A test machine that kicks soccer balls has a 5-lb simulated foot attached to the end of a 6-ft long pendulum arm of negligible mass. Knowing that the arm is released from the horizontal position and that the coefficient of restitution between the foot and the 1-lb ball is 0.8, determine the exit velocity of the ball (a) if the ball is stationary, (b) if the ball is struck when it is rolling toward the foot with a velocity of 10 ft/s.

a) v₂ = 26.6 ft/s

b) v₂ = 31.9 ft/s

Explanation:

a) If we use the conservation of energy for the soccer arm between tap and lowest position:

The velocity of the ball in the tangencial direction is:

v₂*sinθ = v₁*sin30

If v₁ = 0

θ = 0º

The coefficient of restitution is:

where O=θ

The total momentum is:

, where O = θ

If we multiply by g:

Clearing v₂:

v₂ = 26.6 ft/s

b) The velocity of the ball is:

v₂ * sinθ = v₁ * sin30

if v₁ = 10 ft/s

v₂ * sinθ = 10 * sin30

sinθ = 5/v₂

The coefficient is:

where O = θ

solving for v₂:

v₂ = 31.9 ft/s