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 = N m 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 m 2 /s 2 = J = W s kg m 2 /s 2 originates from the definition of the force unit N via Newton’s law F = m a. A Newton is the force that accelerates 1kg by 1m/s 2. Joule (J) comes from thermal energy, Watt-second (Ws) from electric energy. Furthermore: kiloWatt-hours (kWh), electron-Volt (eV), … Conversion at: Kinetic Gravitational Electric Thermal Solar Chemical Nuclear …

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 : v2v2 E kin =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/d 2, and the energy E like 1/d (d=distance from the center of the Earth): F = G  m 1  m 2 d 2 E = G  m 1  m 2 d

Electric Force and Energy Charged particles interact by an electric force F el which is analogous to the gravitational force. The electric force is proportional to the product of two charges q 1  q 2 (instead of two masses m 1  m 2 ). The signs are opposite, because equal charges repel each other, while equal masses attract each other. E el = G el  q 1  q 2 d F el = G el  q 1  q 2 d 2

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 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.) Not only the energy is conserved, but also the momentum. momentum = mass  velocity p = m  v (Compare particles versus waves in quantum physics: Lect. 21, Slide 11)

Power (1 Horsepower = 750 Watts) Power = = Watts (W) Energy Joules (J) Time second (s)

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.).