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Center of mass of the human figure

  1. Oct 21, 2006 #1
    The drawing shows a human figure approximately in a sitting position. For the purposes of this problem, there are three parts to the figure, and the center of mass of each one is shown in the drawing. These parts are: (1) the torso, neck, and head (total mass = 41.5 kg) with a center of mass located on the y axis at a point 0.359 m above the origin, (2) the upper legs (mass = 15.2 kg) with a center of mass located on the x axis at a point 0.153 m to the right of the origin, and (3) the lower legs and feet (total mass = 9.06 kg) with a center of mass located 0.478 to the right of and 0.299 m below the origin. Find the (a) x coordinate and (b) the y coordinate of the center of mass of the human figure. Note that the mass of the arms and hands (approximately 12% of the whole-body mass) has been ignored to simplify the drawing.

    I can't submit the drawing, but I'm really stumped on this problem. Perhaps some kind of hint to get me started? I know how to find the center of mass of something but the X and Y coordinates? Help!
  2. jcsd
  3. Oct 21, 2006 #2


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    Gold Member

    Don't you apply the "seesaw principle"? Fulcrumology?

    A 1 pound weight, 2 feet from the fulcrum will be balanced by a 2 pound weight 1 foot from the fulcrum.
  4. Oct 21, 2006 #3
    I've never heard of that before. The only equation that I could use is Xcm = m1x1 + m2x2.../ m1 + m2.... how would I apply it though :(

  5. Oct 22, 2006 #4

    Doc Al

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    Staff: Mentor

    That's exactly the equation you need. You have the coordinates and mass of each piece. Use that equation to find the x and y coordinates of the center of mass of the entire body. (You'll need to apply it twice, once for x-coordinates, once for y-coordinates.)

    Xcm = (m1x1 + m2x2 + ...)/(m1 + m2 + ...)
  6. Oct 22, 2006 #5
    ok this is what I have so far.

    Xcm = (15.2)(.153)+ (9.06)(.478)/ (15.2 + 9.06) From this I got .27437. I've submitted this answer for online grading and its not it... I get a total of 5 tries.

    Ycm = (15.2)(.153)+ (9.06)(.478) / (15.2+ 9.06)

    Doc you have any clue what I'm doing wrong?

  7. Oct 22, 2006 #6

    Doc Al

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    Staff: Mentor

    You left out one of the pieces! You forgot the "torso, neck, and head". (The "+ ..." in the center of mass equation indicates that you keep on adding terms for all the pieces... m1, m2, m3, m4, whatever. In this problem, you have three pieces to consider so you must extend the equation appropriately.)

    First thing for you to do: Write out the center of mass equation for three pieces.
  8. Oct 22, 2006 #7

    here is the image of the actual problem
  9. Oct 22, 2006 #8
    the reason I didn't added the head is because I didn't think there is a x cordinate for it? it just says center of mass located on the y axis at a point .39 m above the origin. Where is the x coordinate for this? Also I'm wondering if the value is below the orgin does this make it a negative value?

    Thanks a lot Doc
  10. Oct 22, 2006 #9

    Doc Al

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    Of course it has an x coordinate, just like any other point. Hint: Every point on the y-axis has the same x coordinate. What is it?
  11. Oct 22, 2006 #10
    wow I GOT it!!!

    you are awsome.

    Thanks a lot Doc I love this forum !
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