| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | January |
| Marks | 7 |
| 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 M1 equilibrium problem requiring resolution of forces and application of Newton's first law. Part (i) is trivial (R = mg), while parts (ii)-(iii) involve standard resolution of a force at an angle and balancing vertical/horizontal components—routine textbook exercises with no problem-solving insight required. |
| Spec | 3.03e Resolve forces: two dimensions3.03f Weight: W=mg3.03i Normal reaction force3.03m Equilibrium: sum of resolved forces = 0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(R = 5g = 49\) N | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Diagram showing: Weight \(5g\) down, Normal reaction \(R\) up, Friction \(F\) horizontal, Applied force 10 N at 40° to vertical | B2 | B1 each for correct forces (lose one for each error/omission) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Resolve vertically: \(R + 10\cos 40° = 5g\) | M1 | |
| \(R = 49 - 10\cos 40° = 41.3\) N | A1 | |
| Resolve horizontally: \(F = 10\sin 40°\) | M1 | |
| \(F = 6.43\) N | A1 |
# Question 3:
**(i)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $R = 5g = 49$ N | B1 | |
**(ii)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Diagram showing: Weight $5g$ down, Normal reaction $R$ up, Friction $F$ horizontal, Applied force 10 N at 40° to vertical | B2 | B1 each for correct forces (lose one for each error/omission) |
**(iii)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Resolve vertically: $R + 10\cos 40° = 5g$ | M1 | |
| $R = 49 - 10\cos 40° = 41.3$ N | A1 | |
| Resolve horizontally: $F = 10\sin 40°$ | M1 | |
| $F = 6.43$ N | A1 | |3 A box of mass 5 kg is at rest on a rough horizontal floor.\\
(i) Find the value of the normal reaction of the floor on the box.
The box remains at rest on the floor when a force of 10 N is applied to it at an angle of $40 ^ { \circ }$ to the upward vertical, as shown in Fig. 3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{52d6c914-b204-4587-a82e-fbab6693fcf8-2_293_472_2131_794}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{center}
\end{figure}
(ii) Draw a diagram showing all the forces acting on the box.\\
(iii) Calculate the new value of the normal reaction of the floor on the box and also the frictional force.
\hfill \mbox{\textit{OCR MEI M1 2007 Q3 [7]}}