Unsure if means for calculating work is correct

[KrabLord]

The correct answer is 9600w, where w is weight. I arrived at this answer by taking
[MATH]\int_{1}^{5} 800whdh = 9600w[/MATH] .
I am uncertain if my reasoning is correct, however. My reasoning is as follows: The water moves five feet (hence the upper bound), but the top foot of the pool is empty, hence the lower bound being 1.

Is this reasoning correct? Either way, could someone please explain this to me better than I can?

 

[Steven G]

I would hope that no one can explain your work better than you can.

I agree that the water from the top of the pool must go up 1 ft. I also agree that the water at the very bottom must go up 5 ft. So the limits are correct.

What is the formula for doing such work problems? What part are you unsure of? Please give us something to work with so that we can help you.

 

[KrabLord]

I would hope that no one can explain your work better than you can.

I agree that the water from the top of the pool must go up 1 ft. I also agree that the water at the very bottom must go up 5 ft. So the limits are correct.

What is the formula for doing such work problems? What part are you unsure of? Please give us something to work with so that we can help you.

*Why* are those the correct boundaries? I cannot offer a deeper explanation for those boundaries being correct. You have answered my question, however: "the water from the top of the pool must go up 1 ft... the water at the very bottom must go up 5 ft." I would not have been able to articulate that. Thanks!

 

[Steven G]

Obviously I gave you the reasons for the boundaries so I was not asking you how you got it. I was asking why you chose that integrand to integrate.

I am concerned that you claim that you could not articulate the reason for the limits. If you were the one who arrived at the limits then how did you get it? If you do not know how to arrive at the limits then you need to learn how!

Look at the water in the pool as if it is partitioned into narrow horizontal slabs. The top slab must go up 1 ft. The slab below that must go up (say) 1.1ft. The slab below that must go up 1.2ft...The slab below that go must go up 2.5ft ... The last slab must go up 5ft.
You must see that.

 

[KrabLord]

Obviously I gave you the reasons for the boundaries so I was not asking you how you got it. I was asking why you chose that integrand to integrate.

I am concerned that you claim that you could not articulate the reason for the limits. If you were the one who arrived at the limits then how did you get it? If you do not know how to arrive at the limits then you need to learn how!

Look at the water in the pool as if it is partitioned into narrow horizontal slabs. The top slab must go up 1 ft. The slab below that must go up (say) 1.1ft. The slab below that must go up 1.2ft...The slab below that go must go up 2.5ft ... The last slab must go up 5ft.
You must see that.

Yes, I saw that and it was my reasoning, however only very fuzzily. Your agreement with my poor reasoning, at once, made it clear to me. I wanted to be sure my reasoning was right.