Question

A ball having a mass of 130 g strikes a wall with a speed of 6.5 m/s perpendicular to the wall and rebounds with only 42% of its initial kinetic energy. (a) What is the speed of the ball immediately after rebounding? (b) What is the magnitude of the impulse on the wall from the ball? (c) If the ball was in contact with the wall for 9.5 ms, what was the magnitude of the average force on the ball from the wall during this time interval?

Answer 1

given,

mass of ball = 130 g = 0.13 kg

speed = 6.5 m/s

t = 9.5 ms = 0.0095 s

rebound with 42 % of initial kinetic energy

a)
`(1)/(2)mv_2^2 =0.42* (1)/(2)mv_1^2`

`v_2^2 =0.42* (6.5)^2`

v₂ = 4.212 m/s

b) impulse is equal to change in momentum

`I = m (v_1-v_2)`

`I = 0.13*(6.5 -(-4.21))`

I = 1.393 kg m/s

c) Force =
`(I)/(t)`

=
`(1.393)/(0.0095)`

F = 146.63 N