2 A particle \(P\) of mass 2.4 kg is moving in a straight line \(O A\) on a horizontal plane. \(P\) is acted on by a force of magnitude 30 N in the direction of motion. The distance \(O A\) is 10 m .
\begin{enumerate}[label=(\alph*)]
\item Find the work done by this force as \(P\) moves from \(O\) to \(A\).
The motion of \(P\) is resisted by a constant force of magnitude \(R \mathrm {~N}\). The velocity of \(P\) increases from \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at \(O\) to \(18 \mathrm {~ms} ^ { - 1 }\) at \(A\).
\item Find the value of \(R\).
\item Find the average power used in overcoming the resistance force on \(P\) as it moves from \(O\) to \(A\).
When \(P\) reaches \(A\) it collides directly with a particle \(Q\) of mass 1.6 kg which was at rest at \(A\) before the collision. The impulse exerted on \(Q\) by \(P\) as a result of the collision is 17.28 Ns .
\item
- Find the speed of \(Q\) after the collision.
- Hence show that the collision is inelastic.
It is required to model the motion of a car of mass \(m \mathrm {~kg}\) travelling at a constant speed \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) around a circular portion of banked track. The track is banked at \(30 ^ { \circ }\) (see diagram).
\includegraphics[max width=\textwidth, alt={}, center]{b9741472-f230-4e2d-9c8b-47f7e168e938-03_355_565_269_274}
In a model, the following modelling assumptions are made.
For a particular portion of banked track, \(r = 24\).
(b) Find the value of \(v\) as predicted by the model.
A car is being driven on this portion of the track at the constant speed calculated in part (b). The driver finds that in fact he can drive a little slower or a little faster than this while still moving in the same horizontal circle.
(c) Explain