A ball of mass 1 kg moving with a speed of 10 ms-1 rebounds after a perfect elastic collision with the floor. Calculate the change in linear momentum of the ball. - Science

Question

A ball of mass 1 kg moving with a speed of \(10 \, \text{ms}^{-1}\) rebounds after a perfect elastic collision with the floor. Calculate the change in linear momentum of the ball.

Solution

Mass of the ball, \(m = 1 \, \text{kg}\).
Initial velocity of the ball (before collision), \(u = 10 \, \text{ms}^{-1}\). We'll consider the downward direction as positive.

Since the collision is perfectly elastic, the ball rebounds with the same speed but in the opposite direction.
Final velocity of the ball (after collision), \(v = -u = -10 \, \text{ms}^{-1}\).

The formula for change in linear momentum (\(\Delta P\)) is:

\[\Delta P = m(v - u)\]
Substituting the values:
\[\Delta P = 1 \times (-10 - 10)\]
\[\Delta P = 1 \times (-20)\]

The change in linear momentum of the ball is:

\[\Delta P = -20 \, \text{kg} \cdot \text{m/s}\]

(The negative sign indicates the change in momentum is in the upward direction).