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Fluids Archimedes’ Principle
Name______
Fluids apply a force to objects which are immersed in them called a buoyant force. We
know that pressure is greater at greater depths, so there is an upward force .
P1A
h
P2A
For a submerged object, we know that P2=P1 + ρgh, and that the difference between the
force up and the force down is the buoyant force FB.
So FB = P2A- P1A= ρghA
where hA is the volume of fluid is the volume displaced by
the object
ρghA=mg so that means that
FB=Wfluid displaced
A solid object will float in a liquid if the density of the object is less than
or equal to the density of the liquid.
Example: See example 8 on page 310
Problems- Archmedes’ Principle
1.
A duck is floating on a lake with 25% of its volume beneath the water. What is
the average density of the duck? So mass of the water= (density of water) * ¼ the
volume of the duck. ρduckVduckg= ρwater (1/4Vduck)g.
Answer: 250 kg/m3
2. What is the radius of a hydrogen-filled balloon that would carry a load of 5750 N ( in
addition to the weight of the hydrogen) when the density of air is 1.29 kg/m3. The
buoyant force must be equal in magnitude to the weight of the balloon and its load.
ρ of air is 1.29 kg/m3 and the ρ of hydrogen is 0.0899 kg/m3.
Answer: 4.89 m
3.
Only a small part of an iceberg protrudes above the water, while the bulk likes
below the surface. The density of the ice is 917 kg/m3 and that of seawater is 1025
kg/m3. Find the percentage of the iceberg’s volume that lies below the surface.
ΡiceViceg= ρwater Vwaterg. You need to find Vwater/Vice
Answer: 89.5%.