Lecture 5 Emc2

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Lecture 5 Emc2
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Listen to Einstein explain this formula
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History of Energy
18th and 19th century chemists and
physicists were rather confused by the concept of
energy
Louis Bernard Guyton de Morveau (1737-1816)
thought the increase in weight of heated metals
was due to the replacement of phlogiston by
heavier air
Georg Ernst Stahl (1659-1734) developed the
phlogiston theory of combustion, now known to be
wrong
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Phlogiston

• Combustible materials made up of two
  partsphlogiston and ash
• When burned, phlogiston is released into theair,
  leaving ash behind
• Phlogisticated air can no longer sustain
  combustion

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Problems with Phlogiston

• When some materials such as tin or lead are
  burned,the resulting ash weighs more than the
  original material
• But today we know that combustion is due to
  oxidation
• Oxygen combines with the material to cause an
  increase in mass

Priestly discovered oxygen in 1774, but did not
believe in oxidation theory. Instead, he called
it dephlogisticated air.
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Explanations for Other Phenomena

• Electricity was the flow of two fluids called
  vitreous and resinous
• Magnetism was the flow of two other fluids
  called austral and boreal
• Heat was the flow of a single fluid called
  caloric

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Caloric

• Hotter bodies contain more caloric than colder
  ones
• Heating a body involves caloric flowing to it
  from elsewhere

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Joules Experiment

• Showed the equivalence of heat and mechanical
  energy
• The falling weights rotate the paddles, causing
  the temperature of the water to rise

James Prescott Joule (1818-1889)
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Principle of Energy Conservation
The different forms of energy -
chemical, - electrical, -
magnetic, - mechanical, - heat,
etc., can be transformed into each other, but
the total amount of energy always remains the
same
Julius Robert von Mayer (1814-1878) was the first
to realise a relation between mechanical work and
heat energy
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Conservation of mass (matter)
Atoms can neither be created nor destroyed
John Dalton (1766-1844) performed experiments
that verified the postulate for the conservation
of mass
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Einsteins equation E mc2combines
the principles of energy and mass conservation
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Concept of Mass

• The mass of an object measures its resistance to
  motion
• But if the object is already moving, then its
  mass measures how difficult it is to stop
• In this case, the stopping power required is
  better described by

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Momentum
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Conservation of momentum
pinitial pfinal
When two objects collide, the total
momentum remains unchanged
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Thought experiment to show mass increase
Case (a) Train is at rest Two persons throw
balls to each other in such a way that they
collide and return to the persons.
Case (b) Train moving at relativistic speed The
two persons throw the balls in such a way that
the balls would still collide and return to the
persons.
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Thought Experiment (contd)

• According to the person on the ground, his
  companions ball is moving more slowly because of
  time dilation
• But momentum must be conserved, so he would think
  the balls mass has increased

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Mass increases for moving objects
m gm0
where m0 is the mass of the object when it is
at rest. m0 is known as the rest mass and m is
the relativistic mass.
Note When an object approaches the speed of
light, its mass becomes larger and larger.
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Imagine watching Luke zooming past at 0.99c

• He wants to go faster, so he adds more power to
  the engines of his X-wing
• His speed will go up slightly, but his mass will
  go up drastically
• With more mass, more power is needed to increase
  his speed further, and so on

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Conclusion

• Luke would need an infinite amount of power to
  reach the speed of light
• In other words, it is impossible to accelerate a
  massive object up to the speed of light

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So how can a photon travel at the speed of light?

• A photon has no rest mass m0 0
• Because it is impossible to find a photon at
  rest
• So the above arguments are not valid
  m 0/0 can be anything

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In the formula Emc2
It is the relativistic mass which appears
E mc2 ?m0c2
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Implications

• An object at rest has energy Em0c2, the
  so-called rest mass energy
• This is a new prediction of relativity
• The faster an object moves, the more mass, and
  therefore energy, it has

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Kinetic Energy

• The difference between the total energy of an
  object and its rest mass energy is the kinetic
  energy
• By the binomial theorem, this formula reduces to
  the usual Newtonian one for small speeds
• But there are significant deviations at
  relativistic speeds

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Further implications of mass-energy equivalence

• A ball in motion has more mass than one at rest
• A hot gold sphere has more mass than a cold one
• So conservation of mass is not true, although
  this change of mass is very minute (since c is so
  large)