Nano PHYSICS . MECHANICS . WORK AND ENERGY . ENERGY DIAGRAMS AND CONSERVATION METHODS

Turning Points and Equilibrium

Turning points occur where kinetic energy is zero. Equilibrium occurs where force is zero, which means the slope of U(x) is zero.

Physics · Mechanics · Work and Energy · Energy Diagrams and Conservation Methods · Turning Points and Equilibrium
Access for this nano-lesson
Unsigned visitors can show & copy prompts for Steps 1-3. Signed-in free accounts can also Run with AI for Steps 1-2. Paid accounts unlock everything (Steps 1-6 + Help prompts + AI).
Steps 1-3 Free Steps 4-6 Paid
STEP 1
Orient: turning points and equilibrium
Free
Establish energy diagrams as tools for tracking energy forms and motion limits.
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Goal: define energy diagrams using system choice, energy forms, graph meaning, and units.
STEP 2
Conceptual grounding: build the energy-diagram model
Free
Build a workflow for systems, energy forms, total energy, curves, turning points, and assumptions.
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Goal: connect bar charts and potential curves to energy bookkeeping and motion prediction.
STEP 3
Real-world connection: interpret energy diagrams and curves
Free
Apply diagram reasoning to springs, gravity, friction, stability, and conservation-method previews.
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Goal: explain allowed regions, turning points, equilibrium, stability, and conservation previews in physical contexts.
STEP 4
Check your understanding: diagnostic mini-quiz
Paid
Attempt each question before revealing the energy-diagram reasoning.
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Goal: identify and correct system, dissipation, graph-reading, turning-point, and stability errors before they become calculation errors.
STEP 5
Practice: solve increasingly rich energy-diagram situations
Paid
Apply the model to situations that grow in complexity.
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Goal: write concise, physically justified energy-diagram explanations and solutions.