Energy conservation is the principle that energy is not created or destroyed in an isolated system; it can only change form or be transferred. In mechanics, we often focus on mechanical energy (kinetic + potential), which is conserved when only conservative forces act.
Mechanical energy
Define
E_mech = K + U
If all forces are conservative (no friction/drag), then
ΔE_mech = 0
and energy simply swaps between K and U.
Conservative forces and potential energy
For a conservative force, work depends only on endpoints and can be written in terms of potential energy:
W_conservative = -ΔU
This yields the familiar relation
ΔK + ΔU = 0
Nonconservative forces (friction, drag)
When nonconservative forces are present, mechanical energy can change. A useful bookkeeping form is:
ΔE_mech = W_nonconservative
A decrease in mechanical energy does not violate energy conservation: the "missing" energy typically becomes internal energy (heat), sound, permanent deformation, etc. If you include those forms, total energy is still conserved.
Power (rate of energy transfer)
Energy transfer per time is power:
P = dW/dt = F · v
dE/dt = P
Choice of zero for potential energy
The absolute value of U depends on a reference level; only differences ΔU matter physically. Changing the zero of U does not change the equations of motion.
Common pitfalls
- "Energy conservation" does not mean kinetic energy is always constant; it means total energy accounting is consistent.
- Mechanical energy is conserved only under appropriate conditions (typically no friction/drag).