| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Applied force in addition to weights |
| Difficulty | Moderate -0.8 This is a straightforward pulley equilibrium problem requiring basic resolution of forces and understanding that tension is constant in a light rope over a smooth pulley. Part (i) involves simple trigonometry to resolve the tension into components, and part (ii) is a direct application of equilibrium conditions with vertical forces. Both parts are standard textbook exercises with no novel problem-solving required. |
| Spec | 3.03a Force: vector nature and diagrams3.03k Connected particles: pulleys and equilibrium3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces |
| Answer | Marks | Guidance |
|---|---|---|
| \(\uparrow\; 250\cos70 = 85.5050\ldots \approx 85.5\text{ N}\) | M1, A1, A1 | Resolving in at least 1 of horiz or vert. Accept \(\sin\leftrightarrow\cos\). No extra terms. Either both expressions correct (neglect direction) or one correct in correct direction. cao Both evaluated and directions correct. |
| Answer | Marks | Guidance |
|---|---|---|
| \(250 \div 2 = 125\text{ N}\) | B1 | Accept \(125g\) only if tension taken to be \(250g\) in (i). |
## Question 3:
### Part (i)
Resolving:
$\leftarrow\; 250\sin70 = 234.92\ldots \approx 235\text{ N}$
$\uparrow\; 250\cos70 = 85.5050\ldots \approx 85.5\text{ N}$ | M1, A1, A1 | Resolving in at least 1 of horiz or vert. Accept $\sin\leftrightarrow\cos$. No extra terms. Either both expressions correct (neglect direction) or one correct in correct direction. cao Both evaluated and directions correct.
### Part (ii)
$250 \div 2 = 125\text{ N}$ | B1 | Accept $125g$ only if tension taken to be $250g$ in (i).
---3 Fig. 2 shows a sack of rice of weight 250 N hanging in equilibrium supported by a light rope AB . End A of the rope is attached to the sack. The rope passes over a small smooth fixed pulley.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{5a1895e1-abe3-4739-876a-f19458f0f6ed-3_451_475_426_870}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{center}
\end{figure}
Initially, end B of the rope is attached to a vertical wall as shown in Fig. 2.\\
(i) Calculate the horizontal and the vertical forces acting on the wall due to the rope.
End B of the rope is now detached from the wall and attached instead to the top of the sack. The sack is in equilibrium with both sections of the rope vertical.\\
(ii) Calculate the tension in the rope.
\hfill \mbox{\textit{OCR MEI M1 Q3 [4]}}