Two blocks of masses m1, m2 are connected by a light spring on a smoot

1.	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» 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.

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»

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.