| Exam Board | OCR |
|---|---|
| Module | Further Mechanics AS (Further Mechanics AS) |
| Session | Specimen |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Coupled circular motions |
| Difficulty | Challenging +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. |
| Spec | 6.05c Horizontal circles: conical pendulum, banked tracks6.05e Radial/tangential acceleration |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (i) | T cos30(cid:32)2g |
| Answer | Marks |
|---|---|
| PQ | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| [2] | 3.3 | |
| 1.1 | Resolving vertically for Q | 22.632130… |
| 6 | (ii) | r(cid:32)1.5sin60(cid:14)0.75sin30 |
| Answer | Marks |
|---|---|
| (cid:90)(cid:32)1.84rads-1 | B1 |
| Answer | Marks |
|---|---|
| [3] | 3.1b |
| Answer | Marks |
|---|---|
| 1.1 | May be implied in N2L for Q |
| Answer | Marks | Guidance |
|---|---|---|
| n | 1.8384425… | |
| 6 | (iii) | v (cid:32)2.39ms-1 |
| P | B1FT | |
| [1] | 1.1 | e |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (iv) | T cos60(cid:32)2.5g(cid:14)T cos30 |
| Answer | Marks |
|---|---|
| AP | M1 |
| Answer | Marks |
|---|---|
| [3] | 3.1b |
| Answer | Marks |
|---|---|
| 1.1 | m |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (v) | p |
| Answer | Marks |
|---|---|
| BP | e |
| Answer | Marks |
|---|---|
| [4] | 3.1b |
| Answer | Marks |
|---|---|
| 3.2a | N2L for P (4 terms) |
| Answer | Marks |
|---|---|
| BP | –54.0909226… |
| Answer | Marks |
|---|---|
| 6(ii) | a |
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…
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\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]}}