| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics Major (Further Mechanics Major) |
| Year | 2020 |
| Session | November |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Two jointed rods in equilibrium |
| Difficulty | Challenging +1.2 This is a standard statics problem requiring moments about a point, resolution of forces, and friction at limiting equilibrium. While it involves multiple steps (finding tension via moments, then using friction coefficient at the limiting case), the techniques are routine for Further Maths mechanics. The geometry with the string constraint adds mild complexity, but the problem follows a predictable structure without requiring novel insight. |
| Spec | 3.03u Static equilibrium: on rough surfaces3.04b Equilibrium: zero resultant moment and force3.04c Use moments: beams, ladders, static problems |
| Answer | Marks | Guidance |
|---|---|---|
| 9 | (a) | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| (8W)(acosθ)=... | B1 | 1.1 |
| …=(2acosθ)(Tsinθ)+(2asinθ)(Tcosθ) | B1 | 1.1 |
| T =2Wcosecθ | A1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| 9 | (b) | M1* |
| Answer | Marks |
|---|---|
| correctly | R is the normal |
| Answer | Marks | Guidance |
|---|---|---|
| C | A1 | 3.3 |
| Answer | Marks | Guidance |
|---|---|---|
| C C | M1dep* | 3.4 |
| C C | Allow equals |
| Answer | Marks | Guidance |
|---|---|---|
| greatest distance of the ring from A | A1 | 3.1b |
| Answer | Marks | Guidance |
|---|---|---|
| 2.4a=4acosθ⇒cosθ=0.6 | B1 | 3.1a |
| Answer | Marks | Guidance |
|---|---|---|
| 3µ 3 2 | A1 | 2.2a |
Question 9:
9 | (a) | M1 | 3.1b | Taking moments about A for the rod –
correct number of terms
(8W)(acosθ)=... | B1 | 1.1
…=(2acosθ)(Tsinθ)+(2asinθ)(Tcosθ) | B1 | 1.1 | oe e.g. 2aTsin2θ
T =2Wcosecθ | A1 | 1.1 | oe
[4]
9 | (b) | M1* | 3.3 | Resolving vertically and horizontally at
the ring – correct number of terms. Allow
this mark if only one direction stated
correctly | R is the normal
C
contact force between
the ring and the rod
R =W +Tsinθ
C
F =Tcosθ
C | A1 | 3.3 | F is the frictional
C
force between the ring
and the rod
F ≤µR ⇒2Wcotθ≤µ(3W)
C C | M1dep* | 3.4 | Use of F ≤µR with their F and R
C C | Allow equals
3µ 2
cotθ≤ ⇒tanθ≥ least value of tan gives
2 3µ
greatest distance of the ring from A | A1 | 3.1b | 2
tanθ=
3µ
2.4a=4acosθ⇒cosθ=0.6 | B1 | 3.1a | oe e.g. stating the angle or sinθ=0.8
2 4 1
= ⇒µ=
3µ 3 2 | A1 | 2.2a
[6]\includegraphics{figure_9}
Fig. 9 shows a uniform rod AB of length $2a$ and weight $8W$ which is smoothly hinged at the end A to a point on a fixed horizontal rough bar. A small ring of weight $W$ is threaded on the bar and is connected to the rod at B by a light inextensible string of length $2a$. The system is in equilibrium with the rod inclined at an angle $\theta$ to the horizontal.
\begin{enumerate}[label=(\alph*)]
\item Determine, in terms of $W$ and $\theta$, the tension in the string. [4]
It is given that, for equilibrium to be possible, the greatest distance the ring can be from A is $2.4a$.
\item Determine the coefficient of friction between the bar and the ring. [6]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics Major 2020 Q9 [10]}}