Conceptual Physics

(Sean Pound) #1
below the water’s surface, since the density (and weight) of the displaced water
changes only slightly with depth. If this is so, how can a submarine dive or surface? The
submarine changes its weight: It either adds weight by allowing water into its ballast
tanks or reduces its weight by blowing the water out with compressed air.

Fish approach the issue in a slightly different way. They change their volume by inflating
or deflating an organ called a swim bladder, filled with gas released from the blood of
the fish. When they increase their volume, they rise because they displace more water
and experience increased upward buoyancy.

Archimedes’ principle can also be used to analyze the buoyancy of human beings.
People with a high percentage of body fat float more easily than do their slimmer
counterparts. This is because fat is less dense than water, while muscle is denser than
water. In one test for lean body mass, a person is weighed out of water, and then
weighed again while submerged. The difference in the two weights equals the buoyant
force, which allows a calculation of the volume of the displaced water. The average
density of the person, based on his volume and his dry weight, can be used to
determine what percentage of his body is fat.

Triathletes, whose body fat is likely to be very low, demonstrate their appreciation of the
principles of buoyancy by preferring to wear wetsuits during swimming events. Lean
people tend to sink, and a wetsuit helps an athlete float since it is less dense than
water, reducing the energy spent on staying up and allowing more to be spent on
moving forward. Because of this effect, triathlons ban wetsuits in warm water events
where they are not strictly necessary for survival. You wouldn’t want to give those
triathletes any breaks before they bike 180 kilometers and then run over 40 kilometers!
Objects fabricated from materials denser than water can float. A steel boat floats since
its hull encloses air, which means the average density of the volume enclosed by the
boat is less than that of water. Observe what happens when someone steps into a small
boat: It sinks slightly as more water is displaced to balance the person’s weight. If the
boat is overloaded with cargo, or if water enters the hull, its average density will surpass
that of water and the boat will sink (fast-forward to the end of the film A Perfect Storm
for a graphic example of the latter problem).
Often, the concept of buoyancy is applied to water, but it also applies to other fluids,
such as the atmosphere. Blimps and hot air balloons use buoyancy to float in the air. A
blimp contains helium, a gas lighter than air. The weight of the air it displaces is greater
than the weight of the blimp, so it floats upward until it reaches a region of the
atmosphere where the air is less dense and the weight of the blimp equals the weight of
the displaced air.

Archimedes’ principle


Buoyant force:
·upward force on an object in a fluid
·equals weight of the displaced fluid

This chunk of African ironwood


weighs 43 N, and it displaces


0.0030 m^3 of water. What is the


buoyant force on it?


m = ȡV


m = (1000 kg/m^3 )(0.0030 m^3 )


m = 3.0 kg


mg = (3.0 kg)(9.80 m/s^2 ) = 29 N


F = 29 N, directed up


13.8 - Sample problem: buoyancy in water


A stainless steel fishing hook with a worm is in the water at the end of a line, dangled with the intent of attracting the wily fish. For the density of
the hook we use the density of stainless steel, 7900 kg/m^3.
We will refer to the combination of the hook and worm as “the bait.”

A stainless steel hook with a worm


dangles underwater at the end of a


fishing line.


What is the net downward force that


the bait combination exerts on the


line?


(^256) Copyright 2000-2007 Kinetic Books Co. Chapter 13

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