Physics
Conservation of Energy
In an isolated system with no friction, the total mechanical energy stays constant. Kinetic energy (½mv²) and potential energy (mgh for gravity, ½kx² for springs) can convert into each other, but their sum is fixed. This single principle solves a huge class of problems faster than kinematics would.
How to Approach Conservation of Energy
Pick two states
An initial state (where the object starts) and a final state (where you want to know something). Energy conservation links the two — no need to track every moment in between.
Write KE + PE at each state
Initial: ½m·v₁² + m·g·h₁ + ½k·x₁². Final: ½m·v₂² + m·g·h₂ + ½k·x₂². Set them equal: KE₁ + PE₁ = KE₂ + PE₂.
Solve for the unknown
Plug in known values, cancel m if it appears everywhere, isolate the unknown. Almost always faster than using kinematics with a, t, and equations of motion.
Frequently Asked Questions
When does conservation of energy not work?+
When friction, air resistance, or non-conservative forces remove energy from the system. Then energy isn't conserved — work-energy theorem (W_nc = ΔKE + ΔPE) is the more general tool.
Why is energy easier than kinematics?+
Energy doesn't depend on the path — only the initial and final states. Kinematics requires tracking acceleration over the full trajectory, which is harder for curved or constrained motion.
Does energy conservation include heat?+
Yes — total energy (mechanical + thermal + chemical + ...) is always conserved. 'Lost' energy from friction becomes heat. Mechanical conservation is the special case with no friction.
Related Topics
More step-by-step guides in Physics and adjacent subjects.
Stuck on a Conservation of Energy problem?
Snap a photo or type the question. ScanSolve walks you through every step — same as the worked examples above. 5 free solves per day, no card required.