Math Problem Statement
A 20 foot rope that weighs 80 lb hangs over a 100 foot well with a 20 lb bucket attached. How much work is required to lift the rope and bucket up 12 ft?
Solution
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Math Problem Analysis
Mathematical Concepts
Work and Energy
Integration
Physics of Mechanical Systems
Formulas
Work = Force × Distance
Weight per foot of rope = Total weight of rope / Length of rope
Total work to lift rope = ∫ from 0 to 12 of 4(20 - x) dx
Total work to lift bucket = Weight of bucket × Distance lifted
Theorems
Fundamental Theorem of Calculus
Suitable Grade Level
Undergraduate (Physics/Calculus level)
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