| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2011 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Equilibrium on slope with horizontal force |
| Difficulty | Moderate -0.3 This is a straightforward equilibrium problem requiring resolution of forces in two perpendicular directions (parallel and perpendicular to the slope). While it involves multiple forces and requires careful angle work with the horizontal force, it's a standard M1 exercise with clear methodology—resolve forces, apply equilibrium conditions, solve for P. Slightly easier than average due to being a direct application of a core technique with no conceptual surprises. |
| Spec | 3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 0 |
| Answer | Marks |
|---|---|
| B1 | Any one force in correct direction correctly labelled with arrow or all forces with correct directions and arrows. |
| B1 | All correct (Accept words for labels and weight as \(W, mg, 147 \text{ (N)}\)) No extra or duplicate forces. Do not allow force and its components unless components are clearly distinguished, eg by broken lines. |
| 2 |
| Answer | Marks | Guidance |
|---|---|---|
| \(Pcos20 - 15 \times 9.8 \times sin20 = 0\) | M1 | Attempt to resolve at least one force up plane. Accept mass not weight. No extra forces. If other directions used, all forces must be present but see below for resolving vertically and horizontally. |
| \(P = 53.50362\ldots\) so \(53.5\) (3 s.f.) | A1 | Accept only error as consistent s \(\leftrightarrow\) c. |
| A1 | cao | |
| 3 |
| Answer | Marks | Guidance |
|---|---|---|
| \(R cos 20° = 15g\), \(R sin 20° = P\) | M1 | Attempt to resolve all forces both horizontally and vertically and attempt to combine into a single equation. No extra forces. Accept \(s \leftrightarrow c\). Accept mass not weight. |
| \(P = \frac{15g}{cos 20°} \times sin 20°\) | A1 | Accept only error as consistent s \(\leftrightarrow\) c. |
| \(P = 53.5\) (3 s.f.) | A1 | cao |
| 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Triangle drawn and labelled | M1 | All sides must be labelled and in correct orientation; three forces only; condone no arrows |
| \(\frac{P}{15g} = tan 20°\) | A1 | Oe |
| \(P = 53.5\) (3 s.f.) | A1 | cao |
| 3 | ||
| 5 |
**(i)**
| B1 | Any one force in correct direction correctly labelled with arrow or all forces with correct directions and arrows.
| B1 | All correct (Accept words for labels and weight as $W, mg, 147 \text{ (N)}$) No extra or duplicate forces. Do not allow force and its components unless components are clearly distinguished, eg by broken lines.
| | 2 |
**(ii) Either** Up the plane
$Pcos20 - 15 \times 9.8 \times sin20 = 0$ | M1 | Attempt to resolve at least one force up plane. Accept mass not weight. No extra forces. If other directions used, all forces must be present but see below for resolving vertically and horizontally.
$P = 53.50362\ldots$ so $53.5$ (3 s.f.) | A1 | Accept only error as consistent s $\leftrightarrow$ c.
| A1 | cao
| | 3 |
**Or Vertically and horizontally**
$R cos 20° = 15g$, $R sin 20° = P$ | M1 | Attempt to resolve all forces both horizontally and vertically and attempt to combine into a single equation. No extra forces. Accept $s \leftrightarrow c$. Accept mass not weight.
$P = \frac{15g}{cos 20°} \times sin 20°$ | A1 | Accept only error as consistent s $\leftrightarrow$ c.
$P = 53.5$ (3 s.f.) | A1 | cao
| | 3 |
**Or Triangle of forces**
Triangle drawn and labelled | M1 | All sides must be labelled and in correct orientation; three forces only; condone no arrows
$\frac{P}{15g} = tan 20°$ | A1 | Oe
$P = 53.5$ (3 s.f.) | A1 | cao
| | 3 |
| | 5 |
---
4 Fig. 4 shows a block of mass 15 kg on a smooth plane inclined at $20 ^ { \circ }$ to the horizontal. The block is held in equilibrium by a horizontal force of magnitude $P \mathrm {~N}$.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{2efbb554-fe60-42ce-9213-8c66bfdb1d85-2_280_718_1781_715}
\captionsetup{labelformat=empty}
\caption{Fig. 4}
\end{center}
\end{figure}
(i) Show all the forces acting on the block.\\
(ii) Calculate $P$.
\hfill \mbox{\textit{OCR MEI M1 2011 Q4 [5]}}