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

a)

let the final speed of lighter car after collision is v2

using conseravtion of momentum

m1 * v1 + m2 * v2 = m1 * u1 + m2 * u2

1760 * 1.64 - 1305 * 1 = 1305 * v2 + 1760 * 0.235

solving for v2

v2 = 0.89 m/s

the speed of lighter car is 0.89 m/s

b) Change in kinetic energy = final kinetic energy - initial kinetic energy

Change in kinetic energy = 0.5 * 1760 *(0.235^2 - 1.64^2 ) + 0.5 *1305 *(0.89^2 - 1)

Change in kinetic energy = -2453.9 J

the Change in kinetic energy of system is -2453.9 J

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