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Applications of Integration: Work

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Wize University Calculus 1 Textbook > Applications of Integration for Physical Science

Work

3 Activities

A triangular moat is dug around a point. If the x-axis represents the ground, the triangle is bounded by points (0,2), (3,2), (1,0)(0,2), \, (3,2), \, (1,0), and the axis of rotation is x=4x=4.
(a) How much water is required to fill the moat? (Provide an exact answer only.)
(b) How much work is required to empty the moat, if the pump empties three metres above the ground? (The density of water is 1.) (Leave your answer in terms of π,g\pi, g.)
More Work Questions:
Applications of Integration: Work
A chain with a total mass of 100 kg is hanging from the top of a 200 m building to the ground. Write down and solve a definite integral to determine the minimum work done in lifting the chain to the top of the building.
Applications of Integration: Work
A chain with a total mass of 100 kg is hanging from the top of a 200 m building to the ground. Write down and solve a definite integral to determine the minimum work done in lifting the chain to the top of the building.
Applications of Integration: Work
How much work is required to empty a conical tank of height 3m, (upper) radius 1m, of a liquid of density ρ\rho by pumping the liquid 1.5 meters above the top of the tank?
Practice: Work
A chain with a total mass of 100 kg is hanging from the top of a 200 m building to the ground. Write down and solve a definite integral to determine the minimum work done in lifting the chain to the top of the building.
Applications of Integration: Work
A chain with a total mass of 100 kg is hanging from the top of a 200 m building to the ground. Write down and solve a definite integral to determine the minimum work done in lifting the chain to the top of the building.
Applications of Integration: Work
How much work is required to empty a conical tank of height 3m, (upper) radius 1m, of a liquid of density ρ\rho by pumping the liquid 1.5 meters above the top of the tank?