1
Order-of-Magnitude/Fermi Problems
T. Ferguson, August 19, 2010.
(This note is based on one originally written by Prof. R. Holman.)
1.1
Introduction
One skill that all physicists should possess is the ability to estimate the approximate numerical
answer

Physical Analysis, 33-231 Solutions to Exam 3
Fall Semester 2010
Problem 1. (a) The characteristic equation is: 9r 2 + 6r + 4 = 0. So we get:
r =
62 (4)(9)(4)
6
18
1
6 3
1
i
=
= .
3
18
3
3
Thus, this is a two-complex-root case, and we know that the solu

Physical Analysis, 33-231 Homework Assignment 4
Due MONDAY, September 20, 2010.
dy
Problem 1. (a) Using partial fractions, solve the dierential equation: (x2 1) dx = 2y for y(x),
given the initial condition y(2) = 5. (b) Without using Maple, check your an

Physical Analysis, 33-231 Homework Assignment 3
Due Wednesday, September 15, 2010.
Problem 1. Many new cars are now wired so that their headlights are always on whenever the engine
is running, even in broad daylight. We would like to estimate by what perc

Physical Analysis, 33-231 Homework Assignment 2
Due Wednesday, September 8, 2010.
1) Estimate the magnitude of the orbital angular momentum of the Earth about the Sun. Remember
that the angular momentum of an object about a point is L = r p, where r is a

Physical Analysis, 33-231 — Solutions to Exam 2
Fall Semester — 2010
Problem 1. (a) To ﬁnd the critical points, we set: % = y2(y w 2)(y + 3) = 0, which has solutions
ofc = 0, 2, "-3. For c = 0, if 0 < y < 2, then the 3 terms in ﬁg- = y2(y—2)(y—3) are (+)(

Physical Analysis, 33-231 Solutions to Practice Exam 3
Fall Semester 2010
Problem 1. (a) The characteristic equation is: 9r 2 + 12r + 4 = 0. So we get:
r =
12
(12)2 (4)(9)(4)
2
= .
3
18
Thus, this is a repeated-root situation, and the solution is:
2
y(x)

Physical Analysis, 33—231 — Solutions to Exam 2
Fall Semester - 2009
Problem 1._ (a) The gain in population in a time At due to births is: AP(births) = ﬁPAt = (60 +-
ﬁlP) PAt = [0.01P+0.001P2]At. The loss in population in a time At due to deaths is: AP(de

Solutions to Practice Exam 1, Physical Analysis Fall Semester 2010
Problem 1. (a) TRUE: You should have done the following calculation:
(1 kg) (1000 gm/kg)
= 103 gm/cm3 .
3 (100 cm/m)3
(1 m)
(b) FALSE: Using our approximation (1 + )p 1 + p, with = 0.02 an

EXAM 2
Physical Analysis, 33-231
October 27, 2009
NAME:
No calculators, books, or notes are allowed for this exam.
Read each problem carefully before attempting to solve it.
Explain briey but completely all your steps and all your reasoning.
WRITE LAR

Practice Exam 3 Physical Analysis, 33-231, Fall 2010
Problem 1.
(a) (10 points) Solve the dierential equation:
d2 y
dy
9 2 + 12
+ 4y = 0
dx
dx
for y(x), given the initial conditions y(1) = 9 and dy(1) = 2. Give all the numerical values in your nal
dx
answ

Practice Exam 1 Physical Analysis, Fall 2010
Problem 1. True/False. For each of the following statements, write out your answer as either TRUE or
FALSE. Then give a short but complete explanation or calculation showing why you think the statement
is true