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A 300-foot cable weighing 6 pounds per foot is hanging from a winch 300 feet above ground level. Find the work (in ft-lb) done in winding up the cable when there is a 200-pound load attached to the end of the cable.

Respuesta :

Answer:

Explanation:

Given

Length of cable [tex]L=300 ft[/tex]

Weight density [tex]\lambda =6 pound/ft[/tex]

Winch height [tex]h=300 ft[/tex]

additional load [tex]W=200\ pound[/tex]

Work done

[tex]W=\int_{0}^{300}\lambda ydy+W\times distance\ moved[/tex]

[tex]W=\int_{0}^{300}6\cdot ydy+200\times 300[/tex]

[tex]W=3\left [ y^2\right ]^{300}_{0}+60,000[/tex]

[tex]W=3,30,000 lb-ft[/tex]