A ball of mass m and another ball of mass 3m are placed inside a smooth metal tube with a massless spring compressed between them. When the spring is released, the heavier ball flies out of one end of the tube with speed v0. With what speed does the lighter ball emerge from the other end? Express your answer in terms of v0just vov = ___.

The lighter ball emerges from the other end at a speed of v = √3 · v0

Explanation:

Hi there!

Since the balls had the same elastic potential energy when resting at the side of the compressed spring, both balls must have acquired the same kinetic energy. The kinetic energy, KE, is calculated as follows:

KE = 1/2 · m · v²

Where:

m = mass of the ball.

v = velocity.

In our case:

KE heavier ball = KE lighter ball

1/2 · 3m · v0² = 1/2 · m · v²

multiply by 2 and divide by m both sides of the equation:

3 · v0² = v²

√3 · v0 = v

The lighter ball emerges from the other end at a speed of v = √3 · v0