OCR
GCE
Further Mathematics A
Y543/01: Mechanics
A Level
Merged Question Paper + Mark Scheme + Answer
Booklet
Ace your Mocks!!!
, Oxford Cambridge and RSA
Friday 14 June 2024 – Afternoon
A Level Further Mathematics A
Y543/01 Mechanics
Time allowed: 1 hour 30 minutes
* 1 4 2 1 4 9 8 6 8 6 *
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.
1 A particle P of mass 12.5 kg is moving on a smooth horizontal plane when it collides obliquely
with a fixed vertical wall.
At the instant before the collision, the velocity of P is -5i + 12j m s - 1 .
At the instant after the collision, the velocity of P is i + 4j m s - 1 .
(a) Find the magnitude of the momentum of P before the collision. [2]
(b) Find, in vector form, the impulse that the wall exerts on P. [2]
(c) State, in vector form, the impulse that P exerts on the wall. [1]
(d) Find in either order.
• The magnitude of the impulse that the wall exerts on P.
• The angle between i and the impulse that the wall exerts on P. [3]
2 One end of a light elastic string of natural length 1.4 m and modulus of elasticity 20 N is attached
to a small object B of mass 2.5 kg. The other end of the string is attached to a fixed point O.
Object B is projected vertically upwards from O with a speed of u m s - 1 .
(a) State one assumption required to model the motion of B. [1]
The greatest height above O achieved by B is 8.1 m.
(b) Determine the value of u. [4]
3 The mass of a truck is 6000 kg and the maximum power that its engine can generate is 90 kW. In
a model of the motion of the truck it is assumed that while it is moving the total resistance to its
motion is constant.
At first the truck is driven along a straight horizontal road. The greatest constant speed that it can
be driven at when it is using maximum power is 25 m s - 1 .
(a) Find the value of the resistance to motion. [2]
The truck is being driven along the horizontal road with the engine working at 60 kW.
(b) Find the acceleration of the truck at the instant when its speed is 10 m s - 1 . [2]
The truck is now driven down a straight road which is inclined at an angle i below the horizontal.
The greatest constant speed that the truck can be driven at maximum power is 40 m s -1 .
4 A particle, P, of mass 6 kg is attached to one end of a light inextensible rod of length 2.4 m. The
other end of the rod is smoothly hinged at a fixed point O and the rod is free to rotate in any
direction.
Initially, P is at rest, vertically below O, when it is projected horizontally with a speed of 12 m s -1 .
It subsequently describes complete vertical circles with O as the centre.
O
2.4 m
2.4 m 40°
P A
P
12 m s−1
The angle that the rod makes with the downward vertical through O at each instant is denoted by i
and A is the point which P passes through where i = 40° (see diagram).
(a) Find the tangential acceleration of P at A, stating its direction. [2]
(b) Determine the radial acceleration of P at A, stating its direction. [6]
(c) Find the magnitude of the force in the rod when P is at A, stating whether the rod is in tension
or compression. [2]
The motion is now stopped when P is at A, and P is then projected in such a way that it now
describes horizontal circles at a constant speed with i = 40° (see diagram).
O
2.4 m
40°
P
(d) Find the speed of P. [4]
(e) Explain why, wherever P’s motion is initiated from and whatever its initial velocity, it is not
possible for P to describe horizontal circles at constant speed with i = 90° . [1]
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