work problem

I

intervade

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Apr 6, 2009
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Ok, my problem is: a bucket that weighs 60 lbs when filled with water is lifted at a constant rate by a wench from the bottom of a well that is 80 feet deep. The chain that holds the bucket weighs 2pounds/per foot. Determine the work required to lift the full bucket from the bottom, to the top.

Then, find the work as if the bucket were leaking while lifting the bucket from the bottom of the well, and at the top the bucket only weighed 30lbs. The water leaks at a constant rate.

It also says the bucket is lifted at a constant rate.

Now, I know the work required to lift the bucket alone is 60*80 but I'm not sure where to go from there.

Help would be much appreciated!
 
intervade said:
Ok, my problem is: a bucket that weighs 60 lbs when filled with water is lifted at a constant rate by a wench from the bottom of a well that is 80 feet deep. The chain that holds the bucket weighs 2pounds/per foot. Determine the work required to lift the full bucket from the bottom, to the top.

Then, find the work as if the bucket were leaking while lifting the bucket from the bottom of the well, and at the top the bucket only weighed 30lbs. The water leaks at a constant rate.

It also says the bucket is lifted at a constant rate.

Now, I know the work required to lift the bucket alone is 60*80 but I'm not sure where to go from there.

Help would be much appreciated!
Click to expand...


At any height h - the incremental work done

dW = 60 dh + (80-h)(2) dh
 
Ok! That makes perfect sense, but how do I take in to account the "leaking"? I think the bucket weighs 3/8 lbs less each foot the bucket moves up, and it says the bucket is moving at a constant rate, but I don't know if I can approach it that way.
 
intervade said:
Ok! That makes perfect sense, but how do I take in to account the "leaking"? I think the bucket weighs 3/8 lbs less each foot the bucket moves up, and it says the bucket is moving at a constant rate, but I don't know if I can approach it that way.
Click to expand...

When the bucket has gone up 'h' ft. - how many ponds did it loose. Subtract that from 60 - in the equation I gave you.
 
\(\displaystyle Work \ = \ Force \ X \ Distance\)

\(\displaystyle Determine \ the \ work \ you \ done \ by \ moving \ a \ 50,000-pound \ object \ 2 \ feet \ (no \ friction).\)

\(\displaystyle The \ magnitude \ of \ the \ required \ force \ F \ is \ the \ weight \ of \ the \ object, \ ergo:\)

\(\displaystyle W \ = \ FD, \ W \ = \ (50,000)(0) \ = \ 0 \ ft*lb.\)

\(\displaystyle Hence, \ no \ work \ was \ perform, \ obviously \ you \ must \ come \ from \ a \ family \ of \ idlers.\)

\(\displaystyle I \ remember \ this \ one \ from \ "The \ Truth \ or \ Consequences" \ TV \ show.\)
 
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