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Mathematics
OpenStudy (anonymous):

A cable weighing 0.6 pounds per foot is attached to a small 80-pound robot, and then the robot is lowered into a 40-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? A cable weighing 0.6 pounds per foot is attached to a small 80-pound robot, and then the robot is lowered into a 40-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? @Mathematics

OpenStudy (amistre64):

87*40 + cable weight integrates from 0 to 40

OpenStudy (amistre64):

er perhaps 0 to 20 since it just needs to get up half the cable

OpenStudy (amistre64):

since work = force x distance; the force, cable wise is; weight*length ... but i feel im missing something

OpenStudy (amistre64):

\[\int_{0}^{20}.6x\ dx=.3x^2\] 20^2 = 400 400* .3 = 120.0 for the cable if im recalling it right

OpenStudy (amistre64):

87*40 + 120 = 3480 + 120 = 3600 maybe

OpenStudy (anonymous):

\[\int\limits_{0}^{40} (.6x/2) + 87 = 3720\] Well, that's the answer, but thanks amistre!

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