3. A particle \(P\) of mass 1.5 kg is placed at a point \(A\) on a rough plane which is inclined at \(30 ^ { \circ }\) to the horizontal. The coefficient of friction between \(P\) and the plane is 0.6
- Show that \(P\) rests in equilibrium at \(A\).
A horizontal force of magnitude \(X\) newtons is now applied to \(P\), as shown in Figure 1. The force acts in a vertical plane containing a line of greatest slope of the inclined plane.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{edcc4603-f006-4c4f-a4e5-063cab41da98-04_236_584_667_680}
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\caption{Figure 1}
\end{figure}
The particle is on the point of moving up the plane. - Find
- the magnitude of the normal reaction of the plane on \(P\),
- the value of \(X\).