Consider if I was standing on a boat with no external forces acting on us. Considering I move around on the boat on account of law of conservation of momentum the boat would gain some velocity to preserve the Center of mass. But my professor threw in another situation where in I decide to jump off the boat to land on the shore.He claimed that in this situation because of the reaction force that shore would have to my body that would amount to an external force acting on the system causing the boat to gain momentum and be set in motion. Is this possible? I mean once I jump off the boat and I land on the shore the reaction force acts on me then how is the boat that is away from me to gain any velocity? Or is this because of the Center of mass being accelerated but I don’t see even that happening for I just can’t seem to understand how the so called reaction force from the shore that affects me affects the whole system as such. Or is my understanding of the concept some where wrong?
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$\begingroup$ Well, you can jump off the boat and land in the ocean. Or jump off the boat and grab onto a helicopter. Neither your interaction with the ocean or the helicopter has any backward time traveling result to retroactively influence your act of jumping off the boat in the first place. Your understanding seems to be just fine, your "professor" has issues. $\endgroup$– Jon CusterCommented Aug 8, 2023 at 12:41
3 Answers
At the point when you jump off the boat you will exert a force on the boat (as the boat exerts a force on you) and so the boat will start to move away from you. If you float (without friction) you and the boat will both move apart but your combined center of mass will not have moved.
At the point when you reach the shore the part of that combined mass that is you will experience a force and come to a stop, but the boat will continue to drift away, so the center of mass will start to move. This is expected because the combined you+boat system has experienced a force from the shore, even if it only acted on the you part of the system
Whilst you are in the act of jumping the you & boat system have no horizontal external forces acting thus horizontal linear momentum will be conserved or put another way the centre of mass of the you & boat system will not move.
Once you have lost contact with the boat there will still be no horizontal external forces on the you & boat system and so linear momentum will be conserved and the centre of mass of the you & boat system will not move.
On landing there will be a horizontal external force on you due the ground but there is no way that the boat will feel the effect of that force as you are no longer in contact with the boat.
The situation can be looked on in two ways.
As a you and boat system acted on by an external force on you.
You stop and the boat's motion does not change.
The centre of mass of the you & boat system moves in the direction of motion of the boat.
Two systems, one is you and the other is the boat.
External force on you leads to a change of momentum.
No external force on boat and so momentum does not change.
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$\begingroup$ So all that part of the shore offering a reaction force causing the boat to gain momentum is fabricated? $\endgroup$– OrpheusCommented Aug 8, 2023 at 15:32
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$\begingroup$ @Orpheus If the boat (system) is to change its horizontal momentum it must have a horizontal external force on it. Where is that force when you are gone? $\endgroup$– FarcherCommented Aug 8, 2023 at 18:22
Momentum of the boat-person system is not conserved because the shore acts as an external force on the person component of the system. But that doesn’t affect the momentum of the boat component of the system.
Hope this helps
