- #1
rashedah
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Homework Statement
Consider a rectangular container, dimensions L x b, filled to level h with water. Water sloshes at low amplitude, y0 << h so that its surface remains always flat. Assuming the water has a density of δ, show that the potential energy is[itex] U(y) = \frac{1}{6} b δ g L y^2 [/itex]
Homework Equations
[itex] F = ma [/itex]
[itex] U = \frac{1}{2} k x^2 [/itex]
The Attempt at a Solution
Since F = ma = kx = mgh, I know that k = mg because x and h in this case are y0. And m is bLδ meaning that k = bLδg.
So integrating ky0 to get the potential energy I get
[itex] U(y) = \frac{1}{2} b δ g L y^2 [/itex]
but the answer has a fraction of 1/6, where did the extra 1/3 come from?