Question

Two blocks of masses m₁, m₂ are connected by a light spring on a smooth horizontal surface. The two masses are pulled apart and the released. Prove that the ratio of their acceleration are inversely proportional to their masses.

Answer 1

The forces F₁ and F₂ due to masses m₁ and m₂ respectively act on the stretched spring in opposite directions. Thus, the system as a whole is at

Thus F₁ + F₂ = 0

or, m₁a₁ + m₂a₂ = 0

Where a₁ and a₂ are accelerated of the masses m₁ and m₂ respectively in the opposite direction.

Now, m₁a₁ = -m₂a₂

or, a₁/a₂ = -m₂/m₁

which was to be established.