A body of mass M is suspended by a spring of spring constant k. A particle of mass m is dropped from height h

Question

The particle sticks to the block after impact. How to determine the velocity of the block after the impact?

Answer 1

Let:

u be the speed of the particle when it meets the mass,

v be the speed of the particle and block after collision.

u^2 = 2gh

Conserving momentum:

(M + m)v = mu

v = m sqrt(2gh) / (M + m).

The force exerted by the spring only comes into play once the block and mass have started moving. A larger value h gives a larger value for v, and increases the amplitude of the ensuing SHM.