7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8a687d17-ec7e-463f-84dd-605f5c230db1-24_394_1027_248_461}
\captionsetup{labelformat=empty}
\caption{Figure 8}
\end{figure}
A particle \(P\) of mass 0.5 kg is attached to one end of a light elastic string of natural length 2 m and modulus of elasticity 3 N . The other end of the string is attached to a fixed point \(O\) on a rough plane. The plane is inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 2 } { 7 }\)
The coefficient of friction between \(P\) and the plane is \(\frac { \sqrt { 5 } } { 5 }\)
The particle \(P\) is initially at rest at the point \(O\), as shown in Figure 8.
The particle \(P\) then receives an impulse of magnitude 4 Ns, directed up a line of greatest slope of the plane.
The particle \(P\) moves up the plane and comes to rest at the point \(A\).
- Find the extension of the elastic string when \(P\) is at \(A\).
- Show that the particle does not remain at rest at \(A\).