Physicists should be able to estimate the order-of-magnitude of
anything. How many atoms of Julius Caesar do you inhale with each
breath? How
much waste does a nuclear power plant generate? This 1 credit course
will develop concepts, relations and numbers useful for estimation. We
will discuss the concepts as a group and attack the problems as a
group. I intend to lecture as little as possible. The course will not
cover new material but will make use of already acquired (or at least
already taught) knowledge. It will try to
help students apply physics to real-life questions and understand which
physical effects are appropriate on which scales. The corequisite is
Physics 232.
Your grade in the class will depend on
tests, homework and class participation.
Midterm: March 9
FINAL EXAM: Apr 29, 3:45-6:45
Here is the master list of questions
| Date |
Problems Solved in Class |
Homework Problems (Due next class) |
| 1/21 | 1, 10 | 13, 18, 21 |
| 1/28 |
5, 14, 23 | 16, 22, 26 |
| 2/4 |
32, 33, 38 | 36, 41, 46 |
| 2/11 |
27', 37, 42, 43 | 47, 49, 56 |
| 2/18 |
50, 53 | 57, 58, 59, 60 |
| 2/25 |
70, 71 | 78, 80 |
| 3/4 | 81, 87 |
76, 79, 82 |
| 3/11 | Midterm |
|
| 3/18 |
30, 91, 93, 94, | 92, 105, 107 |
| 3/25 | 110, 112, 116, 118, 126, 128 | 108, 133, 135 |
| 4/1 | Scaling. Length, area, volume, strength | see below |
| 4/8 | scaling: planet temps, range vs v, terminal velocity | see below |
| 4/15 | Dimensional analysis: dropped rock, Schwarz. radius, deep water waves, A-bomb blast |
see below |
| 4/22 | Kepler's Law Gravitational light bending power radiated by accelerating charge |
see below |
Scaling homework due 4/8
Read Scaling,
by Sanjoy Mahajan, part of his course "Lies and Damn Lies" linked to
at the bottom of this page.
1) You build a 1/N scale model of a bridge for a catastrophe
video and then film its collapse. At what speed (e.g., sqrt(N) times faster or N^2 times slower) should you play back the film so that the bridge
collapse looks realistic? What are the speed ratios for N = 10 and
for N = 100 (NB: HO Scale is 1:87)?
2) How does walking speed depend on scale? Assume that legs
swing back and forth just like a pendulum. If you make an
animal N times larger in each linear dimension, how much faster
(or slower) will the animal walk? Consider how both stride length and
period depend on the length.
Scaling homework due 4/15
Read Dimensional Analysis,
by Sanjoy Mahajan, part of his course "Lies and Damn Lies" linked to
at the bottom of this page.
1) Using the drag equation (F = C rho A v^2), estimate the ratio of the top human swimming speed to the top bicycling speed. Compare this to your estimate of the top swimming and cycling speeds. Why does this comparison fail for swimming and running?
2) How does moment of inertia scale with length (at constant density)?
3) You make a capacitor with a metal spoon and a metal fork, separated by a certain distance. How does the capacitance change if you double all linear dimensions?
Dimensional Analysis Homework due 4/22
For each problem, follow the dimensional analysis steps listed above.
1) Two iceskaters each have the same mass and speed. One is
skating due south and the other is skating due north such that their distance
of closest approach is b. They grab hands when they are
closest together and proceed to rotate around their center of mass,
still separated by a distance b. Use dimensional analysis to
find the frequency of their rotation.
2) Assume the Earth has constant density. Drill a hole thru the
center of the Earth. Drop an object of mass m down the hole.
Use dimensional analysis to find the period of the resulting
oscillations. Ignore the rotation of the Earth.
3) The electromagnetic energy density in a black-body
cavity E/V depends on the temperature T plus certain
fundamental constants. Use dimensional analysis to find the dependence of E/V on these
quantities. I suggest that instead of T, you use k_B T,
Boltzmann's constant times T.
Dimensional Analysis Homework due 4/28
For each problem, follow the dimensional analysis steps listed above.
1) Find the radius of the hydrogen atom in terms of the charge of
the proton.
2) Find the speed of air molecules at STP
3) In shallow water, where the wavelength is much greater than the
depth, the speed of gravity driven water waves does not depend on the
wavelength. Find the speed of the waves. How does it vary with
depth?
3a) Predict the speed of tidal waves, which are shallow water (!)
waves created by underground earthquakes. How long should it take a
tidal wave to cross an ocean?
Important equations (memorize these):
kinematics equations
Important numbers (memorize these):
conversion factors: useful numbers:
US population = 3 x 10^8
world population = 7 x 10^9
N_A = 6x10^23 thingies/mole
r_atom = 10^-10 m
rho_water = 1 (ton/m^3, kg/L, g/cm^3, pound/pint)
rho_iron ~ 10 * rho_water (actually 8)
Latent heat of vaporization of water = 2 kJ/g
Chemical energy of gasoline = 4 x 10^7 J/kg
drag force F = (1/2) C A rho v^2
Note that the atom size can be derived from Avogadro's number and
the
density of water.
Order of Magnitude Physics A high level, 3 credit, course on estimation from CalTech.