Oxford Cambridge and
RSA Examinations GCE
Further Mathematics
AY533/01: Mechanics AS
Level question paper
and marking scheme
, Oxford Cambridge and RSA
Wednesday 14 June 2023 – Afternoon
AS Level Further Mathematics A
Y533/01 Mechanics
Time allowed: 1 hour 15 minutes
* 9 9 7 5 3 3 5 8 9 1 *
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for AS 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 it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 60.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2023 [T/508/5499] OCR is an exempt Charity
DC (CJ/CGW) 323131/3 Turn over
, 2
1 Two particles A, of mass m kg, and B, of mass 3m kg, are connected by a light inextensible string
and placed together at rest on a smooth horizontal surface with the string slack. A is projected
along the surface, directly away from B, with a speed of 2.4 ms -1 .
(a) Find the speed of B immediately after the string becomes taut. [2]
(b) Find, in terms of m, the magnitude of the impulse exerted on B as a result of the string
becoming taut. [2]
2
O
3.2 m
P
60°
−1
P u ms
A small body P of mass 3 kg is at rest at the lowest point of the inside of a smooth hemispherical
shell of radius 3.2 m and centre O.
P is projected horizontally with a speed of u ms -1 . When P first comes to instantaneous rest OP
makes an angle of 60° with the downward vertical through O.
(a) Find the value of u. [4]
(b) State one assumption made in modelling the motion of P. [1]
© OCR 2023 Y533/01 Jun23
, 3
3 A crate of mass 45 kg is sliding with a speed of 0.8 ms -1 in a straight line across a smooth
horizontal floor. One end of a light inextensible rope is attached to the crate. At a certain instant
a builder takes the other end of the rope and starts to pull, applying a constant force of 80 N for
5 seconds.
While the builder is pulling the crate, the rope makes a constant angle of 40° above the horizontal.
Both the rope and the velocity of the crate lie in the same vertical plane (see diagram).
80 N
0.8 m s−1
40°
It may be assumed that there is no resistance to the motion of the crate.
(a) Determine the work done by the builder in pulling the crate. [4]
(b) (i) Find the kinetic energy of the crate at the instant when the builder stops pulling the crate.
[2]
(ii) Explain why the answers to part (a) and part (b)(i) are not equal. [1]
(c) Find the average power developed by the builder in pulling the crate. [1]
(d) Calculate the total impulse exerted on the crate by the builder. [2]
4 A rower is rowing a boat in a straight line across a lake. The combined mass of the rower, boat
and oars is 240 kg. The maximum power that the rower can generate is 450 W.
In a model of the motion of the boat it is assumed that the total resistance to the motion of the boat
is 150 N at any instant when the boat is in motion.
(a) Find the maximum possible acceleration of the boat, according to the model, at an instant
when its speed is 0.5 ms -1 . [2]
At one stage in its motion the boat is travelling at a constant speed and the rower is generating
power at an average rate of 210 W, which is assumed to be constant. The boat passes a pole and
then, after travelling 350 m, a second pole.
(b) Determine how long it takes, according to the model, for the boat to travel between the two
poles. [4]
(c) State a reason why the assumption that the rower’s generated power is constant may be
unrealistic. [1]
© OCR 2023 Y533/01 Jun23 Turn over
RSA Examinations GCE
Further Mathematics
AY533/01: Mechanics AS
Level question paper
and marking scheme
, Oxford Cambridge and RSA
Wednesday 14 June 2023 – Afternoon
AS Level Further Mathematics A
Y533/01 Mechanics
Time allowed: 1 hour 15 minutes
* 9 9 7 5 3 3 5 8 9 1 *
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for AS 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 it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 60.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2023 [T/508/5499] OCR is an exempt Charity
DC (CJ/CGW) 323131/3 Turn over
, 2
1 Two particles A, of mass m kg, and B, of mass 3m kg, are connected by a light inextensible string
and placed together at rest on a smooth horizontal surface with the string slack. A is projected
along the surface, directly away from B, with a speed of 2.4 ms -1 .
(a) Find the speed of B immediately after the string becomes taut. [2]
(b) Find, in terms of m, the magnitude of the impulse exerted on B as a result of the string
becoming taut. [2]
2
O
3.2 m
P
60°
−1
P u ms
A small body P of mass 3 kg is at rest at the lowest point of the inside of a smooth hemispherical
shell of radius 3.2 m and centre O.
P is projected horizontally with a speed of u ms -1 . When P first comes to instantaneous rest OP
makes an angle of 60° with the downward vertical through O.
(a) Find the value of u. [4]
(b) State one assumption made in modelling the motion of P. [1]
© OCR 2023 Y533/01 Jun23
, 3
3 A crate of mass 45 kg is sliding with a speed of 0.8 ms -1 in a straight line across a smooth
horizontal floor. One end of a light inextensible rope is attached to the crate. At a certain instant
a builder takes the other end of the rope and starts to pull, applying a constant force of 80 N for
5 seconds.
While the builder is pulling the crate, the rope makes a constant angle of 40° above the horizontal.
Both the rope and the velocity of the crate lie in the same vertical plane (see diagram).
80 N
0.8 m s−1
40°
It may be assumed that there is no resistance to the motion of the crate.
(a) Determine the work done by the builder in pulling the crate. [4]
(b) (i) Find the kinetic energy of the crate at the instant when the builder stops pulling the crate.
[2]
(ii) Explain why the answers to part (a) and part (b)(i) are not equal. [1]
(c) Find the average power developed by the builder in pulling the crate. [1]
(d) Calculate the total impulse exerted on the crate by the builder. [2]
4 A rower is rowing a boat in a straight line across a lake. The combined mass of the rower, boat
and oars is 240 kg. The maximum power that the rower can generate is 450 W.
In a model of the motion of the boat it is assumed that the total resistance to the motion of the boat
is 150 N at any instant when the boat is in motion.
(a) Find the maximum possible acceleration of the boat, according to the model, at an instant
when its speed is 0.5 ms -1 . [2]
At one stage in its motion the boat is travelling at a constant speed and the rower is generating
power at an average rate of 210 W, which is assumed to be constant. The boat passes a pole and
then, after travelling 350 m, a second pole.
(b) Determine how long it takes, according to the model, for the boat to travel between the two
poles. [4]
(c) State a reason why the assumption that the rower’s generated power is constant may be
unrealistic. [1]
© OCR 2023 Y533/01 Jun23 Turn over
