Energy

1
Energy

• Physics 1010
• Dr. Don Franceschetti
• February 13, 2006

2
Guide Questions about Energy

• What is energy? Can you see it? Touch it? Feel
  it?
• If not, then why is it so important?
• How many different forms does it take?
• What am I buying at the gas pump? the
  supermarket? with my MLGW money?
• If its conserved, why do I have to pay so much
  for it?

3
Hewitt says

• The combination of matter and energy makes up the
  universe. Matter is substance and energy is the
  mover of substance. (Pause to reconsider
  Newtons first law)
• The idea of matter is easy to grasp. Matter is
  stuff that we can see Energy is abstract

4
Work

• Work force times distance
• WF// d
• Measured in
• Joules Nm kg m2 / s2
• Hes not doing work!

5
Sometimes work can be recovered

• To lift a rock of mass m by a distance h, you
  must exert at least a force equal to its weight
  (mg). So the work you do is at least mgh.
• If the rock falls a distance h, the work done by
  the force of gravity is mgh. So in a sense you
  can get the work back.

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The work done by gravity on the falling rock

• h(1/2)gt2 (falling from height h to height 0)
• vgt
• Work mgh (1/2)mg2t2 (1/2)mv2
• We call this last quantity the kinetic energy of
  the falling rock and we have
• Work stored in rock returned as kinetic energy

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Potential Energy

• We call the work stored in the rock its potential
  energy. Not that PE is determined by position.
• We call any force, like gravity, for which we can
  get work done against the force back, a
  conservative force.

8
Converting P. E. to K. E.

• Mass on Spring (Hooke)
• Pendulum (Galileo)
• Diver
• Elastic Collisions

9
Timekeeping devices

• Depend on cycle
• Potential-kinetic-potential
• Usually are isochronous (period independent of
  amplitude)
• Essential to determine longitude

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If the force is not conservative where does the
energy go?

• Heat
• Non-conservative forces
• Friction
• Air resistance
• Water resistance
• Heat is just kinetic energy on the atomic scale

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Work Energy Theorem

• Work done by net force DKE
• Compare Impulse-Momentum theorem
• Impulse D(mv)

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Conservation of Energy

• Energy cannot be created or destroyed it may be
  converted from one form to another, but the total
  amount of energy never changes.
• But (thermodynamics) It is impossible to convert
  heat energy back into other forms 100

13
Power

• Power Work / time interval
• Measured in Watts
• WattJoule/s
• Electrical Power is sold in
• kWh3,600,000 J
• Horsepower 746 W (a very strong horse)

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Historical note

• The steam engine was the first device to make
  motional energy out of heat energy.
• Energy became portable.
• James Watt greatly improved an earlier design.
• Steam engine lead to internal combustion engine.
• Always heat exhaust.

15
The Guys

• James Watt (1796-1819)
• Self-taught machinist
• Improved Steam Engine
• Worked at U of Glasgow
• "The best heritage to which a man can be born is
  poverty." (Garfield, quoted by Carnegie)

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The Guys

• James Prescott Joule (1819-1889)
• Family owned a brewery
• Established mechanical equivalent of heat
• Died broke
• Great tomb in Westminster Abbey

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Conservation of Energy Has a Weird History

• Dr. Julius Mayer
• As a ships surgeon noticed that the blood of
  sailors in the tropics was brighter in color that
  that of sailors in Northern Latitudes
• Proposes Conservation of Energy in 1842

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Energy the central idea in physics

• Kinetic and Potential Energy
• Heat is a form of energy
• 1 calorie 4.184 J
• Energy content of food measured in Calories4,184
  J
• Light is a form of electromagnetic energy
• Einstein mass is a form of energy
• E mc2
• 1 kg completely converted to energy is
  90,000,000,000,000,000 Joules or 25,000,000,000kWh

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Mass is converted to other forms of energy

• In chemical reactions too small an amount to
  notice
• In nuclear fission
• U ? Ba Kr neutronsenergy
• (energy is KE of particles and electromagnetic
  radiation)
• In nuclear fusion
• 4H ?He 2 positrons neutrinos energy
• In matter-antimatter annihilation
• electron positron ? energy

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Optional History lesson

• Whenever an exception is found to a law that
  physicists really like, they redefine the terms
  to keep the law, if possible.
• So we generalize from KE to PE to heat energy to
  mass energy and

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Lord Kelvin and the Age of the Earth

• 19th century geology Earth is millions of years
  old
• Darwin Earth is millions of years old
• Kelvin Sun is a body undergoing gravitational
  collapse. Release of gravitational energy by sun
  could last only a few thousand years
• We now know sun is powered by fusion and is about
  5 billion years old. It is middle aged as stars
  go.

22
Puzzle of Beta decay

• Some elements emit electrons by
• neutron ? proton electron with kinetic energy
• Kinetic Energy didnt add up.
• Fermi predicts neutrino to conserve energy
  discovered thirty years later

23
Feynmanns theory of the antiparticles (for
geniuses only)

• time

Gamma ray
electron
Electron
Anti Electron
Gamma ray
24
Impulse-Momentum and Work Energy theorems

• Newtons first law tells us that when the net
  force on an object is zero, its velocity does not
  change.

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And when the net force is not zero

• The impulse of the net force equals the change in
  momentum
• Ft change in mv
• The work done by the net force equals the change
  in kinetic energy
• F//d change in (1/2) mv2

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Consider a 1000 kg car traveling at 10 m/s that
comes to a stop due to a breaking force of 2,000N

• What impulse must have been provided?
• Change in mv is
• 10,000 kg m/s or 10,000 N s
• How much work must have been done?
• Change in (1/2)mv2 is
• 50,000 kg m2/s2 or 50,000 Joules

27
Consider a 1000 kg car traveling at 10 m/s that
comes to a stop due to a breaking force of 2,000N

• How long did the car take to stop?
• 2,000N t 10,000 N s
• t 5 s
• How far did it travel?
• 2,000N d 50,000 Nm
• d 25 m

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Suppose the car is going twice as fast

• How long did the car take to stop?
• 2,000N t 20,000 N s
• t 10 s twice as long
• How far did it travel?
• 2,000N d 200,000 Nm
• d 100 m four times as far!

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Machines

• Are devices that change the size or direction of
  force
• Work in work out
• Lever fDFd
• Pulleys fDfd

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Efficiency

• Actually you lose a little work
• Efficiency Useful Energy Output
• Total Energy Input