3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{184043b7-1222-44fb-bc9f-3f484f72147b-08_408_606_246_731}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
A particle \(P\) of mass \(m\) is held at rest at a point on a rough inclined plane, as shown in Figure 3.
It is given that
- the plane is inclined to the horizontal at an angle \(\alpha\), where \(\tan \alpha = \frac { 5 } { 12 }\)
- the coefficient of friction between \(P\) and the plane is \(\mu\), where \(\mu < \frac { 5 } { 12 }\)
The particle \(P\) is released from rest and slides down the plane.
Air resistance is modelled as being negligible.
Using the model,
- find, in terms of \(m\) and \(g\), the magnitude of the normal reaction of the plane on \(P\),
- show that, as \(P\) slides down the plane, the acceleration of \(P\) down the plane is
$$\frac { 1 } { 13 } g ( 5 - 12 \mu )$$
- State what would happen to \(P\) if it is released from rest but \(\mu \geqslant \frac { 5 } { 12 }\)