Question

A highly elastic rubber ball is tossed at a moveable wooden wall panel that is initially at rest. The ball’s initial velocity is 7.00 m/s to the right. After the elastic collision, the ball returns with a velocity of 4.90 m/s to the left, while the panel moves 2.09 m/s to the right. If the panel’s mass is 2.25 kg, what is the mass of the ball?

Answer 1

Given that the initial velocity of the ball is

`u_b=7\text{ m/s}`

towards right.

The final velocity of the ball is

`v_b=4.90\text{ m/s}`

towards the left.

The mass of the panel is M = 2.25 kg.

The initial velocity of the panel is

`u_p=\text{ m/s}`

The final velocity of the panel is

`v_p=\text{ 2.09 m/s}`

towards the right.

Let the mass of the ball be m.

According to the conservation of momentum

`mu_b+Mu_p=-mv_b+Mv_p`

Substituting the values, the mass of the ball will be

`\begin{gathered} m*\text{ 7+2.25}*0=-m*4.90+2.25*2.09 \\ 7m+4.90m=4.702\text{ } \\ m=0.395\text{ kg} \end{gathered}`

Thus, the mass of the ball is 0.395 kg.