Conservation of Energy
Learning Objectives
- Students will understand energy conservation in mechanical systems
- Students will calculate energy transformations between potential and kinetic
- Students will apply conservation of energy to solve problems
Core Concepts
- Total mechanical energy: E = KE + PE
- In absence of non-conservative forces: E_initial = E_final
- Energy transforms but total is conserved
Formulas
$$E_{total} = KE + PE = \frac{1}{2}mv^2 + mgh$$
Total mechanical energy (constant if no friction)
$$E_i = E_f$$
Conservation of energy in isolated system
$$KE_i + PE_i = KE_f + PE_f$$
Energy conversion between kinetic and potential
Interesting Fact
Einstein showed matter and energy are related: E = mc²
Key Scientist
Hermann von Helmholtz
Formalized conservation of mechanical energy
Modern Research
Conservation laws in particle physics constrain possible interactions; energy conservation is enforced at every quantum interaction.
Want to truly master this? Try the interactive lesson!
Start Lesson