A cable weighing 0.8 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?

Question

perl · Answer

Total work = (work done by robot+wrench) + ( work done on chain)

perl · Answer

(80+7)*60 + integral .8x dx , x=0..60 , and this is wrong

jamesj · Answer

So clearly the work for the 7 pound wrench and robot itself is easy, using W = mgh

The cable is slightly less obvious

jamesj · Answer

But it's easy to analyze just by using the center of mass of the cable. When the robot is at the bottom, the CM of the cable is at a depth of 30 feet...

jamesj · Answer

when the robot reaches the top, the CM is at a depth of 15 feet

perl · Answer

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