Choosing a System for Energy

A falling ball has constant energy if you call the system 'ball plus Earth,' because gravity is then an internal force, and internal forces store energy as potential energy instead of spending it. Call the system just 'the ball,' and gravity becomes an outside force doing work on it, so the ball's own mechanical energy keeps changing as it falls. Same ball, same motion, different bookkeeping, because you moved the boundary. Nothing physical changed — only your accounting choice did.

This is exactly why potential energy exists: it's a bookkeeping trick for internal conservative forces, built by taking the antiderivative of force with respect to position so you never have to compute that force's work by hand again. Put Earth inside the system and gravity's work becomes -mgh stored as PE. Leave it outside, and you must track gravity's work directly as energy entering or leaving. Friction is different — it's never conservative, so no matter where you draw the boundary, friction either does external work on your chosen system or, if the floor is inside the boundary, converts mechanical energy into heat that leaves as thermal energy you usually don't track in detail.

This choice is also what connects energy methods to Newton's second law. Both give the same final answer, but force methods need the full vector path and time history, while energy methods only need start and end states once you've fixed a sensible boundary. Picking the system well is the move that turns a messy multi-force problem into a one-line energy equation.