Conservation of Energy
Energy cannot be created or destroyed, only transformed.
Formula
Variables
Example
KE and PE trade off
How it works
Conservation of energy means the total amount of energy in a closed system stays the same, even though it can change form, such as from motion to heat or from electrical to light energy. This works because physical processes do not make energy appear from nothing or vanish; they only move it between objects or convert it from one type to another. If no energy enters or leaves the system, the total energy remains constant.
When to use it
Use this when analyzing systems where energy changes form, such as falling objects, moving vehicles, springs, electrical circuits, and heating processes. It is especially useful when you want to compare the energy at the start and end of a situation without tracking every force in detail.
Worked example, step by step
A 2.0 kg ball starts from rest at the top of a hill 5.0 m high. Initial energy: E_total = PE + KE = mgh + 0 = (2.0)(9.8)(5.0) + 0 = 98 J At the bottom, assume all gravitational potential energy becomes kinetic energy. So E_total = KE = 98 J Use KE = 1/2 mv^2: 98 = 1/2 (2.0)v^2 98 = 1.0v^2 v^2 = 98 v = 9.9 m/s Final answer: the ball’s speed at the bottom is 9.9 m/s.
Common mistakes to avoid
- Forgetting that the formula applies to a closed system with no energy entering or leaving
- Assuming energy is lost instead of transformed into another form such as heat, sound, or light
- Mixing up total energy with one type of energy, such as only counting kinetic energy
Did You Know?
Energy is never created or destroyed, only transformed — a principle no experiment has ever violated.
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More in Physics Laws & Theorems
View allNewton's First Law (Inertia)
BasicAn object stays at rest or in uniform motion unless acted on by a net force.
Newton's Second Law
BasicNet force equals mass times acceleration (rate of change of momentum).
Newton's Third Law
BasicFor every action there is an equal and opposite reaction.
Conservation of Momentum
IntermediateTotal momentum of an isolated system stays constant.
Conservation of Energy
BasicEnergy cannot be created or destroyed, only transformed.
Archimedes' Principle
IntermediateBuoyant force equals the weight of fluid displaced.