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 1800-kg car traveling to the right 1.51 m/s at collides with a 1310-kg car going to the left at 1.09 m/s. Measurements show that the heavier car's speed just after the collision was 0.220 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

Let's write the momentum conservation equation:
m1v1 + m2v2 = m1V1 + m2V2
with
m1 = 1800 kg
m2 = 1310 kg
v1 = 1.51 m/s
v2 = - 1.09 m/s
V1 = 0.220 m/s

Then
V2 = (m1v1 + m2v2 - m1V1) / m2 =
= (1800*1.51 - 1310*1.09 - 1800*0.220) / 1310 = 0.6825 m/s (to the right)

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

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