Question

Figure (9-E22) shows a small body of mass m placed over a larger mass M whose surface is horizontal near the smaller mass and gradually curves to become vertical. The smaller mass is pushed on the longer one at a speed v and the system is left to itself. Assume that all the surfaces are frictionless. (a) Find the speed of the larger block when the smaller block is sliding on the vertical part. (b) Find the speed of the smaller mass when it breaks off the larger mass at height h. (c) Find the maximum height (from the ground) that the smaller mass ascends. (d) Show that the smaller mass will again land on the bigger one. Find the distance traversed by the bigger block during the time when the smaller block was in its flight under gravity.

Answer 1

The mass ‘m’ is given a velocity ‘v’ over the larger mass M.
a) When the smaller block is travelling on the vertical part, let the velocity of the bigger block be v₁ towards left.
From law of conservation of momentum, (in the horizontal direction)

c) Now, the vertical component of the velocity v₂ of mass ‘m’ is given by,

To find the maximum height (from the ground), let us assume the body rises to a height ‘h’, over and above ‘h’.

d) Because, the smaller mass has also got a horizontal component of velocity ‘v₁’ at the time it breaks off from ‘M’ (which has a velocity v₁), the block ‘m’ will again land on the block ‘M’ (bigger one). Let us find out the time of flight of block ‘m’ after it breaks off. During the upward motion (BC),