Description
You’ve used some version of “potential energy” since middle school — but can you actually prove where the formulas come from? In this video we nail that down for real: deriving the general relationship between work and potential energy, stating (and verifying) the formulas for gravity and springs, and untangling why the reference point for U doesn’t matter even though its value changes depending on where you put it.
✅ State the general relationship between work and potential energy, ΔU = −W = −∫F·dr
✅ State the potential energy formulas for gravity near Earth’s surface and for a spring
✅ Use F = −dU/dx to recover a force from its potential energy function
⏱️ Timestamps
0:00 – Hook: can you prove where potential energy comes from?
0:50 – Review: K is energy of motion, U is energy of relative position
1:20 – The general definition: ΔU = −W = −∫F·dr
2:01 – Two results: Ug = mgy and Uel = ½kx²
2:31 – Checking our work: F from U for gravity
3:14 – Checking our work: F from U for a spring
3:45 – Worked example: U = 0 is arbitrary, but ΔU isn’t
6:28 – Energy is a scalar — what a negative sign actually means
7:00 – Worked example: roller coaster and conservation of mechanical energy
This video is part of the MasteryFlip approach to AP Physics C — watch, take notes, then come to class ready to work problems together. Curious about the MasteryFlip Framework? Check out the ReachEveryStudent Podcast, new episodes every Monday at reacheverystudent.com.