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*From*: Zeev Wurman <zeev@ieee.org>*Date*: Sat, 9 Jan 2021 14:50:53 -0800

Such arguments have been made for decades if not centuries, and the

pseudo-precise calculations don’t add much to the discussion.

To convince students a much simpler arrangement is offered, making

essentially the same point: pour a pound of bird-shot into a rubber

balloon, tie it off, and drop it into a water container; do the same to

another balloon, inflate it, tie it off, and drop it into water. Anyone

will accept that the inflated balloon “weighs” less in water. Now just ask

for explanation which should be readily given.

On Sat, Jan 9, 2021 at 2:06 PM Brian Whatcott <betwys1@sbcglobal.net> wrote:

You may be familiar with the question: which is heavier, one tonne of--

feathers, or one tonne of steel?If you take the view that weight is due

solely to gravitational force, then there is no doubt how you would answer.

Suppose you take the slightly more sophisticated view that weight is the

net force due to gravitational force less centrifugal force in a rotating

frame, and though the value of g varies from place to place, on this

account, you may still hold that their weights are the same.

But now, suppose you take the slightly more sophisticated view yet, that

weight is what a scales indicate, where gravitational force is opposed by

both centrifugal force in this rotating frame and a buoyancy force due to

the air displaced.

I will readily concede the inadvisability of mentioning centrifugal force,

but you soon ascertain that the density of this steel is 8000 kg/m^3 ,

the air density is 1.2 kg/m^3and for convenience we agree a density value

for the feathers equal to that for a closed hollow tube of keratin,

which is 2.4 kg/ m^2 and which forms 15% of the feather volume.Let us next

agree to calculate a cumulative volume for the steel: 1000/8000 m^3or 0.125

m^3 which displaces 0.15 m^3 of air, which weighs 1.2 *0.15= 0.18

kg.Hence in mid latitudes for which the g constant incorporating a

centripetal component is 9.81 N/kg, the steel weighs (1000kg - 0.18)*9.81

newtons = 9808 N .

Finally we calculate the volume of the feathers using a density figure

of 85% of 1.2 kg/m^3 and 15% of 2.4 kg /m^3 = (1.02 kg + 0.36 kg)/m^3 =

1.38 kg/m^3We quickly find the volume of 1000 kg feathers is 1000/1.38 m^3

= 725 m^3discounting the external volume of air trapped by the

feathers. This gives a buoyancy of 725 * 1.2 * 9.81 newtons.This leaves us

with the weight of feathers as measured by a scales:1000 *9.81N -

725*1.2*9.81 N = 9810N - 8535N = 1275 N

This leaves us with the uncomfortable weight comparison of 1 tonne of

steel weighing more than seven times as heavy as 1 tonne of feathers.(An

argument due to Prof. Cristobal Cortes, U.Zaragoza)

If I object that the feathers, which are hollow and filled with air are

leaky, then I can discount the internal air volume, and count only the

volume of the keratin structure which is 15% of the feather's volume, then

the effective buoyancy is greatly reduced to 15/100 of 8535N = 1280 N

giving a total feather weight of 8530N In THIS case, the steel weighs only

9808/8530 of the feather weight - a mere 15% more. I welcome

critiques of Cristobal's and my estimates....

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**Follow-Ups**:**Re: [Phys-L] Weight of equal masses***From:*John Denker <jsd@av8n.com>

**References**:**[Phys-L] Weight of equal masses***From:*Brian Whatcott <betwys1@sbcglobal.net>

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