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 1760-kg car traveling to the right 1.64 m/s at collides with a 1305-kg car going to the left at 1.00 m/s. Measurements show that the heavier car's speed just after the collision was 0.235m/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

1st car mass= m1 = 1760 Kg

1st car velocity = v1 = 1.64 m/s (we take right as positive direction)

2nd car mass = m2 = 1305 Kg

2nd car velocity = v2 = -1 m/s (negative since going left)

Heavier car velocity after collision v1c = 0.235 m/s (right)

let 2nd car velocity after collision be v

by conservation of momentum: m1 v1 + m2 v2 = m1 v1c + m2 v

=> v = 0.8949 m/s (its positive hence moving to right after collision)

b) Loss of KE during collision = KE before collision - KE after collision

= 0.5 m1v12 + 0.5 m2v22 - 0.5 m1 vic2 - 0.5 m2 v2 = 2448.2 J

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