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E=mc 2 Physics 100 Chapt 19

E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

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Page 1: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

E=mc2

Physics 100

Chapt 19

Page 2: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

Einstein’s hypotheses:

1. The laws of nature are equally valid in every inertial reference frame.

2. The speed of light in empty space is same for all inertial observers, regard- less of their velocity or the velocity of the source of light.

Page 3: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

Summary (so far)

•Moving clocks run slow

•Moving objects appear shorter

•Moving object’s mass increasesBy

a fa

ctor o

f

Page 4: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

GPS system

3 m precision requires corrections for relativity

Page 5: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

What is the significance of the increase

mass of a moving object??

m=m0

increase in mass = m – m0

increase in m=m0-m0=(-1)m0

Summer1905

Page 6: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

Increase in m = (-1)m0

11 – v2/c2

v/c

-1 =??

Page 7: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

Mathematicians tell us:

11 – v2/c2

v/c

= 1 + ½ + other stuff v2

c2

11 – v2/c2

1 + ½ v2

c2

The “other stuff”is pretty huge

near v=c

What about here?

Page 8: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

Below v/c = 0.5, “other stuff” is not so large

1 + ½ v2

c2

v/c

11 – v2/c2

0.5

11 – v2/c2

= 1 + ½ + other stuff v2

c2

At v=0.5c the “other stuff”is

about 10%

How aboutdown here?

Page 9: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

Below v/c = 0.1, “other stuff” is negligible

v=0.1c

1 + ½ v2

c2

11 – v2/c2

11 – v2/c2

= 1 + ½ + other stuff v2

c2

Page 10: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

Below v/c = 0.1, = 1+½

– 1 = ½

v2

c2

v2

c2

This covers all velocities

ever encountered bymankind in 1905

Page 11: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

Increase in mass = (-1)m0

for v<0.1c = -1 = ½

v2

c2increase in mass = ½ m0

(increase in mass)c2 = ½ m0 v2

v2

c2

Kinetic energy

Multiply both sides by c2

Page 12: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

For v < 0.1c

m = m0 + increase in m

mc2= m0c2 + (increase in m)c2

mc2= m0c2 + kinetic energy

Multiply both sides by c2

Page 13: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

Einstein’s hypothesis:

mc2= m0c2 + kinetic energy

holds for all velocities(not only for v<0.1c)

Kinetic energy = (m - m0)c2 = ½ m0v2 +

“otherstuff”

Since this is only significantfor huge speeds, Newton, etchad no way of knowing about it

Page 14: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

mc2= m0c2 + kinetic energy

This must also be a form of energy:

”rest mass

energy”

This must be the total energy

E = mc2

Page 15: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

Mass is a form of energy

E = mc2The 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)

Page 16: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

Mass contains an enormous amount of

energy

Page 17: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

Electric power usage on Oahu

Power =1,300 MegaWatts = 1,300 x 106 Watts

Energy usage = Power x time

Power = 1.3 x 109 J/s

Energy usage/yr =1.3x109 J/s x (3.2 x 107 s/yr)

=1.3 x 3.2 x 109+7 J/yr

=4.2 x 1016 J/yr

# of secs in 1 yr

Page 18: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

How much mass would be needed to produce 4.2 x 1016 J ?

E = mc2 m = E c2

m = 4.2x1016 J 9x1016 m2/s2

m = kg

m = 0.47 kg

4.29

About the mass

of an apple

Page 19: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

Nuclear Power Plant

Converts about 1kg of massenergy/yr

Page 20: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

Another nuclear power plantSun’s power output=4x1026Watts

Page 21: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

Sun converts mass to energy

Power = energy generated in one sec:

E1sec= 4x1026J = m1secC2

m1sec=E1sec

C2= 4x1026J

9x1016m2/s2

m1sec= 4/9x1026-16 kg = 0.44x1010 kg

m1sec= 4.4x109 kg over 4 million tons each second!!

Page 22: E=mc 2 Physics 100 Chapt 19. Einstein’s hypotheses: 1. The laws of nature are equally valid in every inertial reference frame. 2. The speed of light in

Another nuclear power plant4.4x109 kg energy / sec