Classic man on boat problem A man is standing on one side of a boat and the boat is stationary.  We ignore friction between water and boat (and air friction).  Thus there are no external forces on the man+boat system.  So momentum is conserved, and centre of mass does not move.  I understand that if the man moves to the other side the boat moves in opposite direction that the man moves in.  
My question is, if there's no friction on the boat, once the boat starts moving in the opposite direction, what force exactly stops the boat from moving once the man has reached the other side of the boat.  
 A: The exact dynamics associated with each step will depend on how the man walks.
If he makes small jumps and stops after each jump, the boat will also stop after each jump. To stop after each jump, the man would have to grab something on the boat, in which case the boat will be stopped by that force, or land feet first, in which case the boat will lose its momentum and kinetic energy straightening him up, i.e., working against the gravity.
If the man walks normally up to the last step, the boat would continue moving as well, with little jerks associated with each step. The last step though would have to be different: the man will have to grab something on the boat or lean backwards before finishing the step.  
A: The dynamics of walking are quite complicated and I think this is clouding the issue somewhat. So imagine a similar experiment where the man is on a bicycle in the long, thin boat.
As he pedals, the wheels and act on the boat, which starts to slip "backwards" in the water. When he gets near the end of the boat, he has to pull the brakes, which slow the wheels, which act on the boat to stop it slipping. The work done when pedalling is exactly equal to the work done on the brakes.
From the man's POV, he has simply cycled from one end of the boat to the other.
From a viewer on side of the lake, the man stayed where he was the whole time, and the boat slipped along under him.
