Ocr 2024
OXFORD CAMBRDGE
AND RSA 2024
[Type the document subtitle]
OCR 2024
2024
[Type the company address]
, Oxford Cambridge and RSA
Friday 7 June 2024 – Afternoon A
Level Further Mathematics B (MEI) Y421/01
Mechanics Major
Time allowed: 2 hours 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
QP
(MEI)
• 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 your final answers to a degree of accuracy that is appropriate to the context.
• 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 120.
• 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 is an exempt Charity
Turn over
, 2
Section A (26 marks)
1 A car A of mass 1200 kg is about to tow another car B of mass 800 kg in a straight line along a
horizontal road by means of a tow-rope attached between A and B. The tow-rope is
modelled as being light and inextensible. Just before the tow-rope tightens, A is travelling at
a speed of
1.5 m s-1 and B is at rest. Just after the tow-rope tightens, both cars have a speed of v m s-1.
(a) Find the value of v. [2]
(b) Calculate the magnitude of the impulse on A when the tow-rope tightens. [2]
2 One end of a light spring is attached to a fixed point. A mass of 2 kg is attached to the other end
of the spring.
The spring hangs vertically in equilibrium. The extension of the spring is 0.05 m.
(a) Find the stiffness of the spring. [2]
(b) Find the energy stored in the spring. [2]
(c) Find the dimensions of stiffness of a spring. [1]
A particle P of mass m is performing complete oscillations with amplitude a on the end of a
light spring with stiffness k. The spring hangs vertically and the maximum speed v of P is given
by the formula
v = Cm a ab k c ,
where C is a dimensionless constant.
(d) Use dimensional analysis to determine a, b, and c. [4]
© OCR 2024 Y421/01 Jun24
OXFORD CAMBRDGE
AND RSA 2024
[Type the document subtitle]
OCR 2024
2024
[Type the company address]
, Oxford Cambridge and RSA
Friday 7 June 2024 – Afternoon A
Level Further Mathematics B (MEI) Y421/01
Mechanics Major
Time allowed: 2 hours 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
QP
(MEI)
• 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 your final answers to a degree of accuracy that is appropriate to the context.
• 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 120.
• 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 is an exempt Charity
Turn over
, 2
Section A (26 marks)
1 A car A of mass 1200 kg is about to tow another car B of mass 800 kg in a straight line along a
horizontal road by means of a tow-rope attached between A and B. The tow-rope is
modelled as being light and inextensible. Just before the tow-rope tightens, A is travelling at
a speed of
1.5 m s-1 and B is at rest. Just after the tow-rope tightens, both cars have a speed of v m s-1.
(a) Find the value of v. [2]
(b) Calculate the magnitude of the impulse on A when the tow-rope tightens. [2]
2 One end of a light spring is attached to a fixed point. A mass of 2 kg is attached to the other end
of the spring.
The spring hangs vertically in equilibrium. The extension of the spring is 0.05 m.
(a) Find the stiffness of the spring. [2]
(b) Find the energy stored in the spring. [2]
(c) Find the dimensions of stiffness of a spring. [1]
A particle P of mass m is performing complete oscillations with amplitude a on the end of a
light spring with stiffness k. The spring hangs vertically and the maximum speed v of P is given
by the formula
v = Cm a ab k c ,
where C is a dimensionless constant.
(d) Use dimensional analysis to determine a, b, and c. [4]
© OCR 2024 Y421/01 Jun24
