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Work & Energy · Physics

Energy Diagrams and Energy Methods

Energy visuals make motion predictable: bar charts for bookkeeping and \(U(x)\) curves for stability and turning points.

This topic includes

Subtopics to master

Learn to “read” energy the same way you read graphs in kinematics.

Bookkeeping
Energy Bar Charts
Track how energy moves between forms without getting lost in algebra.
  • Choose system + energies
  • Before/after comparisons
  • Include dissipation if needed
Start subtopicVisual accounting.
Curves
Potential Energy Curves
Plot \(U(x)\) and compare it with total energy \(E\) to predict motion.
  • Allowed regions \(E\ge U\)
  • Turning points \(E=U\)
  • Speed from \(K=E-U\)
Start subtopicPowerful intuition.
Turning points
Turning Points and Equilibrium
Turning points occur where \(K=0\). Equilibrium occurs where \(F=-dU/dx=0\).
  • Find turning points
  • Find equilibrium points
  • Interpret physically
Start subtopicRead motion limits.
Stability
Stability Analysis
Stable equilibrium at minima of \(U(x)\); unstable at maxima (intro-level reasoning).
  • Min vs max logic
  • Small displacement behavior
  • Real examples
Start subtopicWhy systems “settle.”
Practice
Practice & Exercises
Use bar charts and \(U(x)\) graphs to answer speed, region, and stability questions.
  • Energy bar chart drills
  • Allowed-region problems
  • Turning-point identification sets
  • Stable/unstable equilibrium questions
  • Mixed K+U calculations
Open practiceGraph fluency.
Bridge
Conservation Methods Preview
Energy diagrams become the fastest way to solve conservation-of-energy problems — especially with springs and gravity.
  • System selection
  • Assumptions checklist
  • Next topic setup
Start subtopicReady for conservation.