Work and Energy
– Work = Force  Distance
– Work increases the energy of an object.
– Energy can be converted back to work.
– Therefore, energy and work have the same unit:
Newton  meter = Nm
Ch. 6
Energy per gram,
compared to TNT
Chocolate chip cookies and
gasoline contain more energy
per gram than explosives.
Explosives have the oxidizer
built in for rapid release of
energy, adding weight. Fuel
takes oxygen from the air.
That’s why burning airplane
fuel brought the World Trade
Center towers down, not the
impact of the airplanes.
Richard Muller, Physics
and Technology for
Future Presidents
Various Types of Energy
Gravitational energy from lifting a TV:
Energy = Work = Force  Height
(here gravitational force)
The work is the same no matter which
path is taken (no horizontal force).
Dropping the TV from the top converts
gravitational energy to kinetic energy.
When the TV set hits the ground, kinetic
energy is converted to thermal energy,
which is kinetic energy of oscillating
atoms.
Energy comes in many forms:
That leads to many energy units:
N m = kg m2/s2 = J = W s
kg m2/s2 originates from the definition
of the force unit N via Newton’s law
Kinetic
Gravitational
Electric
Thermal
Solar
Chemical
Nuclear …
F = m a . A Newton is the force that
accelerates 1kg by 1m/s2 .
Joule (J) comes from thermal energy,
Watt-second (Ws) from electric energy.
Furthermore: kiloWatt-hours (kWh), electron-Volt (eV), …
Conversion at: http://www.physics.nist.gov/cuu/Constants/energy.html
Kinetic Energy (Energy of Motion)
• A force leads to an acceleration (F = m a).
• The acceleration leads to a velocity.
• Therefore, the kinetic energy is related to the velocity.
Kinetic Energy Formula
Kinetic energy of an object with mass m :
1 22
Ekin = mvv
2
v = velocity
Since the kinetic energy increases with the square of the
velocity, high speed accidents are much more dangerous.
This is particularly true for head-on collisions where the
velocity difference is large.
Gravitational energy
• It takes work to lift an object against the force of gravity.
• The resulting gravitational energy is stored in the object.
• Gravitational energy E = F  h
(F = force = m  g ; h = height difference)
• Far from Earth the force F decreases like 1/d2 , and the
energy E like 1/d (d=distance from the center of the Earth):
F=G
m1  m2
d2
E= G
m1  m2
d
Electric Force and Energy
• Charged particles interact by an electric force Fel
which is analogous to the gravitational force.
• The electric force is proportional to the product of
two charges q1  q2 (instead of two masses m1  m2 ).
• The signs are opposite, because equal charges repel
each other, while equal masses attract each other.
Fel = Gel 
q1  q2
d2
Eel = Gel 
q1  q2
d
Thermal Energy = Heat
• This is the kinetic energy of the thermal motion of atoms.
• The thermal energy is proportional to the absolute
temperature T (measured in degrees Kelvin = K).
• Thermal energy is of “lower grade” than other energies,
because thermal motion is disordered (random). Atoms
move around unpredictably in all directions.
• Thermal energy cannot be converted fully into other forms
of energy, because it is impossible to force the atoms to
move all in the same direction (e.g. for moving a car).
Energy Conversion
• Energy can neither be created nor destroyed.
• It only can change from one form to another.
• Or it can be moved from one place to another.
• Sometimes we say that energy is lost, for example
when driving a gas-guzzling car. It is not really lost,
but converted into thermal energy that heats up the
engine and the exhaust gases.
First Law of Thermodynamics
The sum of all forms of energy is conserved.
Conservation Laws and Symmetries
Not only the energy is conserved, but also the momentum.
momentum = mass  velocity
p = mv
• Energy conservation follows from translation symmetry in time.
(Experiments done yesterday and today give the same result.)
• Momentum conservation is tied to translation symmetry in space.
(Experiments done in New York and Paris give the same result.)
(Compare particles versus waves in quantum physics: Lect. 21, Slide 11)
Power
Power =
Energy
Joules (J)
Time
second (s)
= Watts (W)
(1 Horsepower = 750 Watts)
Power versus Energy
– Distinguish power from energy:
– A power plant produces power (GigaWatts).
– A light bulb uses power (100 Watt).
– The power company charges us for energy (kWh),
since it has to pay for fuel to produce energy.
Pricing of Fossil vs. Solar Energy
– While we pay the power company in $ per kW h ,
solar electricity is priced in $ per kW.
– It takes energy to make solar cells, but after that
there is no further cost for fuel. Sunlight is free.
– To compare the cost of solar and conventional
energy, one has to multiply the cost per kW by
the lifetime of solar cells (20-30 years).
– The energy payback time is the time that it takes
for a solar cell to generate the energy used for its
manufacture (about 1- 4 years). It is independent
of price fluctuations (oil price, inflation, etc.) .