Conservation of mechanical energy

E_k+E_p=\text{const}

Result unit: J (joule)

What it describes

In a frictionless system the sum of kinetic and potential energy stays constant.

E_k

kinetic energy

[J]

E_p

potential energy

[J]

In a frictionless system mechanical energy is not lost — it converts between kinetic and potential. As a body falls it loses

E_p

and gains

E_k

at the same rate.

Motion without resistance (free fall, pendulum, frictionless incline). With friction, part of the energy turns into heat.

A body falls freely from a height of 5 m. Find its speed just above the ground (

g=10

Substitution

mgh=\tfrac12 mv^2\Rightarrow v=\sqrt{2gh}

Result

v=\sqrt{2\cdot10\cdot5}=10

m/s.

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