| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2016 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Block on rough horizontal surface – accelerating (finding acceleration or applied force) |
| Difficulty | Moderate -0.3 This is a straightforward mechanics problem requiring a force diagram and resolving forces in two directions with given values. It involves standard M1 techniques (resolving forces, F=ma) with no conceptual challenges, making it slightly easier than average but still requiring proper method. |
| Spec | 3.03a Force: vector nature and diagrams3.03c Newton's second law: F=ma one dimension3.03e Resolve forces: two dimensions |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Forces: \(T\), \(R\), \(F\), \(Mg\) shown | B1 | B0 if one force missing or an extra force present |
| Labels | B1 | |
| Arrows | B1 | B0 if \(T\) in tension |
| Allow \(T\) given in components provided it is clear they are not additional forces. Allow sin-cos interchange in this case. Give B0 B0 B0 if 2 or more forces missing |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(T \cos \alpha - F = ma\) | M1 | Horizontal equation of motion with the right 3 elements |
| \(40\cos \alpha - F = 5 \times 1.5\) | A1 | A0 if sin-cos interchange |
| \(F = 12.5\) Frictional force of 12.5 N. | A1 | CAO |
**(i)**
| Answer | Mark | Guidance |
|--------|------|----------|
| Forces: $T$, $R$, $F$, $Mg$ shown | B1 | B0 if one force missing or an extra force present |
| Labels | B1 | |
| Arrows | B1 | B0 if $T$ in tension |
| | | Allow $T$ given in components provided it is clear they are not additional forces. Allow sin-cos interchange in this case. Give B0 B0 B0 if 2 or more forces missing |
**(ii)**
| Answer | Mark | Guidance |
|--------|------|----------|
| $T \cos \alpha - F = ma$ | M1 | Horizontal equation of motion with the right 3 elements |
| $40\cos \alpha - F = 5 \times 1.5$ | A1 | A0 if sin-cos interchange |
| $F = 12.5$ Frictional force of 12.5 N. | A1 | CAO |
---1 Fig. 1 shows a block of mass $M \mathrm {~kg}$ being pushed over level ground by means of a light rod. The force, $T \mathrm {~N}$, this exerts on the block is along the line of the rod.
The ground is rough.\\
The rod makes an angle $\alpha$ with the horizontal.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{4c8c96cf-5184-46e4-9c45-a8a80d0a6ff8-2_307_876_621_593}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
(i) Draw a diagram showing all the forces acting on the block.\\
(ii) You are given that $M = 5 , \alpha = 60 ^ { \circ } , T = 40$ and the acceleration of the block is $1.5 \mathrm {~ms} ^ { - 2 }$. Find the frictional force.
\hfill \mbox{\textit{OCR MEI M1 2016 Q1 [6]}}