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 acodent, a 1850 kg car traveling to the right at 1.50 m/s collides with a 1350 kg car going to the left at 1.10 m/s. Measurements show that the heavier car's speed just after the collision was 0.270 m/s in its original direction. You can ignore any road friction during the collision. Calculate the change in the combined kinetic energy of the two-car system during this collision.

Explanation / Answer

(a) m1 = 1850 kg , u1 =1.5 m/s, m2 = 1350 kg , u2 = -1.1 m/s, v1 = 0.27 m/s

From conservation of momentum

m1u1 +m2u2 = m1v1 +m2v2

(1850*1.5) - (1350*1.1) = (1850*0.27) +(1350*v2)

v2 =0.586 m/s

(b)Change in kinetic energy K1 -K2 = (1/2)m1u1^2+(1/2)m2u2^2 - (1/2)m1v1^2 -(1/2)m2v2^2

= (0.5*1850*1.5*1.5)+ (0.5*1350*1.1*1.1) - (0.5*1850*0.27*0.27) - (0.5*1350*0.586*0.586)

K1 -K2 = 2598.8 J

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