# A center of mass problem

If someone is on a boat that rests in a placid river with negligible friction between the boat and the river ,, suppose that person moves a certain distance ,Does that boat move as well , if so why ?

Doc Al
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If someone is on a boat that rests in a placid river with negligible friction between the boat and the river ,, suppose that person moves a certain distance ,Does that boat move as well , if so why ?
What do you think?

What do you think?
I think it will not move

Doc Al
Mentor
I think it will not move
So what happens to the center of mass of the boat+person system?

well ,, if the person moves for a certain distance , surely the center of mass will change in position ,but does that mean the boat has to move ?!

Doc Al
Mentor
Can the center of mass of the system change? What is required for such a change?

yes it can ,, if we change the positions of the particles of that system with respect to a specified reference point .

Doc Al
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yes it can ,, if we change the positions of the particles of that system with respect to a specified reference point .
What is required to change the center of mass of a system that is at rest?

an external force .

Doc Al
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an external force .
Right! Note that the problem states "negligible friction between the boat and the river". So what must be true about the center of mass of this system?

So what must be true about the center of mass of this system?

it will stay the same before and after the movement of the man .

Doc Al
Mentor
it will stay the same before and after the movement of the man .
Exactly. So, if the man moves a distance X closer to shore (say), how can you figure out how much the boat must move in order that the center of mass of the system stay put?

Exactly. So, if the man moves a distance X closer to shore (say), how can you figure out how much the boat must move in order that the center of mass of the system stay put?

so the boat will move the same x-displacement as the man in order to maintain the same center of mass of the system .

Doc Al
Mentor
so the boat will move the same x-displacement as the man in order to maintain the same center of mass of the system .
Why would you think that? Are they the same mass?

Why would you think that? Are they the same mass?

there is a problem here because if the boat moves, the man as well will move .

Doc Al
Mentor
there is a problem here because if the boat moves, the man as well will move .
Of course. So?

If the boat moves a certain distance to the left, how far must the man move? (Note that if you measure the man's movement with respect to the boat, then you have to add the movement of the boat to find his movement with respect to the shore.)

Of course. So?

If the boat moves a certain distance to the left, how far must the man move? (Note that if you measure the man's movement with respect to the boat, then you have to add the movement of the boat to find his movement with respect to the shore.)

you mean if the man moves towards the right , so he is getting closer to the shore, the boat will move in the opposite direction (to the left ).

Doc Al
Mentor
you mean if the man moves towards the right , so he is getting closer to the shore, the boat will move in the opposite direction (to the left ).
Sure. How else can the center of mass remain the same distance to shore?