5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e8329378-c976-4068-95ff-e2d254546d6d-07_366_771_267_589}
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\caption{Figure 2}
\end{figure}
A particle \(P\) of mass 0.5 kg is projected from a point \(A\) up a line of greatest slope \(A B\) of a fixed plane. The plane is inclined at \(30 ^ { \circ }\) to the horizontal and \(A B = 2 \mathrm {~m}\) with \(B\) above \(A\), as shown in Figure 2. The particle \(P\) passes through \(B\) with speed \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The plane is smooth from \(A\) to \(B\).
- Find the speed of projection.
The particle \(P\) comes to instantaneous rest at the point \(C\) on the plane, where \(C\) is above \(B\) and \(B C = 1.5 \mathrm {~m}\). From \(B\) to \(C\) the plane is rough and the coefficient of friction between \(P\) and the plane is \(\mu\).
By using the work-energy principle,
- find the value of \(\mu\).