a 1.2 x 10^4 kg railroad car is coasting along a level, frictionless track at a constant speed of 25m/s, when a 3000 kg load is dropped vertically onto the car from above. What will its new speed be assuming the load stays on the car??

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Explanation:

Because the track is level and frictionless, the net force on this car-load system will be zero in the horizontal direction. As a result, (by Newton's Second Law of mechanics,) the total momentum of this system in the horizontal direction will stay the same.

Momentum of the car-load system in the horizontal direction, before contact:

Combine the two parts to obtain: .

Because the load stays on the car, the car and the load should have the same horizontal velocity after contact. Let denote that velocity. Momentum of the system after contact:

Combine to obtain:

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Because the total momentum of the system will stay the same:

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Solve for to obtain:

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In other words, the new velocity of the system would be .