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A center of mass problem

  1. Oct 30, 2011 #1
    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 ?
     
  2. jcsd
  3. Oct 30, 2011 #2

    Doc Al

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    What do you think?
     
  4. Oct 30, 2011 #3
    I think it will not move
     
  5. Oct 30, 2011 #4

    Doc Al

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    So what happens to the center of mass of the boat+person system?
     
  6. Oct 30, 2011 #5
    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 ?!
     
  7. Oct 30, 2011 #6

    Doc Al

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    Can the center of mass of the system change? What is required for such a change?
     
  8. Oct 30, 2011 #7
    yes it can ,, if we change the positions of the particles of that system with respect to a specified reference point .
     
  9. Oct 30, 2011 #8

    Doc Al

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    What is required to change the center of mass of a system that is at rest?
     
  10. Oct 30, 2011 #9
    an external force .
     
  11. Oct 30, 2011 #10

    Doc Al

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    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?
     
  12. Oct 30, 2011 #11
    it will stay the same before and after the movement of the man .
     
  13. Oct 30, 2011 #12

    Doc Al

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    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?
     
  14. Oct 30, 2011 #13
    so the boat will move the same x-displacement as the man in order to maintain the same center of mass of the system .
     
  15. Oct 30, 2011 #14

    Doc Al

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    Why would you think that? Are they the same mass?
     
  16. Oct 30, 2011 #15
    there is a problem here because if the boat moves, the man as well will move .
     
  17. Oct 30, 2011 #16

    Doc Al

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    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.)
     
  18. Oct 30, 2011 #17
    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 ).
     
  19. Oct 30, 2011 #18

    Doc Al

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    Sure. How else can the center of mass remain the same distance to shore?
     
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