physics

A 500-kg cannon and a supply of 80 cannon balls, each with a mass of 45.0 kg, are inside a sealed railroad car with a mass of 11000 kg and a length of 49 m. The cannon fires to the right; the car recoils to the left. The cannon balls remain in the car after hitting the wall. After all the cannon balls have been fired, what is the greatest distance the car can have moved from its original position?

What is the speed of the car after all the cannon balls have come to rest on the right side?

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1. The center of mass of car and contents remains in the same place.

For greatest amount of displacement, assume that all the cannonballs move from one end to the other

The final speed is zero, since momentum is conserved

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2. I don't quite follow

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3. The problem wants you to assume that the railroad car in on a frictionless track. Such cars do not exist, but assume this one rolls without friction, anyway. I hope you have heard of the law of conservation of momentum.
The initial momentum of the car and its contents is zero. The total momentum of the car and its contents must remain zero. When nothing moves inside the car, the car must also have zero velocity.

The first part of your question is harder to explain. In a problem such as this where you are not dealing with a rigid body, the momentum conservation equation still applies if for total momentum you use the total mass times the velocity of the center of mass.

In your problem, the center of mass does not move in Earth-based coordinates, because of the momentum conservation law. The train will move temporarily while the shooting is going on, and stop when it is over. The center of mass as seen from inside will move, but from outside it will not.

The motion of the center of mass as seen from inside equals the final displacement of the car.

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