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Conservation of mechanical energy
Beginner
Kinetic plus potential stays constant when only conservative forces act.
K + U = constIf only conservative forces do work, K + U stays constant. Use ½mv₁² + mgh₁ = ½mv₂² + mgh₂ for quick speed calculations.
A roller coaster from rest at 40 m reaches 28 m/s at the ground, ignoring friction.
If friction acts, mechanical energy is not conserved.
In more detail
In a system with only conservative forces, the sum of kinetic and potential energy stays constant. This lets you link the speed at one point to the height at another.
Real-world uses
- A falling object's speed can be found from the height it falls through.
- Roller coasters are designed by exchanging potential and kinetic energy.
- A skier at the top of a slope has potential energy that becomes kinetic energy as they descend, with the sum kept roughly constant.
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Frequently asked questions
When does mechanical energy stay constant?
When only conservative forces do work, with no friction, air drag or other losses.
Can I use energy conservation in every problem?
Only where the energy analysis is valid. Include non-conservative work when it is present.
When is mechanical energy not conserved?
When non-conservative forces such as friction or air drag do work on the system.
Related topics in Work, Energy & Power
Force from potential energy · Potential energy curves · Equilibrium types · Energy conservation in free fall · Energy on a pendulum · Energy in spring-mass systems