1.033/1.57: H#4: Champagne Method
(3D-ElastoPlasticity)
Due: Part 1-3 (H#4): December 1, 2003
Part 4 (Q#3): December 5, 2003
MIT 1.033/1.57
Fall 2003
Instructor: Franz-Josef ULM
We consider a rigid innite half-space with an empty hole of diameter 2a and l
3.012 PS 5
Issued: 10.15.04
Due: 10.22.04
3.012
Fall 2004
1. Symmetry.
a. Complete the combination theorem T A = B and illustrate the result with a sketch.
b. If a 4-fold axis is to be combined with a two-dimensional lattice, that lattice must be
square (
3.012 PS 4
Issued:
due:
3.012
Fall 2004
10.06.04
10.13.04 5pm
1. A particular cubic crystal has a lattice constant of 7 . It is irradiated with X-rays produced by
an X-ray tube with a molybdenum target. The strongest intensity produced from such a
target
3.012 Practice Problems for Recitation 3 (10.04.05)
Part I. Chemical work in a multi-component system.
Consider a three-phase, two-component system. Phase is composed entirely
of A molecules, phase is rich in A and dilute in B molecules, and phase is Bric
1.033/1.57: H#4: Champagne Method
(3D-ElastoPlasticity)
Due: Part 1-3 (H#4): December 1, 2003
Part 4 (Q#3): December 5, 2003
MIT 1.033/1.57
Fall 2003
Instructor: Franz-Josef ULM
We consider a rigid innite half-space with an empty hole of diameter 2a and l
3.012 Practice Problems for Recitation 4 (10.18.05)
Part I. Maxwell Relations.
a) As we did in class for G, derive the Maxwell relation for F.
dF = SdT PdV
F
F
dF = dT dV
T V
V T
S
P
=
V T
T V
S P
=
V T T V
b) How might this relation be
2.003 Engineering Dynamics
Problem Set 10 with solution
Problem 1
Figure 1. Cart with a slender rod
A slender rod of length l (2m) and mass
m2(0.5kg)is attached by a frictionless
pivot at A to a block of mass m1(1kg).
The block moves horizontally on rolle
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.013 Electromagnetics and Applications
Quiz 1
Closed book, no calculators
Please note the formulas provided on a separate sheet. There are 4 problems on two p
3.012 PS 5
Issued: 10.15.04
Due: 10.22.04
3.012
Fall 2004
2. Formation of an ideal solution is always thermodynamically favorable. Consider the
mixing process described schematically below for an isolated two-component system.
a. Using the ideal solution
3.012 PS 4
Issued:
due:
3.012
Fall 2004
10.06.04
10.13.04 5pm
1. A particular cubic crystal has a lattice constant of 7 . It is irradiated with X-rays produced by
an X-ray tube with a molybdenum target. The strongest intensity produced from such a
target
2.003 Engineering Dynamics
Problem Set 2 Solutions
This problem set is primarily meant to give the student practice in describing motion. This is
the subject of kinematics. It is strongly recommended that you study the reading on kinematics
provided with
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.013 Electromagnetics and Applications
Quiz 1 Solutions
Problem 1. (34/100 points)
E = 2 x cos(t + z) and H = y sin(t z
a)
t
(t z)
0
velocity
z
t
v
b)
c)
= E