Posted by **Nancy** on Sunday, February 6, 2011 at 9:24pm.

A bucket that weighs 3.2 pounds and a rope of negligible weight are used to draw water from a well that is 82 feet deep. The bucket is filled with 42 pounds of water and is pulled up at a rate of 2.3 feet per second, but water leaks out of a hole in the bucket at a rate of 0.35 pounds per second. Find the work done pulling the bucket to the top of the well.

- Math -
**MathMate**, Sunday, February 6, 2011 at 11:36pm
The net mass of the bucket as a function of time, M(t)

=3.2+42-0.35t

Work done as a function of time

= M(t)*2.3 ft/s * 32.2 ft/s^2

Over the height of the well,

time required to go to the top

= 82'/2.3 '/s

= 82/2.3 s

Total work done

= ∫ M(t)*32.2 * 2.3dt from 0 to 82/2.3

=[45.2t-0.175t²] from 0 to 82/2.3

= 102872 poundal-ft

= 3194.8 lbf-ft (after dividing by g)

- Math -
**mar**, Sunday, May 1, 2011 at 10:39pm
what's the 32.2ft/s^2

- Math -
**Will**, Saturday, October 1, 2011 at 7:13pm
Acceleration due to gravity

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