Potential Energy of water in a wedge

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SUMMARY

The potential energy of water in a symmetric wedge is calculated using the formula E = mgh, where m is the mass of the water, g is the acceleration due to gravity, and h is the height of the water. The discussion highlights the challenge of integrating the varying cross-section of the wedge, which increases linearly from 0 to A as the height h increases. The solution involves determining the center of gravity of the triangular cross-section to facilitate the integration process. The correct potential energy expression for the wedge is derived from understanding the geometry of the water's distribution.

PREREQUISITES
  • Understanding of potential energy concepts in physics
  • Knowledge of integration techniques in calculus
  • Familiarity with the geometry of triangular shapes
  • Basic principles of fluid mechanics
NEXT STEPS
  • Study the integration of variable cross-sectional areas in calculus
  • Learn about the center of mass calculations for triangular shapes
  • Explore potential energy calculations in different geometric configurations
  • Review fluid mechanics principles related to pressure and buoyancy
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Students studying physics, particularly those focusing on mechanics and fluid dynamics, as well as educators looking for examples of potential energy calculations in non-standard geometries.

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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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