What Happens to the Center of Mass When a Penguin Moves on a Sled?

[keltix]

Homework Statement

A penguin stands at the left edge of a uniform sled of length L, which lies on frictionless ice. The sled and the penguin have equal masses. (a) Where is the center of mass of the sled? (b) How and in what direction is the center of mass of the sled from the center of mass of the sled-penguin system? The penguin then waddles to the right edge of the sled and the sled sides on the ice. (c) Does the center of mass of the sled-penguin system move leftward, rightward, or not at all? (d) Now how far and in what direction is the center of the sled from the center of mass of the sled-penguin system? (e) How far does the penguin move relative to the sled? Relative to the center of mass of the sled-penguin system, how far does (f) the center of the sled move and (g) the penguin move?

Homework Equations

None other than concept COM ideas.

The Attempt at a Solution

(a)The center of mass for the less is obviously in the center.
(b) The COM for sled is L/2 right from the COM for sled-penguin system.

IDK how to do the rest.

 

[dwintz02]

First, I'd check your answer for part b. If the center of mass of the sled is L/2 to the right of the center of mass of the sled-penguin system, then by your answer the center of mass of the sled-penguin system is directly under the penguin. Next, tell us what you think will happen when the penguin walks across the sled so we can help you along towards the answer.

 

[keltix]

The book says (a) and (b) are correct.

So, if the penguin moves along the sled, the COM for the sled-penguin system SHOULD change, right?

Or should it not because there are no EXTERNAL FORCES?

The back of the book seems to show contradictory answers. First it says that it won't for (c) and then for (d) it says that the new COM is somewhere else.

Could someone explain when the COM changes and the difference between sled, penguin, and sled-penguin system and the COM for each?

 

[Doc Al]

The wording of (c) and (d) is a bit tricky. Does the location of the COM with respect to the center of the sled change as the penguin moves? Of course. But does it move? (By "move" they mean move with respect to the ice.)

 

[keltix]

"The penguin then waddles to the right edge of the sled and the sled sides on the ice."

the sled is moving w/r/t the ice (and so is the COM)

 

[Doc Al]

Does the penguin move w/r/t the board? Yes! W/r/t the ice? Yes!

Does the sled move w/r/t the ice? Yes!

Does the COM of the "sled + penguin" system change w/r/t the sled? Yes! (Meaning: If you marked the location of the COM on the sled, that mark will change when the penguin moves.)

Does the COM of the "sled + penguin" system move w/r/t the ice? No!

That last one is tricky. Ask yourself: Do any external forces act horizontally on the system?

 

[keltix]

I must be stupid because I don't get the difference between 'move' and 'change.'

 

[Doc Al]

Just replace the word "change" with the word "move".

The key is that the COM moves with respect to the sled but not with respect to the ice. (As the penguin moves to the right, the sled moves to the left just enough so that the COM stays at the same spot on the ice.)

You may have had a similar experience on a rowboat or canoe. You step one way and the boat begins going the other way.

 

[keltix]

OH~!

So the sled moves because the penguin walks!
I figured some other impulse had caused it to move.
I see what you mean.

"You may have had a similar experience on a rowboat or canoe. You step one way and the boat begins going the other way."

Bingo. I think I get it now.