OCR Further Mechanics AS Specimen — Question 6 13 marks

Exam BoardOCR
ModuleFurther Mechanics AS (Further Mechanics AS)
SessionSpecimen
Marks13
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCircular Motion 1
TypeCoupled circular motions
DifficultyChallenging +1.2 This is a structured multi-part circular motion problem with clear geometry and standard force resolution. While it involves 3D visualization and multiple connected particles, the solution follows systematic application of F=mrω² and force balance equations. The geometry is given (not derived), and each part builds logically on the previous one. More challenging than basic circular motion but less demanding than problems requiring geometric insight or complex simultaneous equations.
Spec6.05c Horizontal circles: conical pendulum, banked tracks6.05e Radial/tangential acceleration

\includegraphics{figure_6} The fixed points \(A\), \(B\) and \(C\) are in a vertical line with \(A\) above \(B\) and \(B\) above \(C\). A particle \(P\) of mass 2.5 kg is joined to \(A\), to \(B\) and to a particle \(Q\) of mass 2 kg, by three light rods where the length of rod \(AP\) is 1.5 m and the length of rod \(PQ\) is 0.75 m. Particle \(P\) moves in a horizontal circle with centre \(B\). Particle \(Q\) moves in a horizontal circle with centre \(C\) at the same constant angular speed \(\omega\) as \(P\), in such a way that \(A\), \(B\), \(P\) and \(Q\) are coplanar. The rod \(AP\) makes an angle of \(60°\) with the downward vertical, rod \(PQ\) makes an angle of \(30°\) with the downward vertical and rod \(BP\) is horizontal (see diagram).
  1. Find the tension in the rod \(PQ\). [2]
  2. Find \(\omega\). [3]
  3. Find the speed of \(P\). [1]
  4. Find the tension in the rod \(AP\). [3]
  5. Hence find the magnitude of the force in rod \(BP\). Decide whether this rod is under tension or compression. [4]

Question 6:
AnswerMarks Guidance
6(i) T cos30(cid:32)2g
PQ
T (cid:32)22.6N
AnswerMarks
PQM1
A1
AnswerMarks Guidance
[2]3.3
1.1Resolving vertically for Q 22.632130…
6(ii) r(cid:32)1.5sin60(cid:14)0.75sin30
T sin30(cid:32)2r(cid:90)2
PQ
AnswerMarks
(cid:90)(cid:32)1.84rads-1B1
M1
A1
AnswerMarks
[3]3.1b
3.3
AnswerMarks
1.1May be implied in N2L for Q
N2L for Q with their r
AnswerMarks Guidance
n1.8384425…
6(iii) v (cid:32)2.39ms-1
PB1FT
[1]1.1 e
(1.5sin60)(their (cid:90))
AnswerMarks Guidance
6(iv) T cos60(cid:32)2.5g(cid:14)T cos30
AP PQ
T (cid:32)88.2N
AnswerMarks
APM1
M1
A1
AnswerMarks
[3]3.1b
1.1
i
c
AnswerMarks
1.1m
Resolving vertically for P
Substituting cv for T from (i) and
PQ
solving for T
AP
AnswerMarks Guidance
6(v) p
T (cid:14)T sin60(cid:16)T sin30(cid:32)2.5(1.5sin60)(cid:90)2
BP AP PQ
S
T (cid:32)(cid:16)54.1N so T (cid:32)54.1
BP BP
T (cid:31)0(cid:63) rod BP is under compression
AnswerMarks
BPe
M1
A1
A1
A1FT
AnswerMarks
[4]3.1b
1.1
1.1
AnswerMarks
3.2aN2L for P (4 terms)
FT the sign of T
AnswerMarks
BP–54.0909226…
PPMMTT
Y533 Mark Scheme June 20XX
Assessment Objectives (AO) Grid
n
e
m
i
c
e
p
S
PS = Problem Solving
M = Modelling
10
PPMMTT
Y533 Mark Scheme June 20XX
BLANK PAGE
n
e
m
i
c
e
p
S
11
PPMMTT
Y533 Mark Scheme June 20XX
BLANK PAGE
n
e
m
i
c
e
p
S
12
PPMMTT
AS Level Further Mathematics A
Y533 Mechanics
Printed Answer Booklet
Date – Morning/Afternoon
Time allowed: 1 hour 15 minutes
OCR supplied materials:
• Printed Answer Booklet t
• Formulae AS Level Further Mathematics A
f
You must have:
• Printed Answer Booklet a
• Formulae AS Level Further Mathematics A
* 0 0 0 0 0 0 *
• Scientific or graphical calculator
r
First name
D
Last name
Centre Candidate
number number
INSTRUCTIONS
• Use black ink. HB pencil may be used for graphs and diagrams only.
• Complete the boxes provided on the Printed Answer Booklet with your name, centre number
and candidate number.
• Answer all the questions.
• Write your answer to each question in the space provided in the Printed Answer
Booklet.
• Additional paper may be used if necessary but you must clearly show your candidate
number, centre number and question number(s).
• Do not write in the bar codes.
• You are permitted to use a scientific or graphical calculator in this paper.
• Final answers should be given to a degree of accuracy appropriate to the context.
• The acceleration due to gravity is denoted by gms-2. Unless otherwise instructed, when a
numerical value is needed, use g = 9.8.
INFORMATION
• You are reminded of the need for clear presentation in your answers.
• The Printed Answer Booklet consists of 12 pages. The Question Paper consists of 8 pages.
© OCR 2017 Y533 Turn over
603/1329/8 B10038/1.2

6(i)
t
f

AnswerMarks
6(ii)a
r
D

6(iii)

6(iv)

6(v)
t
f
a
r
D
PPMMTT
11
PLEASE DO NOT WRITtE ON THIS PAGE
f
a
r
D
© OCR 2017 Y533 Turn over
PPMMTT
12
t
PLEASE DO NOT WfRITE ON THIS PAGE
a
r
D
Copyright Information:
OCR is committed to seeking permission to reproduce all third-party content that it uses in the assessment materials. OCR has attempted
to identify and contact all copyright holders whose work is used in this paper. To avoid the issue of disclosure of answer-related
information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright Acknowledgements booklet. This is
produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live
examination series.
If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to
correct its mistake at the earliest possible opportunity.
For queries or further information please contact the Copyright Team, First Floor, 9 Hills Road, Cambridge CB2 1GE.
OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge
© OCR 2017 Y533
Question 6:
6 | (i) | T cos30(cid:32)2g
PQ
T (cid:32)22.6N
PQ | M1
A1
[2] | 3.3
1.1 | Resolving vertically for Q | 22.632130…
6 | (ii) | r(cid:32)1.5sin60(cid:14)0.75sin30
T sin30(cid:32)2r(cid:90)2
PQ
(cid:90)(cid:32)1.84rads-1 | B1
M1
A1
[3] | 3.1b
3.3
1.1 | May be implied in N2L for Q
N2L for Q with their r
n | 1.8384425…
6 | (iii) | v (cid:32)2.39ms-1
P | B1FT
[1] | 1.1 | e
(1.5sin60)(their (cid:90))
6 | (iv) | T cos60(cid:32)2.5g(cid:14)T cos30
AP PQ
T (cid:32)88.2N
AP | M1
M1
A1
[3] | 3.1b
1.1
i
c
1.1 | m
Resolving vertically for P
Substituting cv for T from (i) and
PQ
solving for T
AP
6 | (v) | p
T (cid:14)T sin60(cid:16)T sin30(cid:32)2.5(1.5sin60)(cid:90)2
BP AP PQ
S
T (cid:32)(cid:16)54.1N so T (cid:32)54.1
BP BP
T (cid:31)0(cid:63) rod BP is under compression
BP | e
M1
A1
A1
A1FT
[4] | 3.1b
1.1
1.1
3.2a | N2L for P (4 terms)
FT the sign of T
BP | –54.0909226…
PPMMTT
Y533 Mark Scheme June 20XX
Assessment Objectives (AO) Grid
n
e
m
i
c
e
p
S
PS = Problem Solving
M = Modelling
10
PPMMTT
Y533 Mark Scheme June 20XX
BLANK PAGE
n
e
m
i
c
e
p
S
11
PPMMTT
Y533 Mark Scheme June 20XX
BLANK PAGE
n
e
m
i
c
e
p
S
12
PPMMTT
AS Level Further Mathematics A
Y533 Mechanics
Printed Answer Booklet
Date – Morning/Afternoon
Time allowed: 1 hour 15 minutes
OCR supplied materials:
• Printed Answer Booklet t
• Formulae AS Level Further Mathematics A
f
You must have:
• Printed Answer Booklet a
• Formulae AS Level Further Mathematics A
* 0 0 0 0 0 0 *
• Scientific or graphical calculator
r
First name
D
Last name
Centre Candidate
number number
INSTRUCTIONS
• Use black ink. HB pencil may be used for graphs and diagrams only.
• Complete the boxes provided on the Printed Answer Booklet with your name, centre number
and candidate number.
• Answer all the questions.
• Write your answer to each question in the space provided in the Printed Answer
Booklet.
• Additional paper may be used if necessary but you must clearly show your candidate
number, centre number and question number(s).
• Do not write in the bar codes.
• You are permitted to use a scientific or graphical calculator in this paper.
• Final answers should be given to a degree of accuracy appropriate to the context.
• The acceleration due to gravity is denoted by gms-2. Unless otherwise instructed, when a
numerical value is needed, use g = 9.8.
INFORMATION
• You are reminded of the need for clear presentation in your answers.
• The Printed Answer Booklet consists of 12 pages. The Question Paper consists of 8 pages.
© OCR 2017 Y533 Turn over
603/1329/8 B10038/1.2
--- 6(i) ---
6(i)
t
f
--- 6(ii) ---
6(ii) | a
r
D
--- 6(iii) ---
6(iii)
--- 6(iv) ---
6(iv)
--- 6(v) ---
6(v)
t
f
a
r
D
PPMMTT
11
PLEASE DO NOT WRITtE ON THIS PAGE
f
a
r
D
© OCR 2017 Y533 Turn over
PPMMTT
12
t
PLEASE DO NOT WfRITE ON THIS PAGE
a
r
D
Copyright Information:
OCR is committed to seeking permission to reproduce all third-party content that it uses in the assessment materials. OCR has attempted
to identify and contact all copyright holders whose work is used in this paper. To avoid the issue of disclosure of answer-related
information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright Acknowledgements booklet. This is
produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live
examination series.
If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to
correct its mistake at the earliest possible opportunity.
For queries or further information please contact the Copyright Team, First Floor, 9 Hills Road, Cambridge CB2 1GE.
OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge
© OCR 2017 Y533
\includegraphics{figure_6}

The fixed points $A$, $B$ and $C$ are in a vertical line with $A$ above $B$ and $B$ above $C$. A particle $P$ of mass 2.5 kg is joined to $A$, to $B$ and to a particle $Q$ of mass 2 kg, by three light rods where the length of rod $AP$ is 1.5 m and the length of rod $PQ$ is 0.75 m. Particle $P$ moves in a horizontal circle with centre $B$. Particle $Q$ moves in a horizontal circle with centre $C$ at the same constant angular speed $\omega$ as $P$, in such a way that $A$, $B$, $P$ and $Q$ are coplanar. The rod $AP$ makes an angle of $60°$ with the downward vertical, rod $PQ$ makes an angle of $30°$ with the downward vertical and rod $BP$ is horizontal (see diagram).

\begin{enumerate}[label=(\roman*)]
\item Find the tension in the rod $PQ$. [2]
\item Find $\omega$. [3]
\item Find the speed of $P$. [1]
\item Find the tension in the rod $AP$. [3]
\item Hence find the magnitude of the force in rod $BP$.
Decide whether this rod is under tension or compression. [4]
\end{enumerate}

\hfill \mbox{\textit{OCR Further Mechanics AS  Q6 [13]}}