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Re: Center of buoyancy problem

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  • Re: Center of buoyancy problem

    On Wed, 25 Jan 1995, Hinrichs, Rick wrote:

    > I have a dilemma that I hope someone out there can help me with.
    >
    > W
    > |
    > CB \|/------x-------|
    > Head ___________._____.___________________ Feet
    > ^ CM ^
    > | |
    > |--d--| |
    > B R
    >
    >
    > In the above FBD, we know W, R, and x. We would like to know d (the
    > distance between the CM and CB). Using equations of static
    > equilibrium for translation (B=W-R) and rotation (Bd=Rx), we can
    > arrive at B and then d (no big deal).
    >
    > However, if we move the point of application of the supporting force
    > (R) higher up the leg, keeping the body position the same, we
    > decrease the distance x. Everything else about the body SHOULD have
    > stayed the same, i.e., the same body position in the water, same body
    > weight, same buoyant force, and same locations of the CM and CB. To
    > satisfy the rotational equilibrium condition, Bd=Rx regardless of the
    > value of x. So if x gets smaller then R must increase to produce the
    > same torque. However, [AND THIS IS WHERE I AM HAVING PROBLEMS], if R
    > gets larger, then the only way to satisfy the translational
    > equilibrium condition (B=W-R) is for B to decrease. This doesn't

    I think that here (below) is where your evaluation is faulty. You are
    correct about the amount of bouyant force not changing. However, when the body
    floats differently with the force R applied the center of bouyancy has
    moved, so d is what changes. You have assumed that the position of CB is
    the same under two diferent rotational conditions.
    > make sense, however, because the buoyant force (B) is (by definition)
    > the weight of the displaced water which has not changed. If W, B,
    > and the locations of CB and CM have not changed, then we have an
    > impossible situation. We cannot satisfy both the rotational and
    > translational equilibrium equations. CAN ANYONE OUT THERE SEE THE
    > ERROR IN MY LOGIC?
    >
    > NOTE: We have tried this with the body totally submerged and on the
    > surface and for different amounts of air in the lungs. We have also
    > put supports at two locations (with a strap around the chest as well
    > as the ankles) and have come up with the same dilemma; the FBD is
    > only slightly more complicated).
    >
    The location of CB has to change if the forces creating the rotation of
    the body are changed.




    Hope this has been a help.

    Now can someone tell me why, when composing a reply using PINE, I cannot
    post a reply that contains more text from the original message than new
    text that I have included?



    Leonard G Caillouet
    L.S.U. Kinesiology
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