Question

Figure shows a block P of mass M resting on a horizontal smooth floor at a distance l from a rigid wall. Block is pushed smooth floor at a distance l from a rigid wall. Block is pushed from its mean position another block of mass m1 is placed on it which sticks to it due to friction. Find the value of m1 so that the combined block just collides with the left wall.

Answer 1

When block P is released from rest from a distance 3l/2 toward right from mean position, this will be the amplitude of oscillation,so velocity of block when passing from its mean position is given as

If mass m1 is added to it and just after if velocity of combined block becomes v1 , from momentum conservation we have

If this is the velocity of combined block at mean position, it must be given as

Where A1 and ω1 are the new amplitude and angular frequency of SHM of the block. It is given that combined block just reaches the left wall thus the new amplitude of oscillation must be l so we have