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Spring Quarter 2010
Physics 1B Class Notes
CR
Professor Walter Gekelman
OFFICE
PAB 4907
Democritus
5
th
century
BC
All matter is made of atoms
Aristotle
384322
BC
4 elements, Earth is a sphere
Archimedes
287212
BC
Buoyancy, solid geometry
(pre calculus)
William of Ockham
13001349
No unnecessary assumptions
Nicholas Coperni
cus
14731543
Earth moves around sun
Tycho Brahe
15461601
Best data on planets until
then
Johannes Kepler
15711660
Analyzed Brahe data, Kep
lers laws
Issac Newton
16421727
3 Force laws, calculus, optics
Charles Coulomb
17361806
Force Law of Electricity
Hans Oersted
17771851
Electricity and Magnetism are
related
Andre Ampere
17751836
Electric Current and Magnetic
Fields
Michael Faraday
17911867
Concept of Field, Faraday’s
Law
Boltzman
18441906
Statistical mechanics, ther
modynamics
1
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View Full Document James Clerk Max
well
18311879
Displacement current, Max
wells equations
Michelson
18521931
Perfected interferometer, dis
proved aether
Albert Einstein
18791955
Relativity, quantum mechan
ics, Brownian motion, photoe
lectric effect, etc
THE most general equation of motion is a differential equation and may be written as:
(1)
m
∂
2
y
∂
t
2
+
b
∂
y
∂
t
+
ky
=
F
(
y
,
t
)
The first term is mass times acceleration.
The second term is velocity dependent and is
a frictional drag term.
The third term is a restoring force which will study when we dis
cuss springs and the term on the left hand side a forcing or driving term.
This would be
present if you consider a child on a swing and once a period you give her a push.
(a) Where does equation (1) come from and what do the terms in it mean?
(b) What are the solutions to (1)
(c) What are problems in the real world that the equation addresses?
The answer to (c) is :Planetary motion, motion of satellites about the earth, pendulums,
motion of springs, electrical circuits, vibrations of molecules, motion of cannonballs and
projectiles, ……
Suppose F(y,t) is a constant and b and k = 0
Then we have what you studies in 1A
(1a)
m
∂
2
y
∂
t
2
=
F
=
m
g
with solution
y
−
y
0
=
v
0
t
−
1
2
gt
2
.
We wont go over this you did it
already.
Suppose k = 0
and
F
= m
g
(1b)
since gravity points down
The solution to this equation is:
2
v=
dy
dt

ˆ
j
( )
;
v=
mg
b
1
−
e
−
bt
m
⎛
⎝
⎜
⎞
⎠
⎟
−
ˆ
j
( )
This is the equation of an object with a limiting velocity.
A graph of v is shown below
The abscissa is time and the ordinate is velocity.
The velocity does not continually in
crease as it would if the b term (or drag term was missing) but reaches a limit.
For ex
ample if you jumped out of a plane 5 miles up you would not hit the ground at superson
ics speeds, you limiting velocity would be about 100 MPH.
You could do just as well
driving into a wall at that speed.
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This note was uploaded on 05/12/2010 for the course PHYSICS 1B 318007220 taught by Professor Gekelman during the Spring '10 term at UCLA.
 Spring '10
 gekelman

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