1/26/15 Oregon State University PH 212, Class #10 1

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 ρ = m/V

ρ (pronounced “roh”) is the Greek “r.” Don’t confuse it with p or P!

What are the SI units of density?

1/26/15 Oregon State University PH 212, Class #10 2

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 ρ. The tank is resting on an accurate scale that shows a value FN. Find the inside radius, r, of the tank. [Vsphere = (4/3)πr3]

1/26/15 Oregon State University PH 212, Class #10 3

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 x10 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.

1/26/15 Oregon State University PH 212, Class #10 4

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.

1/26/15 Oregon State University PH 212, Class #10 5

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.

1/26/15 Oregon State University PH 212, Class #10 6

Question:Does water float?

1/26/15 Oregon State University PH 212, Class #10 7

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—inia fluid will experience a force due to the fluid pressure, called the buoyant force. This force is directed oppositeto 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 = (ρVg) displaced fluid

In incompressible fluids, the buoyant force doesn’t depend on depth.

1/26/15 Oregon State University PH 212, Class #10 8

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.

1/26/15 Oregon State University PH 212, Class #10 9

Other implications of buoyancy:

･ If an object floats in a fluid, ρobject ≤ ρfluid.

･ If the object sinks, ρobject > ρfluid.

･ 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:

Vimmersed / Vtotal = ρobject / ρfluid

･ 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.