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Physics of floating

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Something my GCSE Physics classes didn''t cover - Is it possible to calculate the upwards acceleration of an object in a more dense liquid / gas? Is there any generic formula for this that takes into account density, viscosity, force of gravity or whatever else is needed?

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The force is called boyancy (sp?) and should be equil to the mass of the liquid displaced. For example, a 10 kg object needs 98 N (10 Kg * 9.8 m/s^2) of boyant force to keep it above the water. This means it needs to displace 98 N of the liquid. You convert that using the liquid''s density and you can find out how much volume of the liquid would need to be displaced in order for the object to float. Just remember from Mr Wizard that an object always displaces it''s own volume.

Generally, if something is less dense that the liquid surrounding it, it''s going to float. BUT the upward force is on the object is going to be equal to:

F = Density of the liquid * Mass of Liquid Displaced * Gravity constant (9.8)

If F is less than W of the object, the object will sink. Otherwise it will float until it displaces just enough liquid for it to ballence out.

Hope this helped.


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Warden''s reply is close but not quite accurate. His explanation is good, but equation for F is not correct, which you can see because the units are not consistent [i.e., Force is Newtons = kg-m/s^2 but the right-hand-side of his equation for F has units (kg/m^3) * kg * m/s^2 which simplifies to kg^2/(m^2*s^2)]

Just a simple correction. The correct equation is:

F = Density of the liquid * VOLUME of Liquid Displaced * Gravity constant (9.8)

where the right-hand-side has units = (kg/m^3) * m^3 * m/s^2 = kg-m/s^2 = correct units of force.

As Warden did mention, that is the buoyancy (corrected spelling) force only! The net force will include the weight of the object, so if a positive force is upwards:

F_net = F_buoyancy - Weight

That way, when the buoyancy force equals the weight, the net force upwards is zero and the object floats. If the object displaces water that weighs more than the object, there will be a net acceleration upwards.

Something to get you thinking: if you have a weird shaped object, how do you determine what *angle* it will float at, when it is displacing just enough water to float? What forces are acting on the object that cause it to sit at a particular angle?

Something else to get you thinking: what about the air that surrounds the object when the object is partially out of the water---sitting on the surface? Air is a fluid (which is a gas or liquid), and does it contribute to buoyancy force?

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

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