Question

Two particles of masses `m_(1)` and `m_(2)` are connected by a light and inextensible string which passes over a fixed pulley. Initially, the particle `m_(1)` moves with velocity `v_(0)` when the string is not taut. Neglecting fricting in all contacting surface, find the velocities of the particles `m_(1)` and `m_(2)` just after the string is taut.

Answer 1

During the impact a large tension develops. The impulse of tension `T_(1)` is equal to the change of momentum of `m_(1)` which is given as
`m_(1)v_(0)-J=m_(1)v`

Similarly the impulse of tension `T_(2)` is equal to the change in momentum of `m_(2)` which is given as
`J=m_(2)v`......ii
from eqn i and ii we have
`m_(1)(v_(0)-v)=m_(2)v`
This gives `v=(m_(1)v_(0))/(m_(1)+m_(2))`