Beavers water and work

1. Mar 2, 2010

sheepcountme

1. The problem statement, all variables and given/known data
A beaver is building a damn and fills a 5kg bucket with 25kg of water. Then he begins to climb a vertical ladder, but unfortunately there is a whole in the bucket where water leaks out at a constant rate. At the top of the ladder, only 10kg of water is left in the bucket. Find the work done by the beaver in this problem.

Hint: Speed up the ladder is constant and writing an expression for mass of the bucket plus water as a function of height will help.

2. Relevant equations
(I believe):
PE=mgh
KE=(1/2)mv^2
Integrals

3. The attempt at a solution

Well, I want to start with writing the expression and then integrating that, but I don't know what the expression should be... h=Mb+Mw seems too easy, or is this what they meant at first and then to do something with the PE equation and height?? Ack!

2. Mar 3, 2010

ehild

First you need an expression for the mass of water as function of time.
The mass is decreasing at a constant rate. Initially, it is 25kg. The final mass is 10 kg. The total time needed to climb up is T. t is the running time. Draw a plot first, and then write the expression for m(t).

ehild

3. Mar 3, 2010

sheepcountme

Well, we don't know the time and the hint says to write mass as a function of height, so I went ahead and used the old school skills to get mass as a function of height:
m(h)=-1.25h+30

...sooo, now should I be using integrals? Or am I taking the wrong approach?

4. Mar 3, 2010

sheepcountme

Okay, so integrating I get:
12(30-0.655(12)) - 0 = 270 J

Is this correct?

5. Mar 3, 2010

ehild

I do not understand your old school skills. What is h at the top of the ladder? Will be the mass of water equal to 10 kg there?

6. Mar 3, 2010

sheepcountme

h at the top (at 12m) is 15 (10kg water plus 5kg bucket)
h at the bottom (at 0m) is 30 (25kg water plus 5kg bucket)

So I used these as coordinates (0,30) and (12,15) and have the equation
m(h)=-1.25h+30

7. Mar 3, 2010

ehild

So the heigh was given? You did not write it in the first post. Then the mass is all right. But you should integral the force with respect to h. As I see, you have integrated the mass. And I do not know either, where that 0.655 comes from.

ehild

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