Problem M25
In addition to chapters 4-7 of Ashby and Jones Engineering Materials. You may also find the
chapters on polymers in Ashby and Jones, Engineering Materials 2, helpful (this is a green
cover
Massachusetts nstitute of Technology
Physics Department
Physics 8 20
Introduction to Special Relativity
Final Exam Solutions
IAP 2005
.
a)c meters per second when v/c 1
b)A reference frame in which Ne
2
Information
Useful approximations:
c 3 108 m/s
1 year 107 s
Boost (along the x-axis) and its inverse. Suppose V = (v0 , vx , vy , vz ) is a four vector.
Then
0
vx = (vx
0
0
vx = (vx + v0 )
v0 )
0
vy
APPROXIMATE VALUES OF USEFUL CONSTANTS
Constant
c (speed of light)
G (gravitation constant)
k (Boltzmanns constant)
h (Plancks constant)
mproton
eV (electron Volt)
M (solar mass)
L (solar luminosity)
APPROXIMATE VALUES OF USEFUL CONSTANTS
Constant
c (speed of light)
G (gravitation constant)
k (Boltzmanns constant)
h (Plancks constant)
mproton
eV (electron Volt)
M (solar mass)
L (solar luminosity)
Unied Engineering
Fluids Problems F16F17
Fall 2003
F16. 1 (x, y) and 2 (x, y) are known to be physically-possible ows (i.e. satisfy mass conservation), and their corresponding pressure elds p1 (x, y)
Unied Engineering
Fluids Problems F1F2
Spring 2004
F1a. An aircrafts wing is at zero angle of attack when all wheels are on the ground.
Qualitatively describe the ow behind the wing airfoil a short ti
Unied Engineering
Fluids Problems F18-20
Fall 2003
F18. Wind with velocity V is owing over a mountain ridge have the shape Y (x) = Cx.
The ow is to be modeled by superimposing a uniform ow with a sour
Unied Engineering
Fluids Problems F21F22
Fall 2003
F21. As shown in class, the nonlifting irrotational ow past a circular cylinder can be
represented by superimposing the uniform freestream ow and a d