Putting up my shelves

[John Rumm]

Probably the lead - slightly.

[John Rumm]

the lead will also occupy a smaller volume and hence will likely have a lower centre of gravity, so G (m1 m2 / d^2) will be larger, making it heavier even without taking into account the buoyancy.

[Dave]

But a kilo of each was specified. If they were both measured on the same set of scales, how could they weigh differently? :-)

Dave

[Colin Wilson]

I know which one i'd rather have thrown at me :-p

[Frank Erskine]

It all depends on what you mean by a 'kilo'.

[meow2222]

Fixings might be an issue, and the perfectionist's answer is surely resin fixings. But it should be ok with plugs & screws (use plenty of).

What will undoubtedly be an issue is shelf sag. It would take an exceptionally strong material not to sag with just end supports with a

42cm high 2' deep stack of books. You'll need to support these on all 4 sides, not just 3. 2x2 should do.

This should help to avoid the problem:

[Rod]

Dennis,

Just bear in mind that this post has the context of objects on a shelf in a room - not JPL.

So the shelf is going to have to be super strong to hold up a bath as well? Well and truly classified in "unlikely ideas".

And in what way does the water affect the gravitional force acting on the body? Sure, it might make it awkward to measure directly, but the body still has the same force of gravity acting on it - merely has buoyancy countering it.

John,

There is this weird idea in science that things must be measurable. I suspect that in any real world way, the difference would be so small as to be utterly unmeasurable. Certainly in the open air on an ordinary shelf. However well fixed with resin or bolts. But theoretically there might indeed be a difference if the items are re-formed into different shapes.

[dennis]

Not if the pile of feathers were the same height as the lead.

They would still be more buoyant though.

[dennis]

Well he is obviously referring to mass or he wouldn't need to weigh them. ;-)

[Rod]

The word "likely" was used by John to indicate that this was not certain.

The buoyancy depends on shape. It would be possible in the fanastical way you are treating this thread to imagine a model ship made of lead that easily floated. And a super-dense package of feathers that at the least only just floated.

[Bob Mannix]

Indeed, a kilometre of lead would weigh *considerably* more than a kilometre of feathers (all other dimensions being equal). A kilogram mass of both would weigh the same in a vacuum however and a kilogram weight of both would, of necessity, weigh the same anywhere they were weighed..

If we take the mass of each to be 1kg and want to know how much they weigh in air (roughly):

Lets say feathers are made of keratin, which has a density of something like

1300kg/m**3 and round it down to 1000kg/m**3, as the keratin fibres may not be completely solid. Lead has a density of 11,000kg/m**3. To make the maths easy, let's call that 10,000kg/m**3. 1 kilogram of lead will occupy a volume of 100cm**3 1 kilogram of feathers (after they are crushed to exclude the free air that does not form part of them) will occupy 1000cm**3

The buoyancy due to the air on the lead will be 0.12g and that on the feathers 1.2g (at STP in air)

Therefore a kilogram mass of feathers will be lighter by about 1g than the same mass of lead, at STP in air (give or take).

I reckon.

[Bob Mannix]

No. Ships float because they are made of metal (or wood, or concrete) *and* air. You cannot make a solid lead boat of any shape that floats due to buoyancy (a lead monolayer might float due to surface tension). Buoyancy at a water/air interface depends on shape. If the lead boat sunk it would still have a buoyancy (while sinking - granted less than its weight) independent of its shape.

If we assume feathers are made of keratin, you are correct on the second point (as it happens), as the density of keratin is not far off that for water and, at their crush limit, they may either float or not. A feather will float but that has little to do with bouyancy but a lot to do with surface tension. A fully wetted feather, under water would be around zero buoyancy and might sink or float.

[Rod]

Ar, but you could make a hollow cube out of the lead and evacuate it. Then work out its buoyancy... :-)

(Of course you're likely to want to store these things on your shelf along with the books and the china. And 1.2g isn't going to make much difference between resin, cement, bolts or holding the shelf up by mental effort.)

[Bob Mannix]

A hollow lead cube (whether evacuated of not) is still not solid! It would be slightly lighter than if air filled.

(Resin? Bolts? We're way past that :o) Stick some bloody screws in, they are in shear and won't give way - the shelf will bend. Personally I would use spur shelving spaced 1/3, 2/3, 1/3 myself but what do I know - who cares, putting shelves up was how we all learned about DIY to start with, wasn't it?!)

[Rod]

Sorry if it wasn't clear - I meant a hollow model ship. I thought the whole Titanic would be a bit ambitiuous for a single kg of lead so just settled for an average model ship. (I can't help but think that if it is a model is must approximate to the hollowness of the real thing it is based on. But that's me.)

BTW - is there a standard way of defining hollowness of an object?

[The Natural Philosopher]

well, you would hve to fill the quill first. ISTR they used to be used to make fishing floats..

[Rod]

But why should the lead cube be solid? Not part of Andy's question. I was just trying to get the buoyancies the same/similar for the feathers and the lead to remove it from consideration.

The evacuation was simply to avoid anyone suggesting that the weight or the mass of the air inside had any relevance at all.

Perhaps the easiest ways of getting differences are things like weighing one at the top of a mountain the other at ground level. Or over gravitational anomlies. Saves a lot of lead bashing and feather squishing.

[Rod]

But they have already been crushed into a super-dense package. :-)

[stuart noble]

There is a difference between perfection and over specification.

[John Rumm]

Don't get so excited, this was a frivolous response to Andy's comment "Which is heavier? A kilo of feathers or a kilo of lead?" and absolutely nothing to do with shelves, just a meandering off topic for some light hearted amusement.