# Is mechanical energy always conserved? Why or why not?

Dec 30, 2016

Mechanical energy is not always conserved.

#### Explanation:

Mechanical energy is the sum of kinetic and potential energy in a system.

${E}_{m e c h} = K + U$

Mechanical energy is conserved so long as we ignore air resistance, friction, etc. When we don't ignore outside forces, such as those just mentioned, mechanical energy is not conserved.

If you apply a force to an object, e.g. a push, which causes it to slide across the floor, you expect it to come to rest, even if no visible force acts on it, e.g. it collides with another object. What slows it down and ultimately brings it to rest? Friction. If there was no frictional force between the object and the floor and air resistance wasn't a factor, the object would never decelerate as it moved across the floor, and would travel on forever at a constant velocity in that direction until stopped by an outside force (Newton's First Law). When you push the object, the object gains kinetic energy and begins to move across the floor, but eventually it stops. Where did the kinetic energy go?

Energy is "lost" to friction in the sense that it is not converted between potential and kinetic energy but rather into heat energy, which we cannot put back into the object. If we expand our system to include the entire universe, total energy is conserved, but mechanical energy is not. When the object comes to rest and all of its energy has been lost to friction, ${E}_{m e c h} = 0$.

${E}_{s y s t e m} = {E}_{m e c h} + {E}_{t h e r m a l} = K + U + {E}_{t h}$

Note that the above example assumes the floor is level and horizontal so that there is no change in gravitational potential energy.