| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2018 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Friction |
| Type | Friction inequality derivation |
| Difficulty | Standard +0.3 This is a standard M1 friction problem requiring resolution of forces in two directions and application of the friction inequality F ≤ μR. The steps are routine: resolve horizontally and vertically, find R, apply the friction condition, and rearrange. It's slightly easier than average because it's a 'show that' question with a clear target and uses straightforward numbers (40N weight, 20N force). |
| Spec | 3.03m Equilibrium: sum of resolved forces = 03.03u Static equilibrium: on rough surfaces |
| Answer | Marks |
|---|---|
| Resolve horizontally: \(F = 20 \cos \theta\) | M1A1 |
| Resolve vertically: \(R = 40 - 20 \sin \theta\) | M1A1 |
| Use of \(F = R \tan \theta\): \(20 \cos \theta = (40 - 20 \sin \theta) \tan \theta\) | DM1 |
| \(\frac{20 \cos \theta}{\cos \theta} = \frac{40 - 20 \sin \theta}{2 \sin \theta}\) — Given Answer | A1 |
Resolve horizontally: $F = 20 \cos \theta$ | M1A1
Resolve vertically: $R = 40 - 20 \sin \theta$ | M1A1
Use of $F = R \tan \theta$: $20 \cos \theta = (40 - 20 \sin \theta) \tan \theta$ | DM1
$\frac{20 \cos \theta}{\cos \theta} = \frac{40 - 20 \sin \theta}{2 \sin \theta}$ — Given Answer | A1
(6 marks)
**Notes for Question 2**
[Notes section appears incomplete in source material]2.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{04b73f81-3316-4f26-ad98-a7be3a4b738f-06_241_768_214_589}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
A particle $P$ of weight 40 N lies at rest in equilibrium on a fixed rough horizontal surface. A force of magnitude 20 N is applied to $P$. The force acts at angle $\theta$ to the horizontal, as shown in Figure 2. The coefficient of friction between $P$ and the surface is $\mu$.
Given that the particle remains at rest, show that
$$\mu \geqslant \frac { \cos \theta } { 2 + \sin \theta }$$
\includegraphics[max width=\textwidth, alt={}, center]{04b73f81-3316-4f26-ad98-a7be3a4b738f-07_119_167_2615_1777}\\
\hfill \mbox{\textit{Edexcel M1 2018 Q2 [6]}}