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. Assume all surfaces are frictionless. Find the maximum height (measured from the ground) that the small body ascends.

Step-by-step solution

Let the initial velocity of the small body of mass m be v and the larger mass M be at rest. Since there is no external force acting on the system in the horizontal direction, the horizontal component of momentum is conserved. At the maximum height h , the small body is at rest relative to the larger mass. Thus, both masses move with the same horizontal velocity V . Applying conservation of linear momentum in the horizontal direction: mv = (M + m)V V = mv M + m Applying conservation of mechanical energy for the syst