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 1.41 m/s at collides with a 1445-kg car going to the left at 1.08 m/s. Measurements show that the heavier car's speed just after the collision was 0.245 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.
J

Explanation / Answer

a)

let the speed of lighter car is v m/s

Using conservation of momentum ,

1760 * (-0.245) + 1445 * v = 1760 * 1.41 - 1445*1.08

solving for v

v = 0.935 m/s

the speed of lighter car is 0.935 m/s

b)

change in Kinetic energy = KEfinal - KEinitial

change in Kinetic energy = 0.5 *(1760 * 0.245^2 + 1445 * 0.935^2 -1760 * 1.41^2 - 1445*1.08^2 )

change in Kinetic energy = -1907.8 J

the change in kinetic energy is -1907.8   J

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