Conceptual Physics
Study Notes & Questions: Properties of Matter (Chap. 10)
1) The density of a material is the amount of mass per unit volume (p204)
2) Pressure is force per unit area (p207). Pressure increases linearly with
depth in a non-compressible fluid (i.e. a liquid; p209), but it increases
exponentially in a compressible fluid (i.e. a gas; p212). Would a 100 foot
dam holding back the Pacific Ocean have to be made stronger than a
100 foot dam hold back a small lake?
3) Pascal’s Principle: Changes in pressure, in a static fluid, is immediately
(i.e. as fast as molecular motion allows) transferred to all parts of the
fluid.
4) Archimedes’ Principle: The upward force exerted on an object (buoyancy)
immersed in a fluid is equal to the weight of the fluid it displaces. No
mystery here, it is simply a matter of the average densities of two
identically-shaped objects being pulled by gravity.
a) If an object’s average density is less than the surrounding fluid, the
mobile molecules of the fluid will flow under the object (because
gravity pulls them more strongly), so the object itself has no place to
go but up.
b) If the object’s average density is the same as the fluid, gravity pulls
on the two equally and there is no net force to push the object up or
down.
c) If the object’s average density is greater than the fluid’s density, it will
tend to sink, but at a slower rate because the fluid pressure under
the object will partly act against the pull of gravity.
d) The viscosity (internal friction) of the fluid does not affect buoyancy,
but it does govern how fast an object will sink or rise in the fluid.
e) A floating object will only settle in the water until the average density
of the submerged portion is equal to the density of the fluid.
f) A massive steel battleship will not sink because the average density
of its submerged hull plus the air that fills its hollow interior equals
the density of seawater.
1
5) The Bernoulli Effect: the pressure exerted by a fluid on a surface
decreases as the velocity of the fluid across the surface increases.
(p215) Gas molecules at a given temperature have an average speed,
which is usually distributed evenly in all directions, and makes its
pressure equal in all directions. If a situation is set up so that the
motion of the gas molecules are “herded” in a certain direction, they
have less side-to-side motion—this makes for less pressure exerted in
these side-to-side directions.
• An airplane wing is designed to shape the air flow over its top
surface so that the air molecules are “herded” to move more
quickly in the horizontal direction—giving them less motion (hence
less pressure) in the vertical direction. Less pressure on top,
normal pressure on the lower surface: the net pressure on the wing
is upward—the airplane experiences lift.
6) Ideal Gas Law: the pressure times the volume of a fixed amount of gas
equals a constant times the absolute temperature of the gas:
PV = constant *T. (p217). What is Charles’ Law? What is Boyle’s Law?
What happens when the temperature of a gas goes to absolute zero?
7) Elasticity: the spring-like property of a material to bend under force,
respond with a counterforce and return to its original shape. Most
objects have some elasticity, however any object can be subjected to
such high force that it breaks or gets permanently deformed—that is,
the force exceeds the object’s elastic limit. (p218).
• Hooke’s Law: a material that behaves according to Hooke’s Law
has a spring-like elastic restoring force that increases in proportion
to its temporary deformation: F = -k Dx
8) Tension and compression (p219) are manifestations of elasticity at the
molecular level of materials. Why doesn’t an extended metal beam
bend under heavy weights? Why does the I-beam shape work so well?
9) Scaling: the mass of an object scales as the cube of that object, while
the molecular materials that make up that object and their
intermolecular forces do not change. This means that the gravitational
stress, for example, on the molecular composition of large objects is
greater in comparison to that for small objects. (p219)
2