Edexcel M1 2023 January — Question 8

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2023
SessionJanuary
TopicMotion on a slope

8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{84c0eead-0a87-4d87-b33d-794a94bb466c-24_545_764_285_651} \captionsetup{labelformat=empty} \caption{Figure 5}
\end{figure} A parcel of mass 2 kg is pulled up a rough inclined plane by the action of a constant force. The force has magnitude 18 N and acts at an angle of \(40 ^ { \circ }\) to the plane.
The line of action of the force lies in a vertical plane containing a line of greatest slope of the inclined plane. The plane is inclined at an angle of \(30 ^ { \circ }\) to the horizontal, as shown in Figure 5.
The coefficient of friction between the plane and the parcel is 0.3
The parcel is modelled as a particle \(P\)
  1. Find the acceleration of \(P\) The points \(A\) and \(B\) lie on a line of greatest slope of the plane, where \(A B = 5 \mathrm {~m}\) and \(B\) is above \(A\). Particle \(P\) passes through \(A\) with speed \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the direction \(A B\).
  2. Find the speed of \(P\) as it passes through \(B\). The force of 18 N is removed at the instant \(P\) passes through \(B\). As a result, \(P\) comes to rest at the point \(C\).
  3. Determine whether \(P\) will remain at rest at \(C\). You must show all stages of your working clearly.