Calculate energy transformations in mechanical systems using the principle of conservation of energy
This calculator helps you analyze energy conservation in mechanical systems, including potential energy, kinetic energy, and mechanical energy transformations.
The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In mechanical systems, the total mechanical energy (sum of potential and kinetic energy) remains constant in the absence of non-conservative forces like friction.
In an isolated system with no non-conservative forces:
Einitial = Efinal
PEinitial + KEinitial = PEfinal + KEfinal
When an object falls from a height, its potential energy is converted to kinetic energy. At any point during the fall:
mghinitial + ½mvinitial² = mghfinal + ½mvfinal²
In a spring-mass system, energy oscillates between elastic potential energy and kinetic energy:
½kxinitial² + ½mvinitial² = ½kxfinal² + ½mvfinal²
In a pendulum, energy transforms between gravitational potential energy and kinetic energy:
mghinitial + ½mvinitial² = mghfinal + ½mvfinal²
where h = L(1-cos θ) for a pendulum of length L at angle θ.
A roller coaster is a perfect example of energy conservation, where gravitational potential energy at the top is converted to kinetic energy as the coaster descends.
In real-world systems, some mechanical energy is converted to heat due to friction and other non-conservative forces. The efficiency of energy transfer is:
Efficiency = (Efinal / Einitial) × 100%
This conservation of energy calculator helps you: