8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{724254f3-3a6a-4820-b3a1-979458e24437-13_334_538_219_703}
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\caption{Figure 2}
\end{figure}
A particle \(P\) of mass 4 kg is moving up a fixed rough plane at a constant speed of \(16 \mathrm {~ms} ^ { - 1 }\) under the action of a force of magnitude 36 N . The plane is inclined at \(30 ^ { \circ }\) to the horizontal. The force acts in the vertical plane containing the line of greatest slope of the plane through \(P\), and acts at \(30 ^ { \circ }\) to the inclined plane, as shown in Figure 2. The coefficient of friction between \(P\) and the plane is \(\mu\). Find
- the magnitude of the normal reaction between \(P\) and the plane,
- the value of \(\mu\).
The force of magnitude 36 N is removed.
- Find the distance that \(P\) travels between the instant when the force is removed and the instant when it comes to rest.