In this part-question, all the objects move along the same straight line on a smooth horizontal plane. All their collisions are direct.
The masses of the objects \(\mathrm { P } , \mathrm { Q }\) and R and the initial velocities of P and Q (but not R ) are shown in Fig. 1.1.
\begin{figure}[h]
\end{figure}
A force of 21 N acts on P for 2 seconds in the direction \(\mathrm { PQ } . \mathrm { P }\) does not reach Q in this time.
Calculate the speed of P after the 2 seconds.
The force of 21 N is removed after the 2 seconds. When P collides with Q they stick together (coalesce) to form an object S of mass 6 kg .
Show that immediately after the collision S has a velocity of \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) towards R .
The collision between S and R is elastic with coefficient of restitution \(\frac { 1 } { 4 }\). After the collision, S has a velocity of \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the direction of its motion before the collision.
Find the velocities of R before and after the collision.
\section*{(b) In this part-question take \(\boldsymbol { g } = \mathbf { 1 0 }\).}
A particle of mass 0.2 kg is projected vertically downwards with initial speed \(5 \mathrm {~ms} ^ { - 1 }\) and it travels 10 m before colliding with a fixed smooth plane. The plane is inclined at \(\alpha\) to the vertical where \(\tan \alpha = \frac { 3 } { 4 }\). Immediately after its collision with the plane, the particle has a speed of \(13 \mathrm {~ms} ^ { - 1 }\). This information is shown in Fig. 1.2. Air resistance is negligible.
\begin{figure}[h]
Calculate the angle between the direction of motion of the particle and the plane immediately after the collision.
Calculate also the coefficient of restitution in the collision.
Calculate the magnitude of the impulse of the plane on the particle.