Energy can be stored or transferred. Kinetic energy (KE) is due to motion; potential energies (PE) are due to position or configuration. Internal energy (thermodynamics) changes with heat and work. In conservative systems, total mechanical energy E = KE + PE is constant.
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| Energy form | Formula | Description / Units (SI) |
|---|---|---|
| Kinetic Energy (KE) | KE = ½ m v² | Energy due to motion. m = mass (kg), v = speed (m/s). Unit: joule (J). |
| Gravitational Potential Energy (PEg) | PEg = m g h | Energy due to position in a gravitational field. m = mass (kg), g = 9.8 m/s², h = height (m). Unit: joule (J). |
| Elastic Potential Energy (PEelastic) | PEelastic = ½ k x² | Energy stored in springs or deformed elastic objects. k = spring constant (N/m), x = displacement from equilibrium (m). Unit: joule (J). |
| Internal Energy (thermodynamics) | ΔU = Q − W | Change in internal energy = heat added to system (Q) − work done by system (W). First law of thermodynamics. Units: J. |
| Total Mechanical Energy (conserved if no non-conservative forces) | Etotal = KE + PE = constant | In isolated conservative systems (no friction, air resistance, etc.), total mechanical energy is constant. Unit: joule (J). |
About these energy formulas
These five expressions are among the most used in introductory physics and thermodynamics. Kinetic and potential energies are forms of mechanical energy; internal energy belongs to thermodynamics.
SI units
All energies are in joules (J): 1 J = 1 N⋅m = 1 kg⋅m²/s². Mass in kg, speed in m/s, height and displacement in m, spring constant in N/m.
Conservation of energy
When only conservative forces (e.g. gravity, ideal spring) act, E_total = KE + PE stays constant. Non-conservative forces (friction, drag) convert mechanical energy into heat, so E_total is not conserved.