Special Relativity

-Unintuitive
-Very Fast

C = 3 * 10^8 m/s
299,792,458 m/s

Where to Begin?
Einstein, Galileo

Two postulates, logic, conclusion

Spaceship Flyby2
t’ = γt
γ= 1/√1-β^2

orbit satellite
β = 14000km / hr * 1000m / Km * 1hr / 3600s = 3890 m/s

Wret = ΔPE
= PEf – PEo

Dead Reckoning
Direction, speed, duration
East, 12km/h, 2.5hrs
south, 20km/h, 1hr

Conservation of Charge

The total charge in the universe never changes.
Closed System -> No charge being added to or removed from the system.

Friction
Conduction
Induction

Infinite source and sink of electrons
Grounding

Electric Potential Energy
When r is small, Ue is highest.
Ue = K q1q2/r
K = 9*10^9

E = 1000 N/C
d = 1cm
Mp = 1.673 * 10 ^ -27
g = 1.602 * 10 ^ -19C

F = Eg
na = Eg
a = Eg/m

ΔKE = Egx
W = Fx = Egx

Lightning

Electricity
Leyden Jar -> charged

Ben’s contribution
charge +-, conservation of charge

CHARGE is a property of matter
Why is mass so important?

Fe Fg
cause: Q:m
effect: Q:m
Force Law: Fα1/^2:Fα1/r^2
Direction of force

Attraction / Repulsion
– Opposite charges attract
– Like charges repel

Coulomb
Electricity is really strong

proton
1.6 = 10^-19C
neutron = 0
electron
-1.6 * 10^-19C

Making Graphs!

X(t) = XmaxSin(ωt + π/2)

Adjusting the Period
Fs = -Kx
F = ma
ma = -Kx, a = -k/m * x

K = 50 n/m
T = 1sec
m = 1.27Kg

The simple pendulum
SHM: a = -?x
F = ma
-mg*sinΘ = ma

Gmean = 1.6m/s^2
ge = 9.8 m/s^2
Te = Tm
Lm = lm/le Le
= 1.6/9.8 Le

Where am I?!

1) Latitude
2) Longitude

Latitude is easy to exactly find out.
Calculating latitude, tropic of cancer and equator
α is exact same degree of sun shadow

Longitude is completely arbitrary

How to keep the time?
-Need Periodicity

We need chronometer
-periodic, isochronous, predictable

Equilibrium
c = 2πr
2πradians = 360°

cos(3π/4)=-0.707
Sin(3π/4)=0.707

Angular Velocity w
ΔΘ=ωt

A Humbling Moment

All objects are mutually attracted
– Accelerate at 10m/s^2

The Train… of Pysics!
What trajectory would the apple follow?

In physics motion at constant speed is indistinguishable from being at rest!

F:10N
time:4.47sec
acceleration:1 m/s^2

Δx=v0t+1/2at^2
10m = 0 + 1/2a(4.47)^2

N = Normal(perpendicular)
FN mg=weight, mg is equal to FN

Forces and trig
if α=30°、Fr=100N sin(30degree)*100
FRX = 50N, Fry = 86.6N cos(30degree)*100

m = 10Kg
mg = 100N
Fry = 50N
Fn = 150N
Frx = 86.6N
Fw = 86.6N

Components of Motion

2-D motion can be solved as two
1-D motion problems

Δx = V0t + 1/2αt^2
V = V0 + at
V^2 = V0^2 + 2αΔx

Δox = 10m/s
α- 10m/s^2

Dimensional Analysis
E = mc^2, E = M*L*T

Experiment, Evidence Rules, Motion Equation
1D/ 2D ΔX = v0t + 1/2at^2

Explain the cause of motion
Understand “rest”

the motions of stars and apples have in different, but governed by same laws