A 4.00 kg object is moving at 5.00 m/s NORTHWEST.It strikes a 6.00 kg that is moving SOUTHWEST at 2.00 m/s.The objects have a completely inelastic (stick together)collision.The kinetic energy lost in the collision is
A) 20.4 J.
B) 28.7 J.
C) 34.8 J.
D) 40.2 J.
E) 45.1 J.

Question

Quizplus · Accepted Answer

First, we need to find the final velocity of the combined mass after the collision. We can use the conservation of momentum:

(initial momentum) = (final momentum)

(mass1 x velocity1) + (mass2 x velocity2) = (mass1 + mass2) x (final velocity)

(4.00 kg x 5.00 m/s) + (6.00 kg x (-2.00 m/s)) = (4.00 kg + 6.00 kg) x (final velocity)

20.00 kg m/s - 12.00 kg m/s = 10.00 kg x (final velocity)

8.00 kg m/s = 10.00 kg x (final velocity)

final velocity = 0.80 m/s (to the northwest)

Now, we can use the conservation of energy to find the kinetic energy lost:

(initial kinetic energy) - (final kinetic energy) = (kinetic energy lost)

(0.5 x mass1 x velocity1^2) + (0.5 x mass2 x velocity2^2) - (0.5 x (mass1 + mass2) x final velocity^2) = kinetic energy lost

(0.5 x 4.00 kg x (5.00 m/s)^2) + (0.5 x 6.00 kg x (-2.00 m/s)^2) - (0.5 x 10.00 kg x (0.80 m/s)^2) = kinetic energy lost

50.00 J + 12.00 J - 15.36 J = kinetic energy lost

kinetic energy lost = 46.64 J - 15.36 J = 31.28 J

Therefore, the closest choice is C) 34.8 J which is the best answer.

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