Mechanical Energy
The mechanical energy of a body is the sum of its kinetic and potential energies:
E_mec = E_c + E_p
Kinetic Energy
E_c = ½ · m · v²
Energy associated with motion. It depends on the square of the velocity.
Gravitational Potential Energy
E_pg = m · g · h
Energy stored because of height in a gravitational field.
Elastic Potential Energy
E_pe = ½ · k · x²
Energy stored in a compressed or stretched spring. k is the spring constant and x the deformation.
Principle of Conservation
In the absence of non-conservative forces (friction, air resistance):
E_mech initial = E_mech final
In a free fall, all E_pg becomes E_c. In a compressed spring, all E_pe becomes E_c when released.
Work done by a force
W = F · d · cos θ
When a net force acts, it does work that changes the kinetic energy of the body (Work-Energy Theorem).