A mineshaft is 500 ft deep A chain that runs the length of t

A mineshaft is 500 ft deep. A chain that runs the length of the mineshaft is attached to a bucket filled with 200,000 lbs of coal. If the chain is 500 ft long and weighs 4000 lbs, then find the amount of work needed to bring the bucket to the top of the mine.

linear mass density p=4000/500 = 8lbs/ft

m=200000+px

At a certain time let x length of chain be hanging in the mineshaft.

So, weight of the chain = (200000+px)g

So, work done in pulling it up by dx

dW=(200000+px)gdx

So, total work done=W=Integration(dW) from x=500 to x=0

=[200000x+4x^2]32 from x=500 to x=0

=32320000 lbs*ft²/sec²

A mineshaft is 500 ft deep. A chain that runs the length of the mineshaft is attached to a bucket filled with 200,000 lbs of coal. If the chain is 500 ft long a

A mineshaft is 500 ft deep A chain that runs the length of t

Solution

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