Calculating Work Done by a Beaver in Building a Dam

[sheepcountme]

Homework Statement

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.

Homework Equations

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

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!

 

[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

 

[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?

 

[sheepcountme]

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

Is this correct?

 

[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?

 

[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

 

[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