||position (m), velocity (m/s), acceleration (m/s^2). These are vectors, i.e. they have both direction and magnitude.|
|Newton's laws||1st law: a = 0 if no external
force. (Law of inertia.)
Mass (kg) measures resistance to being accelerated.
2nd law: Force = mass x acceleration (as vectors).
Force measured in Newtons, N = kg m/s^2.
3rd law: force of A on B is equal in magnitude and opposite in direction to force of B on A.
||Universal attractive force
between two masses m and M at separation distance r; magnitude F = G mM
/ r^2, where G is Newton's constant
At the surface of the earth the gravitational force on a mass m is F = mg, where g = GM/r^2, M = mass of earth and r = radius of earth.
The "acceleration due to gravity at the surface of the earth" g is approximately 9.8 m/s^2. For our purposes it is accurate enough to use g = 10 m/s^2.
It is called the acceleration due to gravity, since a falling object will satisfy ma = F = mg, so a = g. In particular, since the gravitational force is proportional to the mass m, all objects fall with the same acceleration g, independently of thir mass.
||Total energy of any isolated
system is conserved (does not change in time).
kinetic energy: energy of motion, 1/2 mv^2
potential energy: energy of configuration. For example, gravitational potential energy change of mass m rising height h at surface of earth is mgh.
Energy units: J = kg m^2/s^2 = N-m
||Work is energy transfer from one
system to another.
Work = (force)x(displacement in direction of the force)
Mechanical advantage: do the same work with less force but acting over a longer displacement.
||Friction between two surfaces
arises from microscopic work that is disordered, and leads to thermal
Wheels and bearings reduce the effects of friction.
||Pressure = Force/Area; the units
of pressure are N/m^2 = Pa (Pascal).
Atmospheric pressure is about 100,000 Pa, i.e. 10^5 N/m^2 or 10 N per square centimeter. This is just about the weight of one kilogram per square centimeter. That is, there is about 1kg of air in a vertical column though the atmosphere with a square centimeter cross-section.
Pressure in a gas or fluid leads to buoyancy force when the pressure is increasing with depth.
Archimedes Principle: The buoyancy force is equal to the weight of the displaced fluid or gas.
||Temperature can be defined as a
measure of average kinetic energy per particle in a system in
equilibrium. (Systems in equilibrium have unchanging macroscopic
properties, but have microscopic fluctuations.)
Absolute temperature is measured in degrees Kelvin, K. T= 0 K corresponds to zero kinetic energy. The Celsius temperature scale is shifted down by 273.15 K, so that the freezing point of water is 0 C = 273.15 K. The boiling point of water at atmospheric pressure is 100 C.
||In a gas the molecules are very
far apart compared to their own size. For example air consists of
diatomic oxygen O_2 (21%), diatomic nitrogen N_2 (78%), argon Ar (1%),
and water vapor H_2O (around 1%, depending on humidity), where the
by number, not by weight. Oxygen and nitrogen molecules are oblong,
m in the long dimension, and their average spacing at atmospheric
pressure and room temperature
is around ten times that. One cubic meter of air has a mass of
aproximately 1.25 kg. These molecules are moving fast: at room
temperature about 500 m/s, or 1100 miles per hour.
Ideal gas law: p = k n T, where p = pressure, k = Boltzmann's constant, n = number of particles per unit volume, T = temperature.
||Materials generally expand when
heated and contract when cooled. Water contracts when cooled until it
reaches 4 C, below which it expands. (Ice is less dense than water, and
water begins to expand before it freezes.)
||Heat is the flow of thermal
(microscopic) energy from one system to another. Sometimes heat just
refers to the thermal energy itself.
Heat flows by conduction, convection, and radiation.
||When matter changes between
solid and liquid (melting/freezing), or liquid and gas
(evaporation/condensation), or solid and gas (sublimation/deposition)
energy must be supplied to the molecules to pull them away from the
solid or liquid respectively. This is called the latent heat of
fusion/melting or vaporization/condensation or sublimation/deposition.
||0th law: equilibrium of A&B
and B&C implies equilibrium of A&C
1st law: energy conservation
2nd law: entropy never decreases
Entropy: a measure of disorder
Entropy change when heat Q flows into system at temperature T is Q/T. Units of entropy: J/K.
Heat pump: uses work to transfer heat from cold to hot system.
Heat engine: uses transer of heat from hot to cold to produce work.
Ideal heat pump uses minimal work, ideal heat engine extracts maximal work. To be ideal the pump or engine must not waste heat, i.e. must not increase total entropy: the net entropy is unchanged.