Question

A small ball of mass = 0.1 kg is attached to a small spring of stiffness = 10 kN×m^-1 that has been compressed a distance = 8 mm. The spring is housed at one end of a box of length = 1 m and mass = 1 kg that is, in turn, resting on a smooth horizontal table. The spring is then released and the ball travels to the other end of the box where it sticks to the surface. Determine the displacement of the center of gravity of this system after this event. This question is a component of Einstein’s early proof of the equivalence between mass and energy. The second component considers the ball in terms of a light pulse.

Answer 1

If we take the box + ball as a system and talk of the external forces acting. The only external force acting could have been friction ( which is absent here). Thus no external force acts on the system. Weight is balanced by the normal reactions from the respective surfaces inside and outside the box.

Initially the system is at rest and in absence of external forces acceleration of center of mass will be zero. The center of mass will not move.

Hence the displacement of center of mass is zero

Here we can assume center of gravity and center of mass are same.