Important Forms of Energy

• Kinetic: active energy of a mass in motion
• E_k = ½mv²
• Gravitational Potential: energy stored by a mass due to its position within a gravitational field
• ΔE_p = mgΔh, where Δh is the change in height (m)
• Elastic Potential: energy stored by an object (often springs) that has been deformed
• ΔE_H = ½k(Δx)², where Δx is the extension/compression displacement
• Thermal: energy associated within molecular motion
• Chemical Potential: energy associated with chemical bonds
• Nuclear: energy stored within the atomic nucleus
• Electrical Potential: energy associated with a charge due to its position in an electric field

Work (W)

The amount of energy transferred when an external force moves an object over a distance, measured in joules (J)

• A force does work when it acts on an object, and transfers energy to it
• Calculated by multiplying the displacement of the object upon which the force acts, and the component of the force that is parallel to the object's displacement
• W = F⋅s⋅cos(θ), where F is the force (N), s is the displacement (m), and θ is the angle between the force and the displacement
• Work done is the area under a line/curve of a force vs displacement graph

Energy Conservation

• Conservation of Energy: energy cannot be created or destroyed, but only transferred from one form to another
• Isolated System: the sum of the useful and wasted energy outputs will equal the total energy input
• Sankey Diagrams: used to represent energy transfers
• Mechanical Energy: sum of the kinetic energy, gravitational potential energy, and elastic potential energy of an object, and is conserved in the absense of resistive and electromagnetic forces

Power and Efficiency

Power (P):

• The rate of work done over time, or rate of energy transfer, measured in watts (W): 1 W = 1 J⋅s^-1
• P = ΔW/Δt = F⋅v

Efficiency (η):

• The ratio of the useful energy output to the total energy input
• η = E_out/E_in = P_out/P_in
• Efficiency can also be expressed as a percentage: η% = E_out/E_in × 100% = P_out/P_in × 100%

Energy Density of Fuels

Fuel: a material that can be made to react with other substances in order to produce thermal energy or mechanical energy that can be used to do work.

Energy Density: the amount of energy in a fuel per unit volume, measured in joules per cubic meter

Energy Density of Certain Substances:

• Uranium: 10¹⁸ J⋅m^-3
• Coal: 10¹⁰ J⋅m^-3
• Wood: 10⁹ J⋅m^-3
• Natural Gas: 10⁸ J⋅m^-3