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 1815-kg car traveling to the right at 1.64 m/s collides with a 1330-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

a)

Let's write the momentum conservation equation:

m1v1 + m2v2 = m1V1 + m2V2

with

m1 = 1815 kg

m2 = 1330 kg

v1 = 1.64 m/s

v2 = - 1.09 m/s

V1 = 0.220 m/s

Then

V2 = (m1v1 + m2v2 - m1V1) / m2 =

= (1815*1.64 - 1330*1.09 - 1815*0.220) / 1330 = 0.848 m/s (to the right)

b)

Kinetic energy before the collision:

K1 = 1/2 m1v1² + 1/2 m2v2² = 0.5 (1815*1.64² + 1330*1.09²) = 3230.9 J

Kinetic energy after the collision:

K2 = 1/2 m1V1² + 1/2 m2V2² = 0.5 (1815*0.220² + 1330*0.848²) = 522.127 J

Change in kinetic energy:

K = K2 - K1 = 522.127 – 3230.9 = - 2708.77 J

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