Edexcel M1 2014 June — Question 7

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2014
SessionJune
TopicMotion on a slope

7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b896c631-00a0-46c5-bce9-16d65f6e3095-13_364_833_269_561} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} A particle \(P\) of mass 2.7 kg lies on a rough plane inclined at \(40 ^ { \circ }\) to the horizontal. The particle is held in equilibrium by a force of magnitude 15 N acting at an angle of \(50 ^ { \circ }\) to the plane, as shown in Figure 4. The force acts in a vertical plane containing a line of greatest slope of the plane. The particle is in equilibrium and is on the point of sliding down the plane. Find
  1. the magnitude of the normal reaction of the plane on \(P\),
  2. the coefficient of friction between \(P\) and the plane. The force of magnitude 15 N is removed.
  3. Determine whether \(P\) moves, justifying your answer.