Physics 215 – Elementary Modern Physics
Equations for Test 1
The following equations you should memorize, and understand how to use them:
4D distance
s 2   x    y    z   c 2  t   c 2 2
2
2
Length Contraction
L  Lp 
2
2
Lorentz Factor

1
1  v2 c2
Time Dilation
t  
Work
 
E  W  F  d
Speed of Light
Energy
c  3.00 108 m/s
E   mc 2
Mass Formula
Invariant Mass
2
 2
E 2   pc    mc 2 

2
2
Etot
  ptot c    Mc

2 2
Momentum


p   mv
Force
 dp
F
dt
The following equations you need not memorize, but you should know how to use
them if given to you:
Lorentz Transform
Velocity
Lorentz Boost
Binomial Theorem
of velocity
Formula
n
2
 
x    x  vt 
1     1  n  12 n  n  1  
ux  v
u pc
u x 

2
1  vu x c 2
t     t  vx c 
c E
uy
Doppler Shift
y  y
u y 
Lorentz Transform
 1  vu x c 2 
f0
z  z
of p and E
f 
uz
 1  v cos  c 
u z 
Motion in a
px    px  vE c 2 
 1  vu x c 2 
Magnetic Field
E     E  vpx 
Electromagnetic
p  qRB
py  p y ,
Force


 
pz  pz
F  qE  qu  B
The following equations you should be able to derive from the equations above, with
a bit of deduction:
Inverse
Potential and
Massless
Lorentz Boost
Kinetic Energy
Particles
x    x  vt  

E pc
E0  mc 2
t    t   vx c 2 

2
u c
Ekin     1 mc
y  y
z  z
Layout of the exam: Below is an outline of the exam
This test consists of three parts. Please note that in parts II and III, you can skip one
question of those offered.
Part I: Multiple Choice [20 points]
For each question, choose the best answer (2 points each)
[questions 1-10]
Part II: Short answer [20 points]
Choose two of the following three questions and give a short answer (1-3
sentences) (10 points each).
[questions 11-13]
Part III: Calculation: [60 points]
Choose three of the following four questions and perform the indicated
calculations (20 points each)
[questions 14-17]