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