When cars are equipped with flexible bumpers, they will bounce off each other du

Question

When cars are equipped with flexible bumpers, they will bounce off each other during low-speed collisions, thus causing less damage. In one such accident, a 1765-kg car traveling to the right 1.54 m/s at collides with a 1445-kg car going to the left at 1.09 m/s. Measurements show that the heavier car's speed just after the collision was 0.215 m/s in its original direction. You can ignore any road friction during the collision.

(a) What was the speed of the lighter car just after the collision?

(b) Calculate the change in the combined kinetic energy of the two-car system during this collision.

Explanation / Answer

a)using momentum conservation equation:
m1v1 + m2v2 = m1V1 + m2V2
with
m1 = 1765 kg
m2 = 1445 kg
v1 = 1.54 m/s
v2 = - 1.09 m/s
V1 = 0.215 m/s

Then
V2 = (m1v1 + m2v2 - m1V1) / m2 =
= (1765*1.54 - 1445*1.09 - 1765*0.215) / 1445 = 0.528 m/s (to the right)

speed of the lighter car just after the collision,V2=0.528 m/s (to the right)

b)Kinetic energy before the collision:
K1 = 1/2 m1v1

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