Consider a trough with the shape below. 2 m 5 m 8 m It is full of water, which has a density of 1000 kg/m³. Recall the acceleration due to gravity is g = 9.8m/s². Write, but do not evaluate, a definite integral that calculates the work required to pump all the water over the top of the tank.

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13-12-2022
Physics

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Consider a trough with the shape below. 2 m 5 m 8 m It is full of water, which has a density of 1000 kg/m³. Recall the acceleration due to gravity is g = 9.8m/s². Write, but do not evaluate, a definite integral that calculates the work required to pump all the water over the top of the tank.

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NomulaHarsh NomulaHarsh · Answer 1 · 2022-12-23T07:51:14+01:00

The work required to pump all the water over the top of the tank is W = ∫0^2 (1000 kg/m³)(9.8 m/s²)(5 m)(x) dx.

What is the connection between force and work?

Work is the act of moving anything using force. It is inversely proportional to the force acting on the object and the distance the thing travels. Force times distance equals work.

This integral indicates the work involved in pumping water over the tank's top. The tank's 2 meter length is used to calculate the integral. The acceleration brought on by gravity is 9.8 m/s2, and water has a density of 1000 kg/m3. The water is five meters high. In order to express the length of the tank, the variable x is needed. The entire amount of work needed to pump the water over the tank's top can then be calculated by evaluating this integral.

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