$ .

In a particular experiment the student calculates that a = (0.204 ±0.002) ms^–2 using m₁ = (0.125 ±0.001) kg and m₂ = (0.120 ±0.001) kg.

Calculate the percentage error in the measured value of g.

[3]

a.i.

Deduce the value of g and its absolute uncertainty for this experiment.

[2]

a.ii.

There is an advantage and a disadvantage in using two masses that are almost equal.

State and explain the advantage with reference to the magnitude of the acceleration that is obtained.

[2]

b.i.

There is an advantage and a disadvantage in using two masses that are almost equal.

State and explain the disadvantage with reference to your answer to (a)(ii).

[2]

b.ii.

Markscheme

error in m₁ + m₂ is 1 % OR error in m₁ − m₂ is 40 % OR error in a is 1 % ✔

adds percentage errors ✔

so error in g is 42 % OR 40 % OR 41.8 % ✔

Allow answer 0.42 or 0.4 or 0.418.

Award [0] for comparing the average value with a known value, e.g. 9.81 m s-2.

a.i.

g = 9.996 «m s⁻²» OR Δg = 4.20 «m s⁻²» ✔

g = (10 ± 4) «m s⁻²»

g = (10.0 ± 4.2) «m s⁻²» ✔

Award [1] max for not proper significant digits or decimals use, such as: 9.996±4.178 or 10±4.2 or 10.0±4 or 10.0±4.18« m s⁻² » .

a.ii.

the acceleration would be small/the time of fall would be large ✔

easier to measure /a longer time of fall reduces the % error in the time of fall and «hence acceleration» ✔

Do not accept ideas related to the mass/moment of inertia of the pulley.

b.i.

the percentage error in the difference of the masses is large ✔

leading to a large percentage error/uncertainty in g/of the experiment ✔

Do not accept ideas related to the mass/moment of inertia of the pulley.

b.ii.

Examiners report

Atwoods machine a) is a quite straightforward question that tests the ability to propagate uncertainties through calculations. Almost all candidates proved the ability to add percentages or relative calculations, however, many weaker candidates failed in the percentage uncertainty when subtracting the two masses.

a.i.

Many average candidates did not use the correct number of significant figures and wrote the answers inappropriately. Only the best candidates rounded out and wrote the proper answer of 10±4 ms⁻². Some candidates did not propagate uncertainties and only compared the average calculated value with the known value 9.81 ms⁻².

a.ii.

Q 1 b) was quite well answered. Only the weakest candidates presented difficulty in understanding simple mechanics.

b.i.

In part ii) many were able to appreciate that the resultant percentage error in “g” was relatively large however linking this with what caused the large uncertainty (that is, the high % error from the small difference in masses) proved more challenging.

b.ii.

Syllabus sections

Core » Topic 1: Measurements and uncertainties » 1.2 – Uncertainties and errors

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