| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2013 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Equilibrium on slope with force parallel to slope |
| Difficulty | Moderate -0.8 This is a straightforward equilibrium problem on an inclined plane requiring resolution of forces and Newton's first law. Students need to resolve weight perpendicular and parallel to the plane, then apply equilibrium conditions. The constant speed indicates equilibrium (no acceleration), making this a standard textbook exercise with routine calculations and no novel problem-solving required. |
| Spec | 3.03b Newton's first law: equilibrium3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 03.03r Friction: concept and vector form |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Diagram showing Normal reaction (upward), \(P\) (horizontal), \(10\text{ N}\) at \(30°\) (down-left), \(3g\) (downward) | B1, B1, B1 | 3 marks \(-1\) per error or omission; Forces must have arrows and labels; Accept "weight" and "friction" |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(R = 3g\cos30° = 25.46... = 25.5\) (to 3 significant figures) | B1 | Accept 25 or 26 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P = 10 + 3g\sin30°\) | M1 | Correct elements must be present |
| \(P = 24.7\) | A1 | Cao |
## Question 1:
**Part (i)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Diagram showing Normal reaction (upward), $P$ (horizontal), $10\text{ N}$ at $30°$ (down-left), $3g$ (downward) | B1, B1, B1 | 3 marks $-1$ per error or omission; Forces must have arrows and labels; Accept "weight" and "friction" |
**Part (ii)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $R = 3g\cos30° = 25.46... = 25.5$ (to 3 significant figures) | B1 | Accept 25 or 26 |
**Part (iii)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P = 10 + 3g\sin30°$ | M1 | Correct elements must be present |
| $P = 24.7$ | A1 | Cao |
---1 Fig. 1 shows a block of mass 3 kg on a plane which is inclined at an angle of $30 ^ { \circ }$ to the horizontal.\\
A force $P \mathrm {~N}$ is applied to the block parallel to the plane in the upwards direction.\\
The plane is rough so that a frictional force of 10 N opposes the motion.\\
The block is moving at constant speed up the plane.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{13f555cc-d506-48e5-a0e4-225cae4251dc-3_214_622_657_724}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
(i) Mark and label all the forces acting on the block.\\
(ii) Calculate the magnitude of the normal reaction of the plane on the block.\\
(iii) Calculate the magnitude of the force $P$.
\hfill \mbox{\textit{OCR MEI M1 2013 Q1 [6]}}