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Sagot :
The work w required to pump the water out of the spout will be 705600 joules.
What is work done?
Work done is defined as the product of applied force and the distance through which the body is displaced on which the force is applied.
Work against gravity is done on a thin layer of liquid with a width of y. The vertex of the trough serves as the center of our coordinate system.
It is obvious that the cross-section of the triangle has length y at a height y. A thin layer at height y is a rectangular box with a volume of 8 y , and lifting it requires a force equal to;
[tex]\rm F= \rho gV \\\\\rm F= 9.8 \times 10000 \times 8y \triangle y \\\\[/tex]
The work on the layer is;
[tex]\rm W= 78400 y \triangle y [4-y]\\\\\ W= \int\limits^3_0 {x} \, dx \\\\\ W= \int\limits^3_0{78400y[4-y]} \, dx \\\\\ W=705600 \ Joule.[/tex]
Hence, the work w required to pump the water out of the spout will be 705600 joule.
To learn more about the work done, refer to the link ;
https://brainly.com/question/3902440
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