5 Two particles, \(A\) of mass \(m _ { A } \mathrm {~kg}\) and \(B\) of mass 5 kg , are moving directly towards each other on a smooth horizontal floor. Before they collide they have speeds \(\mathrm { u } _ { \mathrm { A } } \mathrm { m } \mathrm { s } ^ { - 1 }\) and \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively. Immediately after they collide the direction of motion of each particle has been reversed and \(A\) and \(B\) have speeds \(3.25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively (see diagram). The coefficient of restitution between \(A\) and \(B\) is 0.75 .
Before:
\includegraphics[max width=\textwidth, alt={}, center]{d2156252-71f2-4084-89a2-4d246583eb65-4_218_711_552_283}
After:
\includegraphics[max width=\textwidth, alt={}, center]{d2156252-71f2-4084-89a2-4d246583eb65-4_218_707_552_1078}
- Determine the value of \(m _ { A }\) and the value of \(u _ { A }\).
[0pt]
[5] - Show that approximately \(41 \%\) of the kinetic energy of the system is lost in this collision.
After the collision between \(A\) and \(B\), \(B\) goes on to collide directly with a third particle \(C\) of mass 3 kg which is travelling towards \(B\) with a speed of \(5.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The coefficient of restitution between \(B\) and \(C\) is denoted by \(e\).
- Given that, after \(B\) and \(C\) collide, there are no further collisions between \(A , B\) and \(C\) determine the range of possible values of \(e\).