| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2014 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Horizontal force on slope |
| Difficulty | Standard +0.3 This is a standard M1 mechanics question involving resolving forces on a slope with friction. Part (a) is routine limiting equilibrium, part (b) requires resolving a horizontal force into components perpendicular and parallel to the slope, then applying F=ma. All techniques are standard textbook exercises with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces3.03v Motion on rough surface: including inclined planes |
## Question 8(a)
**Resolve perpendicular to slope:** $R = 40g\cos30°$
**Resolve parallel to slope (on point of slipping down, friction acts up):**
$\mu R = 40g\sin30°$
$$\mu = \frac{40g\sin30°}{40g\cos30°} = \tan30° = \frac{1}{\sqrt{3}} \approx 0.577$$
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## Question 8(b)(i)
**Resolve perpendicular to slope:**
$$R = 40g\cos30° + X\sin30°$$
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## Question 8(b)(ii)
Using $\mu = \frac{1}{\sqrt{3}}$, applying Newton's second law up the slope:
$$X\cos30° - 40g\sin30° - \frac{1}{\sqrt{3}}(40g\cos30° + X\sin30°) = 40 \times 0.2$$
Solving gives **$X \approx 277$ N**8 A crate, of mass 40 kg , is initially at rest on a rough slope inclined at $30 ^ { \circ }$ to the horizontal, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{788534a5-abbb-4d6a-87b2-c54e859a128a-18_355_882_411_587}
The coefficient of friction between the crate and the slope is $\mu$.
\begin{enumerate}[label=(\alph*)]
\item Given that the crate is on the point of slipping down the slope, find $\mu$.
\item A horizontal force of magnitude $X$ newtons is now applied to the crate, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{788534a5-abbb-4d6a-87b2-c54e859a128a-18_357_881_1208_575}
\begin{enumerate}[label=(\roman*)]
\item Find the normal reaction on the crate in terms of $X$.
\item Given that the crate accelerates up the slope at $0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$, find $X$.\\[0pt]
[5 marks]
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{788534a5-abbb-4d6a-87b2-c54e859a128a-19_2484_1707_221_153}
\end{center}
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA M1 2014 Q8 [12]}}