Mechanics
Conservation of Mechanical Energy
Total mechanical energy is conserved in absence of non-conservative forces.
Variables
KE₁J
Initial kinetic energy
KE at position 1
In SI units: kg·m²/s²
PE₁J
Initial potential energy
PE at position 1
In SI units: kg·m²/s²
KE₂J
Final kinetic energy
KE at position 2
In SI units: kg·m²/s²
PE₂J
Final potential energy
PE at position 2
In SI units: kg·m²/s²
Derivation
When only conservative forces act, E_total = KE + PE = constant.
Your notes
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Where this formula is listed
- Mechanics formulas, under Work & Energy, alongside Work, Spring Potential Energy, Power and Work-Energy Theorem.
- In the mechanics list it comes after Work-Energy Theorem and before Momentum.
- Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Conservation of Mechanical Energy formula?
Conservation of Mechanical Energy is written KE₁ + PE₁ = KE₂ + PE₂. Total mechanical energy is conserved in absence of non-conservative forces. It belongs to Mechanics, under Work & Energy.
What are the units in KE₁ + PE₁ = KE₂ + PE₂?
In SI units, KE₁ is initial kinetic energy, measured in kg·m²/s²; PE₁ is initial potential energy, measured in kg·m²/s²; KE₂ is final kinetic energy, measured in kg·m²/s²; PE₂ is final potential energy, measured in kg·m²/s².
How is the Conservation of Mechanical Energy formula derived?
When only conservative forces act, E_total = KE + PE = constant. The result is KE₁ + PE₁ = KE₂ + PE₂.