Conservation of Energy

🧭 Plot Summary

This lesson is where everything from Lessons 3.1–3.3 comes together into the single most powerful tool in the unit. A system made of just one object can only have kinetic energy — but a system of objects that interact through conservative forces, or that can change shape reversibly, may have both kinetic and potential energy. Add those together and you get a system's mechanical energy, E_mech = K + U. Here's the key idea this lesson is built around: any change to one type of energy inside a system has to be balanced — either by an equal and opposite change to another type of energy inside that same system, or by a transfer of energy across the system's boundary. Which of those two things happens depends entirely on which objects you decide belong to the system — the exact same physical process can look like an internal trade-off for one choice of system, and an external transfer for another. Zoom out far enough and energy is conserved in every interaction, no exceptions — but a system's mechanical energy specifically stays constant only under two conditions: zero net work done on it from outside, and no nonconservative interactions (like friction) happening inside it. Break either condition and mechanical energy either gets transferred across the boundary or dissipated as heat and sound inside the system — not destroyed, just converted out of the mechanical bookkeeping.

What you'll do in this lesson

• Identify what kinds of energy a system can have, based on how many objects it contains and how they interact.
• Find a system's mechanical energy as the sum of its kinetic and potential energies.
• Explain how an energy change inside a system balances against another energy type, or against a transfer across the system's boundary.
• Recognize that choosing a system is a choice — and that choice determines whether the system's total energy is constant.
• Check the two conditions for conservation of mechanical energy: zero net external work, and no nonconservative interactions inside the system.
• Track where mechanical energy goes when it isn't conserved — transferred across the boundary, or dissipated as heat or sound inside it.

Why it matters

Conservation of energy is the single most reused problem-solving tool for the rest of the course — and choosing a system wisely, before doing any calculation, is exactly the kind of reasoning the AP exam's Mathematical Routines question tests every year.

✅ Self-Check Before You Roll On

Check off each item as you get there. These aren't grades — they're your own signal.