Man on a Raft: Analyzing the Movement on a Frictionless Surface

[SpicVir]

This is a question i thought about recently:
If a man starts to walk on a raft standing still in the water (no friction between the raft and water), how will the raft move?
I'm thinking this:

Is this what would actually happen?

 

[Doc Al]

Is this what would actually happen?

No. The man cannot remain still with respect to the water while the boat moves. If the man exerts a force on the boat, the boat exerts an equal and opposite force on the man.

 

[TurtleMeister]

The distance the man and boat move relative to the water depends on the difference in mass between the man and the boat. If the boat is twice the mass of the man then the man will move twice the distance the boat moves (relative to the water). And always in opposite directions.

 

[SpicVir]

Oh, well... Thanks.
Would this happen without gravity?

Man starts to walk and because friction (between him and the raft), he starts to rotate?

 

[Nick89]

I don't know why you think it would rotate..?

Anyway, instead of just the man staying in place, the center of mass of the man + the boat will remain in place. That means, if the man moves, the boat moves in the opposite direction (and the amount of movement depends on their mass).

The center of mass is given by:
x_{cm} = \frac{x_m m_m + x_b m_b}{m_m+m_b}
where x_m is the position of the man, x_b the position of the boat, m_m the mass of the man, and m_b the mass of the boat.

 

[A.T.]

I don't know why you think it would rotate..?

Well without gravity the man probably would rotate, since the force is not applied trough his center of mass.

 

[LURCH]

That is correct. Without gravity, the man's feet push against the boat and the entire length of his body acts as a lever. The equal and opposite reaction (the boat pushes against his feet) will cause his feet to move forward, but not his center of mass. Result; the man rotates around his center of mass.

 

[Doc Al]

The equal and opposite reaction (the boat pushes against his feet) will cause his feet to move forward, but not his center of mass.

If the boat pushes on his feet, his center of mass will accelerate. (Assuming that's the only horizontal force acting.)

 

[russ_watters]

Oh, well... Thanks.
Would this happen without gravity?

Man starts to walk and because friction (between him and the raft), he starts to rotate?

Without gravity, the entire thing falls apart:

-The person has to push away from the boat to be able to apply any friction to push it sideways, so both will spin and move away from each other at the same time. The actual resulting acceleration depends on the particulars of how he applies the force.
-The boat doesn't float in the water if there is no gravity, it'll just get pushed through it.