| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2012 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Block on rough horizontal surface – equilibrium (finding friction, normal reaction, or coefficient of friction) |
| Difficulty | Moderate -0.8 This is a straightforward equilibrium problem requiring resolution of forces in two perpendicular directions and Pythagoras' theorem. All steps are standard M1 techniques with no problem-solving insight needed—the angle and tension are given, making it more routine than an average A-level question. |
| Spec | 3.03a Force: vector nature and diagrams3.03b Newton's first law: equilibrium3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 03.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Diagram with \(N\) (up), \(50\) (diagonal), \(R\) (left), \(mg\) (down) correctly labelled with arrows | B2 | Subtract one mark per error/omission/addition to minimum zero. Each force must have label and arrow. Accept \(T\) for 50 N. If tension given in components: accept if components replace tension; treat as error if components duplicate tension; accept dotted lines for components as not duplication |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Horizontal equilibrium: \(R = 50\sin30° = 25\) | M1, A1 | May be implied. Allow sin-cos interchange for M1 only. Award both marks for correct answer after mistake in part (i) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Vertical equilibrium: \(N + 50\cos30° = 10g\) | M1 | Relationship must involve all 3 elements. No credit for sin-cos interchange |
| \(N = 54.7\) to 3 s.f. | A1 | Cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Resultant \(= \sqrt{25^2 + 54.7^2}\) | M1 | Use of Pythagoras. Components must be correct but allow ft from both (ii) and (iii) |
| Resultant is \(60.1\ \text{N}\) | A1 | Cao |
# Question 5:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Diagram with $N$ (up), $50$ (diagonal), $R$ (left), $mg$ (down) correctly labelled with arrows | B2 | Subtract one mark per error/omission/addition to minimum zero. Each force must have label and arrow. Accept $T$ for 50 N. If tension given in components: accept if components replace tension; treat as error if components duplicate tension; accept dotted lines for components as not duplication |
## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Horizontal equilibrium: $R = 50\sin30° = 25$ | M1, A1 | May be implied. Allow sin-cos interchange for M1 only. Award both marks for correct answer after mistake in part (i) |
## Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Vertical equilibrium: $N + 50\cos30° = 10g$ | M1 | Relationship must involve all 3 elements. No credit for sin-cos interchange |
| $N = 54.7$ to 3 s.f. | A1 | Cao |
## Part (iv)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Resultant $= \sqrt{25^2 + 54.7^2}$ | M1 | Use of Pythagoras. Components must be correct but allow ft from both (ii) and (iii) |
| Resultant is $60.1\ \text{N}$ | A1 | Cao |
---5 Fig. 5 shows a block of mass 10 kg at rest on a rough horizontal floor. A light string, at an angle of $30 ^ { \circ }$ to the vertical, is attached to the block. The tension in the string is 50 N .
The block is in equilibrium.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{076ad371-b029-4d57-aa0f-8a78ed03ccf3-3_394_579_1644_744}
\captionsetup{labelformat=empty}
\caption{Fig. 5}
\end{center}
\end{figure}
(i) Show all the forces acting on the block.\\
(ii) Show that the frictional force acting on the block is 25 N .\\
(iii) Calculate the normal reaction of the floor on the block.\\
(iv) Calculate the magnitude of the total force the floor is exerting on the block.
\hfill \mbox{\textit{OCR MEI M1 2012 Q5 [8]}}