Two railway trucks, \(P\) and \(Q\), of equal mass, are moving towards each other with speeds \(4 u\) and \(5 u\) respectively along a straight stretch of rail which may be modelled as being smooth. They collide and move apart. The coefficient of restitution between \(P\) and \(Q\) is \(e\).
Find, in terms of \(u\) and \(e\), the speed of \(Q\) after the collision.
Show that \(e > \frac { 1 } { 9 }\).
\(Q\) now hits a fixed buffer and rebounds along the track. \(P\) continues to move with the speed that it had immediately after it collided with \(Q\).
Prove that it is impossible for a further collision between \(P\) and \(Q\) to occur.
A uniform lamina is in the form of a trapezium \(A B C D\), as shown. \(A B\) and \(D C\) are perpendicular to \(B C . A B = 17 \mathrm {~cm} , B C = 21 \mathrm {~cm}\) and \(C D = 8 \mathrm {~cm}\).
Find the distances of the centre of mass of the lamina from
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\(A B\),
\(B C\).
The lamina is freely suspended from \(C\) and rests in equilibrium.