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
- 01
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.
- 02
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.
- 03
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
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