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 1850 car traveling to the right at 1.40 collides with a 1400 car going to the left at 1.10 . Measurements show that the heavier car's speed just after the collision was 0.270 in its original direction. You can ignore any road friction during the collision.
B)Calculate the change in the combined kinetic energy of the two-car system during this collision.

Explanation / Answer

Let's write the momentum conservation equation: m1v1 + m2v2 = m1V1 + m2V2 with m1 = 1850 kg m2 = 1400 kg v1 = 1.40 m/s v2 = - 1.10 m/s V1 = 0.270 m/s Then V2 = (m1v1 + m2v2 - m1V1) / m2 = = (1850*1.40 - 1400*1.10 - 1850*0.270) / 1400= 0.39 m/s (to the right) Kinetic energy before the collision: K1 = 1/2 m1v1² + 1/2 m2v2² = 0.5 (1850*1.40² + 1400*1.10²) = 2660 J Kinetic energy after the collision: K2 = 1/2 m1V1² + 1/2 m2V2² = 0.5 (1850*0.270² + 1400*0.39²) = 174 J Change in kinetic energy: ?K = K2 - K1 = 174 - 2660= - 2486.1 J

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