A small body of mass m is placed over a larger mass M whose surface is horizontal near the small body and gradually curves to become vertical. The small body is pushed on the larger mass at a speed v and the system is subsequently left to itself. Assuming all surfaces are frictionless, the small body will eventually break off and later land back on the larger mass. Find the distance traversed by the larger block duri

Step-by-step solution

Let V be the common horizontal velocity of the small body m and the larger mass M when the small body breaks off. Since the surface becomes vertical at the top, the horizontal velocity of m relative to M is zero, meaning both have the same horizontal velocity V in the ground frame. By conservation of horizontal momentum: mv = (M + m)V V = mv M + m Let v_y be the vertical velocity of the small body at the moment it breaks off. By conservation of mechanical energy: 1 2 mv^2 = 1 2 (M + m)V^2 + 1 2 mv_y^2 + mgh Substit