Density
There are various kinds of density: Mass density = Mass/Volume
Energy density = Energy/Volume
Charge density = Charge/Volume
(What do all these densities have in common?)
The most common is mass density. If you see the word “density” all
by itself—no other word(s) in front of it—it means mass density:
Density = Mass/Volume
 = m/V
 (pronounced “roh”) is the Greek “r.” Don’t confuse it with p or P!
What are the SI units of density?
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Oregon State University PH 212, Class #10
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You can use density, mass and volume together: If you know any
two of these, you know the other....
Example: A spherical tank of mass mtank is filled with liquid of
density  . The tank is resting on an accurate scale that shows a value
FN. Find the inside radius, r, of the tank. [Vsphere = (4/3)r3]
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Oregon State University PH 212, Class #10
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Pressure
Pressure is defined simply as force per unit area: P = F/A
What are the SI units of pressure?
Example: A 10-kg rectangular brick has dimensions of 14 cm x
10 cm x 7 cm. What pressure does it exert as it rests on a flat table?
Notice how you can increase pressure either by increasing the force
or by decreasing the area.
1/25/16
Oregon State University PH 212, Class #10
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Fluid Pressure
In solid materials, the particles are chemically bound in a structure.
In a solid object feeling a force, the particles respond nearly “as one.”
In fluids (liquids or gases), the particles flow freely. This means they
can individually respond to forces, push back, or move and collide —
with each other and other objects—transmitting forces of their own,
in all directions. We can’t measure each tiny force exerted during a
collision, but we see the collective effect as fluid pressure.
Envision a tiny cube immersed in a fluid. The pressure on each
surface of the solid would result from collective force exerted
(perpendicularly) by all the fluid particles colliding with that surface.
1/25/16
Oregon State University PH 212, Class #10
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Incompressible Fluids
In this unit, we’ll look at simple examples of the effects of such fluid
pressure—often simplified by idealizing the fluid as incompressible:
Its density does not change significantly with pressure.
Liquids can be nearly incompressible; gases can’t. For the remainder
of this unit, unless otherwise indicated, assume that all fluids are
incompressible.
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Oregon State University PH 212, Class #10
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Question:
Does water float?
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Oregon State University PH 212, Class #10
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Archimedes’ Principle: Buoyancy
The most useful and widely known consequence of static pressure in
a fluid is simple buoyancy:
“A solid object immersed—or partially immersed—in
ia fluid will experience a force due to the fluid pressure,
called the buoyant force. This force is directed opposite
to the force of gravity, and its magnitude is equal to the
weight of the fluid that is displaced by the object.”
FB = Wdisplaced fluid
FB = (Vg) displaced fluid
In incompressible fluids, the buoyant force doesn’t depend on depth.
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Oregon State University PH 212, Class #10
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Check your understanding: Which object has the greatest buoyant
force magnitude acting on it?
1. A bowling ball, sitting completely submerged at the bottom
of a swimming pool.
2. A basketball, floating 25% immersed in that swimming pool.
3. A ping-pong ball, floating 5% immersed in that swimming pool.
4. There is not enough information.
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Oregon State University PH 212, Class #10
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Other implications of buoyancy:
･ If an object floats in a fluid, object ≤ fluid.
･ If the object sinks, object > fluid.
･ The fraction of a floating object’s volume that
is immersed in the fluid is equal to the ratio
of its density to that of the fluid:
Vobj.immersed / Vobj.total = object / fluid
･ Even when an object does not float (i.e. when
it is denser than the fluid—it sinks), the buoyant
force is still present: Its weight (as would be indicated
by a scale) is reduced by FB.
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Oregon State University PH 212, Class #10
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