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When only conservative forces (gravity, spring) do work, the total mechanical energy E = KE + PE remains constant: KE_i + PE_i = KE_f + PE_f. Nonconservative forces like friction convert mechanical energy to thermal energy, so the conservation law must be modified: ΔKE + ΔPE = W_nc, where W_nc is the work done by nonconservative forces. Energy conservation is often the fastest route to finding speeds and heights in complex scenarios.
Identify initial and final states, then write the full energy equation including any nonconservative work. Practice roller-coaster and pendulum problems to build intuition for energy conversion between kinetic and potential forms.
The work-energy theorem you studied earlier tells you that the net work done on an object equals its change in kinetic energy. Conservation of energy takes this further by splitting forces into two categories: *conservative* forces (like gravity and springs) that store energy in a way that can be fully recovered, and *nonconservative* forces (like friction and air resistance) that convert mechanical energy into forms — heat, sound — that can't be recovered as motion.
When only conservative forces act, something remarkable happens: the sum of kinetic and potential energy stays constant throughout the motion. A ball thrown upward slows down, but the kinetic energy it loses is exactly stored as gravitational potential energy. When it falls back down, that stored energy returns as kinetic energy. At any point along the path: KE + PE = constant. This lets you solve for speeds and heights at any point without tracking the detailed path — just identify the starting and ending states.
The height you choose as your reference for potential energy (PE = 0) is arbitrary, because only *differences* in PE matter. What's critical is using the *same* reference throughout a problem. If you set the ground as PE = 0 at the start of a calculation, it must remain the ground for all subsequent states. A common mistake is implicitly shifting the reference partway through, which produces wrong answers without any obvious algebraic error.
When friction is present, you have to account for the work it does. Friction converts mechanical energy to thermal energy, so KE_f + PE_f = KE_i + PE_i − |W_friction|. The mechanical energy of the sliding object decreases, but the thermal energy of the surfaces increases by the same amount. Total energy is always conserved — the first law of thermodynamics — but in physics problems involving friction, that thermal energy is usually outside the scope of what you are tracking. The practical rule: before applying the simple KE + PE = constant form, always check whether friction or other nonconservative forces are present.