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 1830-kg car traveling to the right 1.61 m/s at collides with a 1340-kg car going to the left at 1.02 m/s. Measurements show that the heavier car's speed just after the collision was 0.225 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?
.....m/s

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

Explanation / Answer

(a) Let's write the momentum conservation equation:
m1v1 + m2v2 = m1V1 + m2V2
with
m1 = 1830 kg
m2 = 1340 kg
v1 = 1.61 m/s
v2 = - 1.02 m/s
V1 = 0.225 m/s

Then
V2 = (m1v1 + m2v2 - m1V1) / m2 =
= (1830*1.61 - 1340*1.02 - 1830*0.225) / 1340 = 0.871 m/s (to the right)

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

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