# Upthrust and Buoyancy

• B
Hi,

Really quick general question but is upthrust independent of surface area. I came across the following:

"Heavy things can float on water if there is sufficient surface area to produce a big enough upthrust at a particular depth"

My thinking that this is incorrect is based on the assumption that whether or not something can float or sink is independent of everything except density because:

Upthrust = weight of displaced fluid = p V g = p (Ah) g

where p is density, V is volume, g is acceleration due to gravity, A is surface area and h is height

Weight = p(Ah) g

So upthrust and weight have identical terms except that the density 'p' is different in both. The 'p' in the weight terms is the density of the object whereas the 'p' in the upthrust term is the density of the fluid.

So increasing the surface area as far as I can tell would not help anything float because increasing it in the upthrust term will also increase it in the weight term. Lead sinks in water full stop. Surely lead can't float simply by increasing its surface area? The only way you would make lead float is to increase its effective density by hollowing it out with air.

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anorlunda
Staff Emeritus
There is such a thing as surface tension. So, yes lead can float if you make it into a foil with enough area. Think of one kg of lead in a foil with the area of the Atlantic Ocean.

Note how each of the bugs feet changes the shape of the surface for an area bigger than the foot.

Sometimes even drops of water float on water. How? Surface tension.

Jimmy87
There is such a thing as surface tension. So, yes lead can float if you make it into a foil with enough area. Think of one kg of lead in a foil with the area of the Atlantic Ocean.

Note how each of the bugs feet changes the shape of the surface for an area bigger than the foot.

View attachment 211773

Sometimes even drops of water float on water. How? Surface tension.
Thanks. Yes, that makes sense about surface tension but the statement refers to increasing the upthrust at a particular depth by increasing surface area. That wouldn't work would it? Also surface tension was not discussed. Ignoring the surface tension, surface area cannot cause an object to float can it?

anorlunda
Staff Emeritus
Thanks. Yes, that makes sense about surface tension but the statement refers to increasing the upthrust at a particular depth by increasing surface area. That wouldn't work would it? Also surface tension was not discussed. Ignoring the surface tension, surface area cannot cause an object to float can it?
Surface tension is relevant to floating.

I think some one mangled the sentence with floating and particular depth in the same sentence.

sophiecentaur
Gold Member
Surface tension is relevant to floating.
But t's only significant for small objects. It's best to ignore it until the basics about Archimedes' Principle have been sorted out.
Archimedes' Principle deals with the problem very well and it tells you that the buoyant force (aka upthrust) is equal to the weight of fluid displaced.
If you are dealing with a floating object then the weight of displaced fluid will be equal to the weight of the object - that's very basic stuff and it is useful to apply it in all such situations.
But it doesn't deal with the issue of the orientation of floating object and the fact that the 'natural' orientation of an object that floats will be where the Potential Energy is minimised.
if there is sufficient surface area to produce a big enough upthrust
I think this comment could relate to objects like open boats, which can displace a lot of water because the air contained in the boat contributes to the displacement of water. So a wide boat will float higher in the water than a deep V shape. The individual setup needs to be considered carefully if you want the 'right' answer and it's not always obvious.