| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Motion down rough slope |
| Difficulty | Standard +0.3 This is a standard M1 inclined plane problem with friction requiring resolution of forces and application of F=μR. Part (a) involves routine force resolution in two directions and substitution of the limiting friction condition. Part (b) requires applying Newton's second law with friction now acting up the plane. While it has multiple steps (10 marks total), all techniques are standard textbook exercises with no novel insight required, making it slightly easier than average. |
| Spec | 3.03r Friction: concept and vector form3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Resolve perp. and \(\parallel\) plane: \(R = 1.2g \cos \alpha\), \(8.4 = 1.2g \sin \alpha + \frac{1}{8}R\) | M1 A1 M1 A1 | |
| \(1.2g(\sin \alpha + \frac{1}{8} \cos \alpha) = 8.4\) | M1 A1 | |
| \(7(8 \sin \alpha + \cos \alpha) = 40\) | M1 A1 | |
| (b) Acc. down plane \(= g \sin 38° - \frac{1}{8}g \cos 38° = 5.07\) ms\(^{-2}\) | M1 M1 A1 A1 | Total: 10 marks |
**(a)** Resolve perp. and $\parallel$ plane: $R = 1.2g \cos \alpha$, $8.4 = 1.2g \sin \alpha + \frac{1}{8}R$ | M1 A1 M1 A1 |
$1.2g(\sin \alpha + \frac{1}{8} \cos \alpha) = 8.4$ | M1 A1 |
$7(8 \sin \alpha + \cos \alpha) = 40$ | M1 A1 |
**(b)** Acc. down plane $= g \sin 38° - \frac{1}{8}g \cos 38° = 5.07$ ms$^{-2}$ | M1 M1 A1 A1 | **Total: 10 marks**\includegraphics{figure_3}
A small packet, of mass $1.2$ kg, is at rest on a rough plane inclined at an angle $\alpha$ to the horizontal. The coefficient of friction between the packet and the plane is $\frac{1}{8}$.
When a force of magnitude $8.4$ N, acting parallel to the plane, is applied to the packet as shown, the packet is just on the point of moving up the plane. Modelling the packet as a particle,
\begin{enumerate}[label=(\alph*)]
\item show that $7(\cos \alpha + 8 \sin \alpha) = 40$. \hfill [6 marks]
\end{enumerate}
Given that the solution of this equation is $\alpha = 38°$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the acceleration with which the packet moves down the plane when it is released from rest with no external force applied. \hfill [4 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q3 [10]}}