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Centre of mass and gravity problem, confused and need help

  1. May 24, 2014 #1
    1. The problem statement, all variables and given/known data

    A uniform plank of length l = 6m and mass M= 90kg rests
    on sawhorses separated by D = 1.5m and equidistant from the
    center of the plank. Cousin Throckmorton wants to stand on the
    right-hand end of the plank. If the plank is to remain at rest, how
    massive can Throckmorton be?

    Diagram:
    throcky.jpg

    2. Relevant equations



    3. The attempt at a solution

    I am confused at the diagram. Why is the centre of gravity not at the centre of mass of the plank which should be in the middle ?
     
  2. jcsd
  3. May 24, 2014 #2
    It is the centre of mass of the system which includes all the masses.
     
  4. May 24, 2014 #3
    Okay, then how do we find it ?, or what is the explanation that says it should be there ? (referring to the cg in the image)
     
  5. May 24, 2014 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The center of mass of the plank is at the middle of the plank. Taking x to be the distance from the left end of the plank, that would be x= 3.0. Throckmorton's center of mass is where he is standing at x= 6.0. The center of mass of the system is a weighted average, weighted by their masses: (90*3+ M*6)/(M+ 90) where M is Throckmorton's weight.
     
  6. May 24, 2014 #5
    Why is it m*6 and not m*3 ? and how do you know where the centre of gravity is ?( cg in the diagram)
     
  7. May 25, 2014 #6
    He's taking moments about the left end.

    He's giving you the formula for the location of CG
     
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