Buoyancy

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Near the surface of Earth, object with weight can float in fluids.  The fluid must exert a force on a floating object equal in magnitude and opposite in direction to the object's weight.  Where does this force come from?

imageConsider again the box-shaped volume of water in equilibrium at some depth in the pool.  The upward force provided by the surrounding water must exactly balance the force of gravity acting on the water in the box.  The upward force provided by the surrounding water must be equal to the weight of water in the box.

If we replace the volume of water with a box of the same shape containing some other material, then the net upward force provided by the surrounding water does not change.  It depends only on the difference in the pressure at the top and at the bottom of the box.  But the weight of the box changes, and therefore the net force on the box changes.  If the weight is greater than that of the corresponding volume of water, the net force is downward and the box will accelerate downward and fall.  If the weight is less than that of the corresponding volume of water, the net force is upward and the box will accelerate upward and rise. 

This is Archimedes' principle.  It holds for all fluids, i.e. it holds for all liquids and gases. 
An object partially or wholly immersed in a gas or liquid is acted upon by an upward buoyant force B equal to the weight w of the gas or liquid it displaces.

B = w

Link:  Buoyancy Brainteasers

Problem:

A 2 kg block of wood is floating in water.  What is the magnitude of the buoyant force acting on the block?

Solution:

Problem:

The density of freshwater is 1 g/cm3 and the density of seawater is 1.03 g/cm3.  Will a ship float higher in freshwater or seawater?

Solution:

Problem:

A Styrofoam slab has a thickness h and a density ρobject.  What is the area of the slab, if it floats with its top surface just awash in fresh water when a swimmer of mass m is on top?

Solution:

Problem:

imageA frog in a hemispherical pod finds that he just floats without sinking into a sea of blue-green ooze with density 1.35 g/cm3.  If the pod has radius 6 cm and negligible mass, what is the mass of the frog?

Solution:

Problem:

A barge is carrying a load of gravel along a river.  It approaches a low bridge, and the captain realizes that the top of the pile of gravel is not going to make it under the bridge.  The captain orders the crew to quickly shovel gravel from the pile into the water.  Is this a good decision?

Solution:

Problem:

imageTwo objects, A and B, have the same volume and are completely submerged in a liquid, although A is deeper than B. Which object, if either, experiences the greater buoyant force?

Solution:

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Module 7: Question 2

Do fluids exert buoyant forces in a "weightless" environment, such as in the space shuttle?  Explain your answer.

Discuss this with your fellow students in the discussion forum!