Written by Jerry Ratzlaff on . Posted in Classical Mechanics

energy bannerEnergy is never created or destroyed First Law of Thermodynamics, but it can be transferred from one object to another.  It also comes in many different forms (kinetic, potential, thermal, chemical, electrodynamic and nuclear) and can be converted from any one of these forms into any other, and vice versa.  Energy can be converted from one form to another in three basic ways: through the action of forces (gravitational forces, electric and magnetic force fields, frictional forces), when atoms absorb or emit photons of light and when nuclear reaction occurs.

Typical units for mechanical energy is foot-pounds and joules, english energy is British thermal unit. \(\;Btu = \frac {ft-lbf}{J}\)

Energy formula

\(\large{ E = m   U }\)         

\(\large{ E = F l =  \frac {ml^2}{t^2}  }\)          


\(\large{ E }\) = energy

\(\large{ m }\) = mass

\(\large{ U }\) = internal energy

\(\large{ F }\) = force

\(\large{ l }\) = length

\(\large{ t }\) = time

Elastic Potential Energy

Elastic potential energy is the energy stored in objects as the result of deformation, such as a spring when stretching or compressing.

Elastic Potential Energy formula

\(\large{ PE = \frac {1}{2} kx^2 }\)         


\(\large{ PE }\) or \(\large{ E_p }\) = elastic potential energy

\(\large{ k }\) = spring constant

\(\large{ x }\) = length or displacement

Electric Potential Energy

Electric potential energy known as voltage, is when two opposite charges are held apart.

Electric Potential Energy formula

\(\large{ V = \frac {W}{C} }\)         


\(\large{ V }\) = voltage or electric potential energy

\(\large{ W }\) = work

\(\large{ C }\) = charge

Heat Energy

Heat energy (also called thermal energy) is the exertion of power that is created by heat, or the increase in temperature by the transfer of particles bouncing into each other by means of kinetic energy.  Here are a few examples of heat energy: fire, geothermal, lightening, oven, steam, the sun, etc.

Internal Energy

Internal energy is the total of all energies associated with the motion of the molecules in the system.

Internal Energy FORMULA

\(\large{ U =  \frac {3} {2}  n R T_a }\)          


\(\large{ U }\) = internal energy

\(\large{ R }\) = ideal gas constant

\(\large{ T_a }\) = absolute temperature

\(\large{ n }\) = moles

Kinetic Energy

Kinetic energy is the energy in moving objects or mass.  If it moves, it has kinetic energy.

Kinetic Energy formula

\(\large{ KE = \frac {1}{2} m v^2 }\)         

\(\large{ KE = \frac {P^2}{2m}   }\)         


\(\large{ KE }\) = kinetic energy

\(\large{ m }\) = mass

\(\large{ v }\) = velocity

\(\large{ P }\) = power

Solve for:

\(\large{ m = \frac {2   KE}{v^2} }\)

\(\large{ v = \sqrt {   \frac {2   KE}{m} }  }\)

Mechanical Energy

Mechanical energy is the sum of kinetic energy and potential energy generating from the force of gravity or the movement released in machine movement.

Mechanical Energy Formula

\(\large{ ME =  PE + KE }\)         


\(\large{ ME }\) = mechanical energy

\(\large{ PE }\) = potential energy

\(\large{ KE }\) = kinetic energy

Potential Energy

Potential energy (Gravitational Potential Energy) is the possessed energy by a body due to its relative position in a gravitational field. As the elevation of the body decreases the less potential energy.

Potential Energy formula

\(\large{ PE = m g  h }\)         


\(\large{ PE }\) or \(\large{ E_p }\) = potential energy

\(\large{ m }\) = mass

\(\large{ g }\) = gravity

\(\large{ h }\) = height

Solve for:

\(\large{ m = \frac {PE} {g   h}  }\)

\(\large{ g = \frac {PE} {m     h}  }\)

\(\large{ h = \frac {PE} {m   g}  }\)

Rest Energy

Rest mass ( \(m_0\) ) of a particle is the mass of a partical that is measured at rest with respect to the observer.

Rest Energy Formula

\(\large{ E_{rest \; mass} = m_0 c^2 }\)         


\(\large{ E_{rest \; mass} }\) = energy rest mass

\(\large{ m_0 }\) = rest mass

\(\large{ c }\)  = speed of light

Rotational Kinetic Energy

Rotational Kinetic Energy formula

\(\large{ KE_r = \frac {1}{2} I \omega^2 }\)         


\(\large{ KE_r }\) = rotational kinetic energy

\(\large{ I }\) = moment of inertia

\(\large{ \omega }\)  (Greek symbol omega) = angular velocity

Spring Energy

Spring energy is the energy stored in elastic materials as the result of their stretching or compressing.

Spring Energy formula

\(\large{ E_s = \frac {1}{2}     k_s   d_{s} {^2}   }\)         


\(\large{ E_s }\) = spring energy

\(\large{ k_s }\) = spring constant

\(\large{ d_s }\) = spring displacement

Thermal Energy

Thermal energy (also called heat energy and heat transfer) is the exertion of power that is created by heat, or the increase in temperature.

Thermal Energy Formula

\(\large{ Q = mc \Delta T }\)         


\(\large{ Q }\) or \(\large{ TE }\) = thermal energy

\(\large{ m }\) = mass

\(\large{ c }\) = specific heat

\(\large{ \Delta T }\) = temperature differential

Solve for:

\(\large{ c = \frac {Q }   {m   \Delta T}  }\)

\(\large{ \Delta T = \frac {Q}{mc}  }\)

Work Energy

Energy is never created or destroyed but external work performed on a conservative system goes into changing the system's total energy.

Work Energy formula

\(\large{ W=\Delta E = E_2 \;-\; E_1 }\)         


\(\large{ W }\) = work

\(\large{ \Delta E }\) = energy differential

\(\large{ E }\) = energy


Tags: Equations for Energy