Oxford Cambridge and
RSA Examinations GCE
Further Mathematics
AY543/01: Mechanics
A Level question paper
and marking scheme
(merged)
, Oxford Cambridge and RSA
Friday 16 June 2023 – Afternoon
A Level Further Mathematics A
Y543/01 Mechanics
Time allowed: 1 hour 30 minutes
* 9 9 7 6 8 8 4 3 8 2 *
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for A Level Further
QP
Mathematics A
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If you need extra space use the lined pages at the end of the Printed Answer
Booklet. The question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Give non-exact numerical answers correct to 3 significant figures unless a different
degree of accuracy is specified in the question.
• The acceleration due to gravity is denoted by g m s–2. When a numerical value is
needed use g = 9.8 unless a different value is specified in the question.
• Do not send this Question Paper for marking. Keep in the centre or recycle it.
INFORMATION
• The total mark for this paper is 75.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
, 2
1 One end of a light inextensible string of length 0.8 m is attached to a particle P of mass m kg. The
other end of the string is attached to a fixed point O. Initially P hangs in equilibrium vertically
below O. It is then projected horizontally with a speed of 5.3 m s -1 so that it moves in a vertical
circular path with centre O (see diagram).
O
0.8 m
1
3r P
P
5.3 m s−1
At a certain instant, P first reaches the point where the string makes an angle of 13 r radians with
the downward vertical through O.
(a) Show that at this instant the speed of P is 4.5 m s -1 . [3]
(b) Find the magnitude and direction of the radial acceleration of P at this instant. [3]
(c) Find the magnitude of the tangential acceleration of P at this instant. [2]
, 3
2 Materials have a measurable property known as the Young’s Modulus, E.
If a force is applied to one face of a block of the material then the material is stretched by a
Stress
distance called the extension. Young’s modulus is defined as the ratio where Stress is
Strain
defined as the force per unit area and Strain is the ratio of the extension of the block to the length
of the block.
(a) Show that Strain is a dimensionless quantity. [1]
(b) By considering the dimensions of both Stress and Strain determine the dimensions of E. [2]
It is suggested that the speed of sound in a material, c, depends only upon the value of Young’s
modulus for the material, E, the volume of the material, V, and the density (or mass per unit
volume) of the material, t.
(c) Use dimensional analysis to suggest a formula for c in terms of E, V and t. [5]
(d) The speed of sound in a certain material is 500 m s -1 .
(i) Use your formula from part (c) to predict the speed of sound in the material if the value
of Young’s modulus is doubled but all other conditions are unchanged. [1]
(ii) With reference to your formula from part (c), comment on the effect on the speed of
sound in the material if the volume is doubled but all other conditions are unchanged. [1]
(e) Suggest one possible limitation caused by using dimensional analysis to set up the model in
part (c). [1]
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