Conservation of Mechanical Energy
Principle stating that total mechanical energy (kinetic + potential) remains constant in the presence of only conservative forces.
What is Conservation of Mechanical Energy?
Sum of kinetic and potential energy, E = K + U, in joules
Key formula / rule: Conservation
Key points
- State when mechanical energy is conserved and solve height-and-speed problems with K + U = constant
Common exam trap
Applying energy conservation on rough surfaces
Definitions
- Name
Mechanical energy
- Definition
Sum of kinetic and potential energy, E = K + U, in joules
- Name
Conservation law
- Definition
When only conservative forces do work, K1 + U1 = K2 + U2; friction and air resistance are non-conservative and dissipate energy as heat
- Name
Exam insight
- Definition
For free fall or a smooth slide, v = √(2gh) whatever the mass or the shape of the path
- Name
Worked example
- Definition
Ball released from 20 m reaches √(2 x 9.8 x 20) ~ 19.8 m/s; losing 20 percent of the energy to friction gives about 17.7 m/s
Learning objectives
State when mechanical energy is conserved and solve height-and-speed problems with K + U = constant
Formulae
- Name
Conservation
- Expression
K1 + U1 = K2 + U2; U = m g h near the earth
- Name
With dissipation
- Expression
DeltaK + DeltaU = Wnonconservative
Common mistakes
Applying energy conservation on rough surfaces
Using different reference levels for potential energy at the two states
Keywords
mechanical energy
conservation
conservative force
potential energy
kinetic energy
friction