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Work by Integration worksheets

Model spring, cable-lifting, and tank-pumping work with force-distance integrals and exact units.

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Model spring, cable-lifting, and tank-pumping work with force-distance integrals and exact units.

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Each generated problem includes bounded solvable givens. Worked pages show the theorem, formula, substitution, or physical slice used to reach the result.

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Build and evaluate bounded physical work integrals.

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  • Keep units or domains beside each line.
  • Ask students to name the theorem or formula before substituting.
  • Distinguish exact values from labeled approximations.

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Math SheetNameScoreTeacherDateWork by IntegrationDefine the force at a general displacement or slice, multiply by distance moved, and evaluate with physical units.1.A spring has constant 44 N/m. Set up a definite integral for the work to stretch it from 0.2 m to 0.5 m.2.A full rectangular tank has horizontal area 5 m^2 and depth 3 m. Pump water to the top (weight density 9800 N/m^3). Find the work.State assumptions, domains, units, and approximation methods.math-sheet.comPage 1 of 3
Math SheetNameScoreTeacherDateWork by IntegrationDefine the force at a general displacement or slice, multiply by distance moved, and evaluate with physical units.3.A 5 m cable weighs 2 N/m and hangs vertically. Set up a definite integral for the work to lift all of it to the top.4.A 7 m cable weighs 3 N/m and hangs vertically. Find the work to lift all of it to the top.State assumptions, domains, units, and approximation methods.math-sheet.comPage 2 of 3
Math SheetNameScoreTeacherDateWork by IntegrationDefine the force at a general displacement or slice, multiply by distance moved, and evaluate with physical units.5.A spring has constant 53 N/m. Set up a definite integral for the work to stretch it from 0.2 m to 0.5 m.6.A full rectangular tank has horizontal area 3 m^2 and depth 2 m. Pump water to the top (weight density 9800 N/m^3). Find the work.State assumptions, domains, units, and approximation methods.math-sheet.comPage 3 of 3

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