A 430 g football is lying on the ground, then is kicked and is moving at 25 m/s. If the duration of the impact was 0.0010 s, what was the average force on the ball?
Tools used for this solution:
Impulse = change in momentum
Impulse = (force ) x (time applied)
Momentum = (mass) x (speed)
Momentum of the ball after the kick = (mass)x(speed) = 0.43kg x 25 m/s = 10.75 kg-m/s .
Impulse exerted by the kicker's toe = 10.75 kg-m/s .
(force) x (time) = 10.75 kg-m/s .
Force x 0.001 sec = 10.75 kg-m/s .
Divide each side by 0.001 sec :
Force = (10.75 kg-m/sec) / (0.001 sec) = 10,750 kg-m/s² = 10,750 newtons.
That's about 2,416 pounds from the kicker's toe, during that ¹/₁₀₀₀ of a second.
(1.21 tons !)