Question

Suppose a child drives a bumper car head-on into the side rail, which exerts a force of 4000 N on the car for 0.200 s.

1. The impulse imparted by this force to the child is
2. The final velocity (in 1 decimal place) of the bumper car if its initial velocity was 2.80 m/s and the car plus driver have a mass of 200 kg neglecting friction between the car and floor is

Answer 1

(1) We can find the impulse imparted by this force to the child as foolows:

$$J=F_{avg}\Delta t=-4000\ N\cdot0.2\ s=-800\ N\cdot s.$$

The sign minus means that the impulse imparted by this force to the child directed in the opposite direction (away from the said rail).

(2)

$$J=\Delta p=mv_f-mv_i,$$ $$v_f=\dfrac{J+mv_i}{m}=\dfrac{-800\ N\cdot s+200\ kg\cdot2.8\ \dfrac{m}{s}}{200\ kg}=-1.2\ \dfrac{m}{s}.$$

The sign minus means that the final velocity of the bumper car directed in the opposite direction (away from the said rail).