Energy Conservation: The Single Idea That Solves Half of Physics
May 9, 2026 · 5 min · energy conservation · physics · kinetic energy
The first law of thermodynamics — energy is conserved — is the single most useful idea in physics. Half of mechanics problems and almost all of thermodynamics yield to it.
What it says
Energy is neither created nor destroyed. It only changes form.
Total energy at the start = total energy at the end + energy lost to heat / sound / friction.
The forms you'll see in school
- Kinetic energy: KE = ½ mv²
- Gravitational potential energy: GPE = mgh
- Elastic potential energy: EPE = ½ kx²
- Heat
- Sound
- Light
The setup
For most problems:
- Pick a starting state (point A) and a final state (point B)
- List all energy at A
- List all energy at B
- Set them equal
If energy is lost to friction or air resistance, add that as an extra term on the B side.
A worked example
A 2 kg ball is dropped from 5 m. What's its speed at the bottom?
At the top: GPE = 2 × 9.81 × 5 = 98.1 J. KE = 0.
At the bottom: GPE = 0. KE = ½ × 2 × v².
Setting them equal: 98.1 = v². So v ≈ 9.9 m/s.
When energy conservation is faster than F = ma
- When you don't need acceleration
- When forces vary and SUVAT doesn't apply
- For problems involving height changes, springs, or elastic collisions
When you have to be careful
- Inelastic collisions: kinetic energy is NOT conserved (some becomes heat / sound). Momentum is.
- Friction: energy is "lost" — really converted to heat. Account for it.
Common pitfalls
- Forgetting that GPE depends on the reference height
- Setting KE equal to GPE without checking the geometry
- Treating elastic and inelastic collisions the same