# Thread: [SOLVED] A leaky bucket...

1. ## [SOLVED] A leaky bucket...

If a leaking bucket weights 2lbs and the water weights 8 lbs; if you lift the bucket 4 ft and all the water leaks out when it reaches 4 ft. How much work is done by the person lifting the bucket?

i dont know how to set the integral correctly, all i know isthe limits are from 0-4, but when i tried to work out the problem, i got 16/5, and i feel as if i did something wrong.

2. Originally Posted by >_<SHY_GUY>_<
If a leaking bucket weights 2lbs and the water weights 8 lbs; if you lift the bucket 4 ft and all the water leaks out when it reaches 4 ft. How much work is done by the person lifting the bucket?

i dont know how to set the integral correctly, all i know isthe limits are from 0-4, but when i tried to work out the problem, i got 16/5, and i feel as if i did something wrong.
variable force as a function of height, $\displaystyle x$ ...

$\displaystyle F = 10 - 2x$

$\displaystyle W = \int_0^4 10-2x \, dx$

3. Originally Posted by skeeter
variable force as a function of height, $\displaystyle x$ ...

$\displaystyle F = 10 - 2x$

$\displaystyle W = \int_0^4 10-2x \, dx$

im sorry but could you explain how you got F? i did the problem alot differently, i thought it was 4-x

4. Originally Posted by >_<SHY_GUY>_<
im sorry but could you explain how you got F? i did the problem alot differently, i thought it was 4-x
at the start, the bucket weighs 10 lbs (2 lb bucket + 8 lb water)

for every foot the bucket is lifted, it loses 2 lbs of water.

$\displaystyle F = 10 - 2x$

note that at $\displaystyle x = 4$ ft, $\displaystyle F = 2$ lbs ... the weight of the empty bucket.

5. Originally Posted by skeeter
at the start, the bucket weighs 10 lbs (2 lb bucket + 8 lb water)

for every foot the bucket is lifted, it loses 2 lbs of water.

$\displaystyle F = 10 - 2x$

note that at $\displaystyle x = 4$ ft, $\displaystyle F = 2$ lbs ... the weight of the empty bucket.
thank you so much youve been such a great help to me