State the law of conservation of energy for conservative forces and explain how it is modified for non-conservative forces.

(N/A) $1$. For conservative forces: The law of conservation of mechanical energy states that if only conservative forces (like gravitational or electrostatic forces) act on a system,the total mechanical energy $(E = K + U)$ remains constant. Mathematically,$\Delta E = \Delta K + \Delta U = 0$,which implies $E_{initial} = E_{final}$.
$2$. For non-conservative forces: When non-conservative forces (like friction or air resistance) act on a system,the total mechanical energy is not conserved. Instead,the work done by non-conservative forces $(W_{nc})$ is equal to the change in total mechanical energy: $W_{nc} = \Delta E = (K_f + U_f) - (K_i + U_i)$. This work is typically dissipated as thermal energy.