How Far Does the Person Move on the Ice?

[Werg22]

Homework Statement

A person of mass M is standing at one end of a board of mass m and length l. The board rests upon frictionless ice surface, and its mass is uniformly distributed along its length. The person now walks to the center of the board and stops. In terms of the given quantities, M, m and l, how far from his starting position relative to the ice surface has he moved? Note that there are no external forces acting on the system, only internal forces.

Homework Equations

The Attempt at a Solution

I am not sure how to determine how the system will move. I have determined where the center of mass of the person-board system is, and I suspect it will enter the solution, but I can't figure anything out at the moment.

 

[Doc Al]

Will the location of the center of mass with respect to the ice of the "person + board" be affected by the motion of the person?

Will the location of the center of mass with respect to the board of the "person + board" be affected by the motion of the person?

 

[Werg22]

I am not sure where the difference lies...

 

[Doc Al]

I am not sure where the difference lies...

In order for the center of mass to move with respect to the ice, there would have to be some external force on the system. (Since it wasn't moving before the person started walking.) But the ice is frictionless.

But with respect to the board, the center of mass does shift: Calculate the position of the center of mass before and after the person moves to the center.

 

[Werg22]

So the new position of the board will be so that the position of the center of mass of the person-board system hasn't changed in respect to the ice? I must say I've been acquainted with the concept of center of mass less than 2 hours ago and haven't caught on its intuitive meaning yet.

 

[Doc Al]

So the new position of the board will be so that the position of the center of mass of the person-board system hasn't changed in respect to the ice?

That's right.

I must say I've been acquainted with the concept of center of mass less than 2 hours ago and haven't caught on its intuitive meaning yet.

Give it time. (This question's a bit tricky.)