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 1750 kg car traveling to the right at 1.40 m/s collides with a 1450 kg car going to the left at 1.10 m/s . Measurements show that the heavier car's speed just after the collision was 0.250 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?

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

Explanation / Answer

m1=1750 kg

v1=1.4m/s

V1 = 0.250 m/s

m2=1450 kg

v2 =-1.1 m/s

using law of conservation of momentum

m1v1 + m2v2 = m1V1 + m2V2

V2 = (m1v1 + m2v2 - m1V1) / m2

= (2450 -1595 - 437.5)/1450 =0.288 m /s

change in KE = KE2 - KE1

KE1= 1/2 m1v1² + 1/2 m2v2² = 0.5*1750*1.4*1.4 + 0.5*1450*1.1*1.1 =2592.25 j

KE2= 1/2 m1V1² + 1/2 m2V2² = 0.5*1750*0.25*0.25 + 0.5*1450*0.288*0.288 = 114.822 j

change in KE = KE2 - KE1 = - 2477.43 J

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