Question

A 0.42 kg soccer ball moving at 12 m/s is kicked with a force of 126 N for 0.02 seconds. (a) calculate the impulse on the ball. (b) calculate the change in momentum on your foot. (c) what is the final velocity ofthe ball

Answer 1

a) We can find the impulse on the ball from the definition of impulse:

$$J=F\Delta t=126\ N\cdot0.02\ s=2.52\ N\cdot s.$$

b) Since the impulse on the ball equals the change in momentum on foot, we can write:

$$J=\Delta p_{foot}=2.52\ N\cdot s.$$

c) Let's first calculate the change in velocity of the ball from the impulse-momentum change equation:

$$F\Delta p=m\Delta v,$$ $$\Delta v=\dfrac{F\Delta p}{m}=\dfrac{J}{m}=\dfrac{2.52\ N\cdot s}{0.42\ kg}=6\ \dfrac{m}{s}.$$

Finally, we can find the final velocity of the ball:

$$\Delta v=v_f-v_i,$$ $$v_f=\Delta v+v_i=6\ \dfrac{m}{s}+12\ \dfrac{m}{s}=18\ \dfrac{m}{s}.$$

Answer:

a) $J=2.52\ N\cdot s.$

b) $\Delta p_{foot}=2.52\ N\cdot s.$

c) $v_f=18\ \dfrac{m}{s}.$