Edexcel M1 2023 June — Question 6

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2023
SessionJune
TopicFriction

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f2737a11-4a15-41e9-9f87-31a705a8948b-16_314_815_246_625} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A particle of weight \(W\) newtons lies at rest on a rough horizontal surface, as shown in Figure 3.
A force of magnitude \(P\) newtons is applied to the particle.
The force acts at an angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 4 } { 3 }\)
The coefficient of friction between the particle and the surface is \(\frac { 1 } { 4 }\)
Given that the particle does not move, show that $$P \leqslant \frac { 5 W } { 8 }$$