| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2016 |
| Session | October |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Friction |
| Type | Particle on inclined plane - force at angle to slope |
| Difficulty | Standard +0.3 This is a standard M1 friction problem requiring resolution of forces in two directions and application of F=μR at limiting equilibrium. While it involves multiple forces at angles, the method is routine: resolve parallel and perpendicular to the plane, use F=μR, and solve. Slightly above average difficulty due to the angled applied force, but still a textbook exercise with no novel insight required. |
| Spec | 1.05a Sine, cosine, tangent: definitions for all arguments3.03e Resolve forces: two dimensions3.03f Weight: W=mg3.03i Normal reaction force3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \((\perp)\quad R = 8\cos50° + 0.5g\cos30°\) | M1 A2 | Resolve perpendicular to plane; 8 with \(40°\) or \(50°\); \(0.5g\) with \(30°\) or \(60°\); \(-1\) each error |
| \((\parallel)\quad F = 8\cos40° - 0.5g\sin30°\) | M1 A2 | Resolve parallel to plane; same angle rules apply |
| \(F = \mu R\) | B1 | |
| \(\mu = 0.39\) or \(0.392\) | DM1 A1 (9) | DM1 dependent on both M marks |
## Question 5:
### Part (a)
| Working | Marks | Guidance |
|---------|-------|---------|
| $(\perp)\quad R = 8\cos50° + 0.5g\cos30°$ | M1 A2 | Resolve perpendicular to plane; 8 with $40°$ or $50°$; $0.5g$ with $30°$ or $60°$; $-1$ each error |
| $(\parallel)\quad F = 8\cos40° - 0.5g\sin30°$ | M1 A2 | Resolve parallel to plane; same angle rules apply |
| $F = \mu R$ | B1 | |
| $\mu = 0.39$ or $0.392$ | DM1 A1 (9) | DM1 dependent on both M marks |5.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{6978be48-561b-49a0-a297-c8886ca66c19-10_419_933_123_525}
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\caption{Figure 2}
\end{center}
\end{figure}
A particle $P$ of mass 0.5 kg is at rest on a rough plane which is inclined to the horizontal at $30 ^ { \circ }$. The particle is held in equilibrium by a force of magnitude 8 N , acting at an angle of $40 ^ { \circ }$ to the plane, as shown in Figure 2. The line of action of the force lies in the vertical plane containing $P$ and a line of greatest slope of the plane. The coefficient of friction between $P$ and the plane is $\mu$. Given that $P$ is on the point of sliding up the plane, find the value of $\mu$.\\
\hfill \mbox{\textit{Edexcel M1 2016 Q5 [9]}}