Work, kinetic energy, potential energy

[Bengo]

Can anyone help me understand this equation: Work = ΔK + ΔU + ΔE (no heat). Where K is kinetic energy, U is potential energy, and E is internal energy.

This is for nonconservative forces only right? I'm just confused about what if some potential energy is converted into kinetic energy, wouldn't that mean we are counting this amount of energy twice?

Does non conservative forces mean energy leaves the system?

Thanks.

 

[haruspex]

ΔK etc. have signs. If some potential energy is converted into equal kinetic energy then the two Δ terms will have opposite signs and equal magnitude, so will cancel.

 

[CWatters]

Work = ΔK + ΔU + ΔE is the equation for the energy gained or lost by a system. It's the sum of all the possible ways to change the energy stored in the system.

Within the system it's possible to convert energy from one form to another but as harupex says the sign will be different so overall the work is constant. eg Man falling off a cliff ΔU is negative, ΔK is positive. No net change in work.

Energy is allways conserved. As wikipedia says..

http://en.wikipedia.org/wiki/Conservative_force

"Nonconservative forces can only arise in classical physics due to neglected degrees of freedom".

In other words the man doesn't hit the ground as fast as expected because you forgot or ignored air resistance. In that case the ΔU and ΔK don't exactly balance. In this case energy has been lost by the system (to the air) but overall energy is still conserved.