Nano PHYSICS . MECHANICS . WORK AND ENERGY . WORK DONE BY A FORCE

Work as a Line Integral

Work along a path is built from force dotted with tiny displacement elements. Learn path, displacement element, dot product meaning, and joule units.

Physics · Mechanics · Work and Energy · Work Done by a Force · Work as a Line Integral
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: work as a line integral
Free
Establish the work idea and why direction matters.
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Goal: define work using force, displacement, direction, and units.
STEP 2
Conceptual grounding: build the work model
Free
Build a workflow for force, displacement, component, sign, and units.
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Goal: identify the component of force that contributes to work.
STEP 3
Real-world connection: interpret work by forces
Free
Apply work reasoning to pushes, pulls, gravity, friction, normal force, and curved motion.
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Goal: explain positive, negative, and zero work in physical contexts.
STEP 4
Check your understanding: diagnostic mini-quiz
Paid
Attempt each question before revealing the work reasoning.
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Goal: identify and correct angle, sign, component, and unit errors before they become calculation errors.
STEP 5
Practice: solve increasingly rich work situations
Paid
Apply the model to situations that grow in complexity.
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Goal: write concise, physically justified work calculations and explanations.