Math Problem Statement
The trough in the figure below has width w=2 ft, length l=18 ft and height ℎ=5 ft. If the trough is full of water, find the force of the water on a triangular end. (Use the density of water =62.4 lb/ft3.) Force = Don't forget to enter units Find the work to pump all of the water over the top of the trough. Work = Turn the force into newtons and work into joules.
Solution
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Math Problem Analysis
Mathematical Concepts
Hydrostatics
Force Integration
Work Integration
Unit Conversion (Imperial to SI)
Formulas
Force due to water pressure: dF = 62.4 * y * (width at y) * dy
Work to pump water: dW = 62.4 * (volume strip) * (5 - y) * dy
Unit conversion: 1 lb = 4.44822 N, 1 ft-lb = 1.35582 J
Theorems
Pressure varies linearly with depth
Principle of Work (integration of force over distance)
Suitable Grade Level
Undergraduate Physics/Calculus
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