| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2008 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Equilibrium with friction on horizontal surface |
| Difficulty | Moderate -0.8 This is a straightforward statics problem requiring resolution of forces in two directions and application of equilibrium conditions. All three parts involve standard M1 techniques with no conceptual challenges: (i) uses T=mg directly, (ii) and (iii) resolve horizontally and vertically with given tension and angle. The multi-part structure adds marks but not difficulty—each step is routine textbook application. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03m Equilibrium: sum of resolved forces = 0 |
| Answer | Marks | Guidance |
|---|---|---|
| \(m \times 9.8 = 58.8\) so \(m = 6\) | M1, A1 | Condone sign error. CWO. |
| Sub: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Resolve \(\rightarrow 58.8\cos 40° - F = 0\) | M1 | Resolving their tension. Accept \(x \leftrightarrow c\). Condone sign errors but not extra forces. |
| \(F = 45.043...\) so \(45.0\) N (3 s.f.) | B1, A1 | Their \(T \times \cos 40°\) (or equivalent) seen. Accept \(\pm 45\) only. cao |
| Sub: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Resolve \(\uparrow R + 58.8\sin 40° - 15 \times 9.8 = 0\) | M1 | Resolving their tension. All forces present. No extra forces. Accept \(x \leftrightarrow c\). Condone errors in sign. |
| \(R = 109.204...\) so \(109\) N (3 s.f.) | A1, A1 | All correct. cao |
| Sub: 3 |
### (i)
$m \times 9.8 = 58.8$ so $m = 6$ | M1, A1 | Condone sign error. CWO.
| Sub: 2
### (ii)
Resolve $\rightarrow 58.8\cos 40° - F = 0$ | M1 | Resolving their tension. Accept $x \leftrightarrow c$. Condone sign errors but not extra forces.
$F = 45.043...$ so $45.0$ N (3 s.f.) | B1, A1 | Their $T \times \cos 40°$ (or equivalent) seen. Accept $\pm 45$ only. cao
| Sub: 3
### (iii)
Resolve $\uparrow R + 58.8\sin 40° - 15 \times 9.8 = 0$ | M1 | Resolving their tension. All forces present. No extra forces. Accept $x \leftrightarrow c$. Condone errors in sign.
$R = 109.204...$ so $109$ N (3 s.f.) | A1, A1 | All correct. cao
| Sub: 3
---\includegraphics{figure_3}
Fig. 3 shows a block of mass 15 kg on a rough, horizontal plane. A light string is fixed to the block at A, passes over a smooth, fixed pulley B and is attached at C to a sphere. The section of the string between the block and the pulley is inclined at 40° to the horizontal and the section between the pulley and the sphere is vertical.
The system is in equilibrium and the tension in the string is 58.8 N.
\begin{enumerate}[label=(\roman*)]
\item The sphere has a mass of $m$ kg. Calculate the value of $m$. [2]
\item Calculate the frictional force acting on the block. [3]
\item Calculate the normal reaction of the plane on the block. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI M1 2008 Q3 [8]}}