19 Two frictionless trolleys A and B, of mass m and 3m respectively, are on a
horizontal track (Fig. 3.28). Initially they are clipped together by a device which
incorporates a spring, compressed between the trolleys. At time t=0 the clip is
released. The velocity of trolley B is u to the right.
B
A Figure 3.28
a Calculate the velocity of trolley A as the trolleys move apart.
b
At time t= t₁, trolley A collides elastically with a fixed spring and rebounds.
(Compression and expansion of the spring take a negligibly short time.)
Trolley A catches up with trolley B at time t = ₂.
i Calculate the velocity of trolley A between t=t, and t = ₂.
ii Find an expression for t, in terms of t₁.
c When trolley A catches up with trolley B at time to the clip operates so as to
link them again, this time without the spring between them, so that they move
together with velocity v.
Calculate the common velocity v in terms of u.
d Initially the trolleys were at rest and the total momentum of the system was
zero. However, the answer to c shows that the total momentum after t = t₂ is
not zero. Discuss this result with reference to the principle of conservation of
momentum.