Statement: If only conservative forces do work on a system, the total mechanical energy is conserved:

$KE_1$ + $PE_1$ = $KE_2$ + $PE_2$

Or equivalently: $delta_{KE}$ + $delta_{PE}$ = 0

Conditions for validity:

1. Only conservative forces (gravity, spring) do work, OR
2. Work by non-conservative forces is zero (e.g., normal force)

When non-conservative forces act: $W_{non-conservative}$ = $delta_{KE}$ + $delta_{PE}$ = delta_E_{mechanical} This means friction etc. cause a change in mechanical energy (usually a decrease, converted to heat).

Problem-solving approach:

1. Identify initial and final states
2. Choose a reference level for PE
3. Calculate KE and PE at both states
4. If only conservative forces: $KE_1$ + $PE_1$ = $KE_2$ + $PE_2$
5. If friction acts: $KE_1$ + $PE_1$ - f*d = $KE_2$ + $PE_2$