# 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.

• What force stops the man from continuing to move....? Commented Apr 13, 2018 at 10:05
• How does the man walk in the first place? Commented Apr 13, 2018 at 10:07
• @user1583209 Is it the frictional force of the boat pushing against the man? What I don't really get is that he takes so many steps to the other side pushing the boat in the opposite direction, but which step pushes the boat to stop it? Commented Apr 13, 2018 at 10:12
• reword the question (second part) for clarity: "Once man starts to move, the boat starts to move too. Once man stops, the boat also stops. What makes the boat stop?" Commented Apr 13, 2018 at 10:15
• @helios321 The "breaking" of the man. Otherwise he would fall into the water. Commented Apr 13, 2018 at 10:15

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.

• Why would there be any difference between the jumping and normal walking? In particular why do you say the last step would need to be different, wouldn't the last step just be the same as every other step with the boat starting to move at the start of each step then coming to a halt by the end of that step. Commented Apr 13, 2018 at 10:47
• @helios321 You're thinking that the man just "stops". In fact, at the end of his last step, he has to apply a significant force to counter the forward motion. Try it; march smartly across the room and try "just stopping" before you hit the wall - you won't. To think of it another way, what if the last patch of floor was slippery ice - would you be able to "just stop"? Commented Apr 13, 2018 at 11:38
• @OscarBravo You are right it does seem the last step of continual walking requires more force to stop the movement. Is that because each inbetween step requires less force to keep moving though the first and last step requires the most force to begin and end the movement? Commented Apr 13, 2018 at 12:27

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.