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A cable weighing 0.6 pounds per foot is attached to a small 80-pound robot, and then the robot is lowered into a 60-foot deep well to retrieve a 7-pound wrench. The robot gets out of the well (carrying the wrench) by climbing up the cable with one end of the cable still attached to the robot. How much work does the robot do in climbing to the top of the well? Work = ________ foot-pounds

Respuesta :

Answer:6060 foot-pounds

Step-by-step explanation:

Given

Weight of cable(w')=0.6 pound per foot

depth of well=60 foot

weight of wrench=7 Pound

Now work done in raising monkey with wrench[tex]=w\cdot h[/tex]

[tex]W_1=(80+7)\cdot 60=5220[/tex] foot-pounds

Now work done in raising rope

robot rises by climbing up the cable with one end of the cable still attached thus robot support half the weight of cable so work done

[tex]W_2==\int_{0}^{60}\frac{w'}{2}xdx[/tex]

[tex]W_2=0.3\times 0.5\times  (x^2)_0^{60}[/tex]

[tex]W_2=540[/tex] foot-pounds

[tex]W_{net}=5220+540=6060[/tex] foot-pounds