Man walking in a frictionless wood. How far does he walk?

Question

A 50 Kg man is on one edge of a 10 meter wood plank.
The wood rest on a frictionless ice through out its length.
The mass of wood is 20 Kg. It is homogeneous and uniform.
The man walk forwards the other end of the wood
How much is the distance walked by man with respect to the ground?

Still no one got the answer
The man exert his effort in walking, isn't it?
If the plank move backward then work is done, isn't it?
think, think, think

Additional detail
Work done by man = work done by the plank
I am sure the centroid of the plank will move back
work is done
think

Note: there is no external force within the system of plank and the man

draw a wood plank with man on the right end
draw a vertical line to the left of the man representing the original ground position of man
let x = distance traveled from this vert line to the person on the right plank
let (10-x) distance traveled by centroid of wood form original ground(vert. line)

work of man = work of plank
50 x = 20 ( 10 - x )
50 x = 200 - 20 x
x = 2.86 meters -> this is the distance traveled by man

The general equation if weight of wood is W
50 x = W ( 10 - x )
. . . . . if W = 50 . . wt wood = wt man
x = 5 meters
. . . ie. . man will travel 5 m .w / r. to ground
. . . . . and the plank will travel also 5 meters

Answer 1

We can't walk without the frictional force, because if there's no friction, we can't even stand on the ground. More than that, our feet need frictional force to keep us going forward.

Answer 2

It is hard to say because if he moves really slow the wood will not slip back and he will indeed move 10 meters forward, if he moves fast and causes the wood to move back then he will not advance, only the wood will move back.
Is this a philosophy or physics question?
When a fox tries to cross a river through the thin ice he is the most cautious of all animals and he will do it very slowly, we humans tend to do it fast and brake the ice, a cat would rather stay on one side and wait for the spring because they are smarter.
But back to your theoretical question, that man should wear elbow pads and helmet because he is going down not forward...
OK I´m thinking...
If 50kg moves forward on a 20kg surface when he reaches the 10 meter distance he would advance only 4 m because the wood weights 40 % of his total weight. Or is it 6 m?
Please let me know which one.
But that experiment to be exact needs to be made in a place with no gravity because there´s no such thing as a frictionless surface when there´s gravity.

Answer 3

The man won't move. The plank will be ejected behind the man, unless also the plank is frictionless (it is not clear from the question which is actually frictionless). In such case the man will not be able to move because of lack of friction with respect to the ground and the plank.
If the plank is not frictionless with respect to the man, then the man will move an amount 20/50 given by the reaction between the 20Kg plank and the 50Kg man.

Answer 4

10 meters. The board is sitting on 10 meters of frictionless ice (The wood rest on a frictionless ice through out its length.) So the board will move backwards as he walks forwards for 10 meteres.

Answer 5

He wouldnt move since when you walk you create an opposite force to the ground in the direction your walking. Since the floor is not attached and is on a frictionless surface the energy transfered to walking will push the plank out under his feet. You need equal and opposite forces.

Answer 6

Whatever his stride is. Since it's frictionless, then he only needs to take one step in order to transverse the distance, or at least make a movement with his body in the opposite direction. The momentum from making that step carries him.

Answer 7

10 meters

Answer 8

- 15 meters if the wood is surrounded by enough ice and is only frictionless on the underside..

Answer 9

when he takes his first step forward the wooden plank starts moving backwards and will continue to move because of lack of friction and the man will move backwards.

Answer 10

Oops. clearly not the right equations. I'll try again with the right ones.