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My first question is as follows:

A cannon and a supply of cannonballs are inside a sealed railroad car of length L. The cannonballs remain in the car after hitting the far wall.

a) After all the cannonballs have been fired, what is the greatest distance the car can have moved from its original position?

b) What is the speed of the car after all the cannonballs have been fired?

Since there are no values provided, this seems to be a thought exercise. While the cannonballs are in the air, the railroad car is moving in the opposite direction. When the cannonballs hit the other side of the car, however, they will probably bounce off, causing the car to move back in the other direction, and the car will stop when the cannonballs again rest on the floor of the car. With ideal values, I'm assuming the car end up right back where it was originally, but I'm not sure how to verify this. The conclusion that both the displacement and speed of the car after firing the cannonballs is zero follows from my conclusion. Are my impressions correct?

Next question:

Find the center of mass of a homogeneous semicircular plate. Let R be the radius of the circle.

There's an example earlier in the book that shows how to find the center of mass of a thin strip of material bent into the shape of a semicircle. I'm wondering if the center of mass of that shape is the same as the one of a semicircularplate. If so, then I can simply use the example in the book for the answer. Is the center of mass the same in both cases?

Help on either of these questions would be appreciated!

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# Momentum and COM questions

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