Potential Energy of water in a wedge

AI Thread Summary
The problem involves calculating the potential energy of water in a symmetric wedge with depth h and width A. The potential energy formula E = mgh is referenced, but the user struggles with integrating due to the changing horizontal cross-section of the wedge. They suggest considering the center of gravity of the triangular shape formed by the water to assist with the calculation. The discussion highlights the importance of understanding the geometry of the wedge to accurately determine the potential energy. Clarifying the center of gravity's position is crucial for solving the problem effectively.
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Homework Statement



A symmetric wedge of depth h and width A is filled to the brim with water of mass m, where acceleraton due to gravity is g. What is the potential energy of the water with respect to the base of the wedge?

Homework Equations


E = mgh



The Attempt at a Solution


E = 0.5*mgh for a cylinder (integrating as the force of any given disc increases linearly from 0 to gh between h=0 and h=h). But I'm having a mental block with how to integrate when the horizontal cross-section increases linearly from 0 to A as h goes from 0 to h. Thanks :D
 
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How about this: Where is the center of gravity of this triangle, and how far above the base is it?
 
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