Conservation of Energy Master Equation

Every energy problem in this unit looks different until you realize they're not, they're all the same six-term equation with most of the terms crossed out. That's the part nobody tells you up front. Students meet frictionless problems, then friction problems, then spring problems, and treat each one like a new topic to memorize, when really there's a single equation underneath all of it and the only thing that changes is which terms happen to be zero. This video builds that equation once, correctly, so every problem afterward becomes a matter of substitution instead of a guess at which formula to use. Covered in this video: The full master equation: W-nc + KE-initial + PE-initial + spring-initial = KE-final + PE-final + spring-final, and what each term means physically Why this is really just conservation of energy written so nothing gets left out, one line that accounts for everything in the system W-nc, the non-conservative work term: positive when something pushes the system, negative when friction fights it, zero when neither is present The four-step method: pick a start and end point, list what energy exists at each one, identify W-nc, then solve for the one unknown Why "frictionless" isn't a different kind of problem, it's this same equation with the friction part of W-nc set to zero The habit that separates a fast solver from a stuck one: writing every term before crossing any of them out, instead of guessing which ones matter This is core to Standard 4.1 and 4.2 (Energy Definitions and Conservation of Energy) and it is the hinge the entire unit turns on. Everything before this video, kinetic, potential, spring, thermal, was building vocabulary. Everything after it, ramps, springs, friction, connected masses, is this exact equation with different terms surviving. Learn this line once and the rest of the unit stops being new material and starts being the same problem in a new costume. AUX — Free Physics Resources https://auxlearning.com