Leonard G. Caillouet

02-01-1995, 08:45 AM

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

> 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