Q:

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

Accepted Solution

A:
Answer:6060 foot-poundsStep-by-step explanation:GivenWeight of cable(w')=0.6 pound per footdepth of well=60 footweight of wrench=7 PoundNow work done in raising monkey with wrench[tex]=w\cdot h[/tex][tex]W_1=(80+7)\cdot 60=5220[/tex] foot-poundsNow 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 Β (x^2)_0^{60}[/tex][tex]W_2=540[/tex] foot-pounds[tex]W_{net}=5220+540=6060[/tex] foot-pounds