OCR A-LEVEL FURTHER MATHEMATICS A (Y543/01) MECHANICS JUNE EXAM PAPER (AUTHENTIC MARKING SCHEME ATTACHED)
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Course
FURTHER MATHEMATICS
Institution
OCR
OCR A-LEVEL FURTHER MATHEMATICS A (Y543/01) MECHANICS JUNE EXAM PAPER (AUTHENTIC MARKING SCHEME ATTACHED)
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. ...
Friday 17 June 2022 – Afternoon
A Level Further Mathematics A
Y543/01 Mechanics
Time allowed: 1 hour 30 minutes
OCR A-LEVEL FURTHER MATHEMATICS A
* 9 4 5 9 2 4 0 7 8 2 *
(Y543/01) MECHANICS JUNE EXAM PAPER
(AUTHENTIC MARKING SCHEME ATTACHED)
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.
–2
• The acceleration due to gravity is denoted by g m s . 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 car has mass 1200 kg. The total resistance to the car’s motion is constant and equal to 250 N.
(a) The car is driven along a straight horizontal road with its engine working at 10 kW.
-1
Find the acceleration of the car at the instant that its speed is 5 m s . [3]
The maximum power that the car’s engine can generate is 20 kW.
(b) Find the greatest constant speed at which the car can be driven along a straight
horizontal
road. [2]
The car is driven up a straight road which is inclined at an angle i above the horizontal where
sin i = 0.05.
(c) Find the greatest constant speed at which the car can be driven up this road. [2]
2 The coordinates of two points, A and B, are (-1, 6) and (5, 12) respectively, where the units of the
coordinate axes are metres. A particle P moves from A to B under the action of several forces.
The force F = 7i - 2j N is one of the forces acting on P.
(a) Calculate the work done by F on P as P moves from A to B. [2]
-1
At the instant when P reaches B its velocity is - i - 5j m s .
(b) Find the power generated by F at the instant that P reaches B. [2]
One end of a light elastic string was attached to the origin of the coordinate system and the other
to P when P was at A, before it moved to B. The natural length of the string is 8 m and its
modulus of elasticity is 24 N.
(c) At the instant that P reaches B, find the following.
• The tension in the string
• The elastic potential energy stored in the string [3]
, 3
3 A particle P of mass 6 kg moves in a straight line under the action of a single force of
magnitude F N which acts in the direction of motion of P.
1
At time t seconds, where t H 0, F is given by F = 5 - 4e-t
2
.
-1
When t = 0, the speed of P is 1.9 m s .
(a) Find the impulse of the force over the period 0 G t G 2. [2]
(b) Find the speed of P at the instant when t = 2. [2]
(c) Find the work done by the force on P over the period 0 G t G 2. [2]
4 When two objects are placed a distance apart in outer space each applies a gravitational force to
the other. It is suggested that the magnitude of this force depends on the masses of both objects
and the distance between them. Assuming that this suggestion is correct, it is further assumed
that the magnitude of this force is given by a relationship of the form
a b c
F = Gm 1 m2 r
where
• F is the magnitude of the force
• m1 and m2 are the masses of the two objects
• r is the distance between the two objects
• G is a constant.
(a) Using a dimensional argument based on Newton’s third law explain why a = b. [1]
It is given that the magnitude of the gravitational force is given by such a relationship and that
- 11 3 -1 -2
G = 6.67 # 10 m kg s .
(b) Write down the dimensions of G. [1]
(c) By using dimensional analysis, determine the values of a, b and c. [3]
24
You are given that the mass of the Earth is 5.97 # 10 kg and that the distance of the Moon
8
from the Earth is 3.84 # 10 m. You may assume that the only force acting on the Moon is
the gravitational force due to the Earth.
(d) By modelling the Earth as stationary and assuming that the Moon moves in a circular orbit
around the Earth, determine the period of the motion of the Moon. Give your answer to the
nearest day. [3]
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