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 1875-kg car traveling to the right 1.49 m/s at collides with a 1440-kg car going to the left at 1.00 m/s. Measurements show that the heavier car's speed just after the collision was 0.230 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? ____ m/s

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

Explanation / Answer

(A)

Applying momentum conservation of two car system for the collision,

momentum before collision = momentum after collision

(1875 x 1.49) + ( 1440 x -1) = (1875 x 0.230) + (1440 v)

v = 922.5 / 1440 = 0.641 m/s ............Ans

(B) Ki = (1875 x 1.49^2 / 2) + (1440 x 1^2 / 2 ) = 2801.34 J

Kf = (1875 x 0.230^2 / 2) + (1440 x 0.641^2 / 2) = 345.43 J

change in KE = Kf - Ki = - 2455.9 J

hence 2455.9 J of KE is lost.

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