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 1845-kg car traveling to the right 1.51 m/s at collides with a 1345-kg car going to the left at 1.00 m/s. Measurements show that the heavier car?s speed just after the collision was 0.225 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

apply the law of conservation of momemtum as

m1u1 + m2u2 = m1v1 +m2v2

so

(1845* 1.51) - (1345 * 1) = 1845 * 0.225) + (1345 * V2)

V2 = 0.762 m/s

---------------------------------

total Inital KE = 0.5 m1u1^2 + 0.5 m2u2^2

total KE = 0.5 * 1845 * 1.51^2 + 0.5 * 1345 * 1^2

KEi = 2775.89 J

Total final KE = 0.5 m1u1^2 + 0.5 m2u2^2

total KE = 0.5 * 1845 * 0.225^2 + 0.5 * 1345 * 0.762^2

KEi = 437.18 J

Chnage in KE = 2775.89 - 437.18 = 2338.71 Joules

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