Nano PHYSICS . MECHANICS . MOMENTUM AND COLLISIONS . ELASTIC COLLISIONS

One-Dimensional Elastic Collisions

Head-on elastic collisions can be solved using conservation laws and sign conventions, with special cases that help check reasonableness.

Physics · Mechanics · Momentum and Collisions · Elastic Collisions · One-Dimensional Elastic Collisions
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: one-dimensional elastic collisions
Free
Establish elastic collisions as interactions conserving both momentum and kinetic energy.
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Goal: define elastic collision using total momentum conservation and total kinetic-energy conservation.
STEP 2
Conceptual grounding: build the elastic-collision model
Free
Build a workflow for systems, signs, components, kinetic energy, special cases, and unknown counting.
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Goal: distinguish momentum equations from kinetic-energy equations and use both appropriately.
STEP 3
Real-world connection: interpret elastic collisions and scattering
Free
Apply elastic-collision reasoning to carts, balls, pucks, 1D head-on motion, and 2D scattering.
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Goal: explain 1D special cases, 2D component setups, and elastic-model limitations in physical contexts.
STEP 4
Check your understanding: diagnostic mini-quiz
Paid
Attempt each question before revealing the elastic-collision reasoning.
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Goal: identify and correct elastic/inelastic, sign, component, kinetic-energy, and unknown-counting errors before they become calculation errors.
STEP 5
Practice: solve increasingly rich elastic-collision situations
Paid
Apply the model to situations that grow in complexity.
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Goal: write concise, physically justified elastic-collision calculations and explanations.
STEP 6
Summary & reflection + explorations
Paid
Consolidate the model and explore changing masses, directions, model assumptions, and dimensionality.
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🔒 ▶ Explore interactive simulation
Goal: carry the model forward into scattering, center-of-mass frames, collision classification, and realistic collision approximations.