3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{05cf68a3-1ba4-487f-9edd-48a246f4194f-08_259_597_214_678}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
A particle of mass 10 kg is placed on a fixed rough inclined plane. The plane is inclined to the horizontal at an angle \(\alpha\), where \(\tan \alpha = \frac { 3 } { 4 }\). The particle is held in equilibrium by a force of magnitude \(P\) newtons, which acts up the plane, as shown in Figure 1. The line of action of the force lies in a vertical plane that contains a line of greatest slope of the plane. The coefficient of friction between the particle and the plane is \(\frac { 1 } { 2 }\).
- Find the normal reaction between the particle and the plane.
- Find the greatest possible value of \(P\).
- Find the least possible value of \(P\).
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