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I’m really really sorry about this but i’m Having a discussion at the moment regarding a mass of one kilogram of feathers and one kilogram of steel.

The person i’m Arguing with states that one kilogram of feathers will be lighter when weighed against the one kilogram of steel because the feathers are more buoyant.

She has done her calculations for the density of feathers and works out that 1 kilogram of feathers will displace 400 litres of water. And because the feathers are more buoyant than the steel they would actually weigh less.

We are talking about a kilogram of feathers as mass, not weight.

The argument goes that if a scale balanced perfectly in a vacuum, it would not in air. The feathers being more buoyant in air would cause the scale to tip towards the steel.

I’m sure she is wrong, and even though buoyancy may be a factor, she calculates that the feathers would only be almost half their weight in air than they are in a vacuum.

So the question is...

If equal masses of 1 kilogram of feathers and steel were balanced in a vacuum, would they still balance in 1 atmosphere. And what would be the difference in weight?

Can you help me resolve this and tell me if buoyancy is a factor, and if so by how much?

Thank you.

Feathers are made from keratin, with a density of about 1.3 grams/cc. The net volume displaced by a kilogram of feathers is then 751 cc's. Steel has a density of 7.86 g/cc and a kilogram of it displaces 127 cc's.

Sea level air has a density of 0.0012 g/cc, so the buoyant force on 751 cc's of keratin is then 0.92 grams and the buoyant force on 127 cc's of steel is 0.155 grams.

This means that if we weigh the keratin in a vacuum, it will weigh 1 kilogram but in air it will weigh 999.08 grams. If we weigh the steel in a vacuum, it will weigh 1 kilogram but in air it will weigh 999.85 grams.

If we place the two bodies- keratin and steel, one kg of each- on a pivoting balance equidistant from the pivot in a vacuum, they will be in balance, but in air the keratin will be lighter by (999.85-999.08) grams or 0.77 grams.

You can argue that her feathers contain a lot of air (never perfectly compressed) so that the volume is not true. You could also take your kilo of steel and make it into a hollow sphere (empty) of the same volume as the feathers (whatever that is) and then it would actually weigh less because you have no air inside. But you could be nice and let her make the point about a bigger volume being more bouyant, she is correct about this but ..... even volume is tricky.

Due to buoyancy one kilogram of hot air balloon indeed weighs less than one kilogram of steel!