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Nuke787
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Homework Statement
A tank of water is 3m long and has a triangular cross section of height 1m and width at the top of 1m. How much work is done pumping the water to the top of the tank? The density of water is 1000kg/m3 and the gravitational constant g has value g m/s2
Homework Equations
Many ways to solve this problem, see below.
The Attempt at a Solution
I solved the problem already by doing 1000g*3*integral from 0 to 1 of ((1/2)x2).
This yields 3000g*(1/6*x3 evaluated at 0 to 1). This will yield 1/6*3000g or 500g.
My problem is my teacher doesn't understand this on the test that I was given and refuses to give me credit until I can explain it in a way he understands. The units in the above equations check out and give you N-m, and the number is correct as well. I have applied this to numerous problems and showed him it works. His problem is he doesn't see "the distance traveled". When solving this problem he does it by slicing in which he is able to see a distance from the top of the tank. Can someone explain to me why this works and hopefully their explanation will make more sense to him than mine. I understand this only works for triangles where the base is changing at the same rate as the height.