Question

A spring is compressed between two trucks of masses m₁ and m₂ (Fig.). When the trucks are released, the spring acts on each with an average force F for a time t. Show that, after the spring ceases to act, the trucks will move on horizontal tracks in such a way that the centre of gravity remains motionless. Neglect friction.

Answer 1

The centre of mass of the system before the beginning of the motion lies on line OO (Fig.). According

to the definition of the centre of mass, the distance l₁ and l₂  of the trucks to the centre of mass at any time l should be inversely proportional to their masses, i.e.,

The velocity acquired by the trucks as a result of the action of the compressed spring is, by Newton's second law, given by

The distance of the trucks from line 00 satisfies the same relation as the distances to the centre of gravity of the trucks, i.e., the centre of gravity of the trucks always remains on line 00. 

The same result may also be obtained directly from the law of conservation of momentum, which in our case gives