4 Two uniform circular discs with the same radius, A of mass 1 kg and B of mass 5.25 kg , slide on a smooth horizontal surface and collide obliquely with smooth contact.
Fig. 4 gives information about the velocities of the discs just before and just after the collision.
- The line XY passes through the centres of the discs at the moment of collision
- The components parallel and perpendicular to XY of the velocities of A are shown
- Before the collision, B is at rest and after it is moving at \(2 \mathrm {~ms} ^ { - 1 }\) in the direction XY
\begin{figure}[h]
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\caption{Fig. 4}
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The coefficient of restitution between the two discs is \(\frac { 2 } { 3 }\).
- Find the values of \(U\) and \(u\).
- What information in the question tells you that \(v = V\) ?
The speed of disc A before the collision is \(8.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- Find the speed of disc A after the collision.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a01b2e46-e213-4f20-bc2e-5852061d8b91-5_398_396_397_475}
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\caption{Fig. 5.1}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a01b2e46-e213-4f20-bc2e-5852061d8b91-5_399_332_399_945}
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\caption{Fig. 5.2}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a01b2e46-e213-4f20-bc2e-5852061d8b91-5_305_326_493_1354}
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\caption{Fig. 5.3}
\end{figure}
Fig. 5.1 shows a vertical light elastic spring. It is fixed to a horizontal table at one end. Fig 5.2 shows the spring with a particle of mass \(m \mathrm {~kg}\) attached to it at the other end. The system is in equilibrium when the spring is compressed by a distance \(h \mathrm {~m}\).