How much work is required to lift the load of the way up the shaft if a cable that weighs kg/meter is lifting a load of 150 kg that is initially at the bottom of a 50 meter shaft?
Since you provided no number, let's say the cable is 2 kg/m. You can fill in your own number in the second equation below.
There are two portions to this:
Lifting the weight:
Force needed is
Lifting the cable:
While lifting the cable, less and less has to be lifted, so the force needed to do this diminishes. If we call the current length of the cable
What we now need is the integral over
Answer : Total Work=
(!) For the calculus-purists: Yes, I embezzled a
I should have made