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8/13/2019 Physics 100 Chapt 19
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8/13/2019 Physics 100 Chapt 19
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Einsteins hypotheses:
1. The laws of nature are equally validin every inertial
reference frame.
2. The speed of light in empty space issame for all inertial
observers, regard-less of their velocity or the velocity ofthe
source of light.
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Summary (so far)
Moving clocks run slow
Moving objects appear shorter
Moving objects mass increases
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8/13/2019 Physics 100 Chapt 19
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GPS system
3 m precision requires corrections for relativity
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8/13/2019 Physics 100 Chapt 19
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What is the
significance ofthe increase
mass of a moving
object??
m=gm0increase in mass=mm0
increase in m=gm0-m0=(g-1)m0
Summer1905
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8/13/2019 Physics 100 Chapt 19
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Increase in m=(g-1)m0
11 v2/c2
v/c
g-1 =??
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8/13/2019 Physics 100 Chapt 19
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Mathematicians tell us:
11 v2/c2
v/c
= 1+ +other stuffv2
c2
11 v2/c2
1+v2
c2
The other stuffis pretty huge
near v=c
What abouthere?
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8/13/2019 Physics 100 Chapt 19
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Below v/c = 0.5, other stuffis not so large
1+v2
c2
v/c
11 v2/c2
0.5
11 v2/c2 = 1+ +other stuffv2c2At v=0.5c theother stuffis
about 10%
How aboutdown here?
l / h ff
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Below v/c = 0.1, other stuffis negligible
v=0.1c
1+v2
c2
11 v2/c2
11 v2/c2 = 1+ +other stuffv2c2
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8/13/2019 Physics 100 Chapt 19
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Below v/c = 0.1, g = 1+g1 =
v2
c2
v2c2
This covers all velocitiesever encountered by
mankind in 1905
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8/13/2019 Physics 100 Chapt 19
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Increase in mass = (g-1)m0for v
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8/13/2019 Physics 100 Chapt 19
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For v < 0.1c
m = m0 + increase in m
mc2= m0c2+ (increase in m)c2
mc2= m0c2+ kinetic energy
Multiply both sides by c2
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Einsteins hypothesis:
mc2= m0c2+ kinetic energy
holds for all velocities
(not only for v
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mc2= m0c2+ kinetic energy
This must also bea form of energy: rest mass
energy
This must be thetotal energy
E = mc2
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8/13/2019 Physics 100 Chapt 19
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Mass is a form of energy
E = mc2 The conversion factorfrom mass to energyis c2, a huge
number!Energy (Joules) = Mass (kg) x (3x108)2
=9x1016
E(Joules) = 90,000,000,000,000,000 x m(kg)
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Mass containsan enormousamount ofenergy
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Electric power usage on Oahu
Power =1,300 MegaWatts = 1,300 x 106Watts
Energy usage = Power x time
Power = 1.3 x 109J/s
Energy usage/yr=1.3x109J/s x (3.2 x 107s/yr)
=1.3 x 3.2 x 109+7J/yr
=4.2 x 1016J/yr
# of secs in 1 yr
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How much mass would be needed
to produce 4.2 x 1016 J ?
E = mc2 m =Ec2
m = 4.2x1016J
9x1016 m2/s2
m = kg
m = 0.47 kg
4.29
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Nuclear Power Plant
Converts about 1kg of mass
energy/yr
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Another nuclear power plant
Suns power output=4x1026Watts
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Sun converts mass to energy
Power = energy generated in one sec:
E1sec= 4x1026J =m1secC2
m1sec=E1secC2
= 4x1026J
9x1016m2/s2
m1sec= 4/9x1026-16
kg = 0.44x1010
kg
m1sec= 4.4x109 kgover 4 million tons
each second!!
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Another nuclear power plant
4.4x109kg energy / sec
