Learning Objectives
By the end of this section, you will be able to:
- Define buoyant force
- State Archimedes' principle
- Understand why objects float or sink
- Understand the relationship between density and Archimedes' principle
When you rise from lounging in a warm bath, your arms feel strangely heavy. This is because you no longer have the buoyant support of the water. Where does this buoyant force come from? Why is it that some things float and others do not? Do objects that sink get any support at all from the fluid? Is your body buoyed by the atmosphere, or are only helium balloons affected? (See Figure 11.22.)
Answers to all these questions, and many others, are based on the fact that pressure increases with depth in a fluid. This means that the upward force on the bottom of an object in a fluid is greater than the downward force on the top of the object. There is a net upward, or buoyant force on any object in any fluid. (See Figure 11.23.) If the buoyant force is greater than the object's weight, the object will rise to the surface and float. If the buoyant force is less than the object's weight, the object will sink. If the buoyant force equals the object's weight, the object will remain suspended at that depth. The buoyant force is always present whether the object floats, sinks, or is suspended in a fluid.
Buoyant Force
The buoyant force is the net upward force on any object in any fluid.
Just how great is this buoyant force? To answer this question, think about what happens when a submerged object is removed from a fluid, as in Figure 11.24.
The space it occupied is filled by fluid having a weight . This weight is supported by the surrounding fluid, and so the buoyant force must equal , the weight of the fluid displaced by the object. It is a tribute to the genius of the Greek mathematician and inventor Archimedes (ca. 287–212 B.C.) that he stated this principle long before concepts of force were well established. Stated in words, Archimedes' principle is as follows: The buoyant force on an object equals the weight of the fluid it displaces. In equation form, Archimedes' principle is
where is the buoyant force and is the weight of the fluid displaced by the object. Archimedes' principle is valid in general, for any object in any fluid, whether partially or totally submerged.
Archimedes' Principle
According to this principle the buoyant force on an object equals the weight of the fluid it displaces. In equation form, Archimedes' principle is
where is the buoyant force and is the weight of the fluid displaced by the object.
Hmm … High-tech body swimsuits were introduced in 2008 in preparation for the Beijing Olympics. One concern, and international rule, was that these suits should not provide any buoyancy advantage. How do you think that this rule could be verified?
Making Connections: Take-home Investigation
The density of aluminum foil is 2.7 times the density of water. Take a piece of foil, roll it up into a ball and drop it into water. Does it sink? Why or why not? Can you make it sink?