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 1
FINAL EXAM: April 26, 3:45-6:45
Here is the master list of questions (updated 2/1/18)
Logarithmic
map of the universe
| Date |
Problems Solved in Class |
Homework Problems (Due next class) |
| 1/11/18 |
21, 23, breaths |
3, 10, 22, read chap 1,2 |
| 1/18/18 |
8, 19, 29, 30, 36 |
38, 46, 48 |
| 1/25/18 |
41, 44, 49, 52 |
54, 56, 60 |
| 2/1/18 |
51, 61, 62, 63, 112 |
64, 65, 69 |
| 2/8/18 |
70, 71, 72 |
75, 76, 78 |
| 2/15/18 |
82, 83 |
80, 86 |
| 2/22/18 |
87, 88 |
91, 94, compare mass of brains to mass of air in our classroom (due 3/15) |
| 3/1/18 |
Midterm |
|
| 3/15/18 |
105, 106, 107, 110, 113 |
116, 118, 128 |
| 3/22/18 |
Dr. Kuhn |
No HW |
| 3/29/18 |
Dimensional Analysis |
see below |
| 4/5/18 |
Scaling |
See below |
Principles of dimensional analysis:
Dimensional Analysis homework due 4/5:
1) use dimensional analysis to determine the formula for the speed of sound (i.e, the average thermal velocity of air molecules). The relevant variables are v, m, k_B*T. Calculate your result and compare it to the speed of sound.
2) use dimensional analysis to determine the formula for the height of the atmosphere. Assume that the atmosphere is isothermal. Calculate your result and compare it to the height we determined in class.
Scaling homework due 4/12
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., 3 times faster or 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?
2) How does jumping height scale with body size for animals
(i.e., how high can animals of different sizes jump)? Consider cats
(which have similar body shapes and range of sizes). Jumping height
will be related to the work done while jumping, W = Fd
where F is the force applied during take-off and d is
the distance over which the force is applied.
Important equations (memorize these):
kinematics equations
Important numbers (memorize these):
Population of the Earth: 7*10^9
Population of the US: 3*10^8
density of water = 1000 kg/m^3 = 1 kg/l = 1 g/cm^3
density of iron = 8 ton/m^3
density of air (@stp) = 1 kg/m^3
1 year = pi * 10^7 s
v_sound = 330 m/s ~ 700 mph at STP
1 Coulomb = 6x10^18 electron charges
G = 7 x 10^(-11) N m^2/kg^2
gasoline energy density = 3x10^7 J/liter
Chemistry stuff:
avogadro's number = N_A = 6*10^23
1 mole of gas at STP has V = 22.4 l
1 mole of gas has m (in grams) = molecular weight
atomic size = 1*10^-10 m
energy of energetic chemical reaction = 1.5 eV
Boltzmann's constant k_B = 1.6 x 10^-23 J/K
Units:
1 m^3 = 10^3 l = 10^6 cm^3
1 ton = 10^3 kg = 10^6 g
1 atmosphere = 1 bar = 10^5 Pascal = 10^5 N/m^2 = 760 mm Hg = 10 m H2O
= 15 psi
1 m/s ~ 2 mph
1 mile = 1.6 km
1 ft = 0.3 m
1 in = 2.5 cm
Solar system sizes:
R_earth = 6.4*10^6 m
D_Earth-Moon = 4x10^5 km
D_Earth-Sun = 1.5x10^8 km
apparent diameter moon = sun = 1 cm / 1 m = 0.01
M_Earth = 6x10^24 kg
M_Moon = 8x10^22 kg
Note that the atom size can be derived from Avogadro's number and
the
density of water.
The Earth and Moon masses can be estimated from their sizes and densities
Order of Magnitude Physics A high level, 3 credit, course on estimation from CalTech.