Potential Energy of water in a wedge

In summary, the problem involves a symmetric wedge filled with water and asks for the potential energy of the water with respect to the base. The potential energy can be calculated using the equation E = mgh, where m is the mass of the water, g is the acceleration due to gravity, and h is the depth of the wedge. However, there may be a mental block in integrating the equation, as the horizontal cross-section increases linearly from 0 to A as h increases from 0 to h. Another question that may help solve the problem is the location of the center of gravity of the triangle and its distance from the base.
  • #1
irkutsk
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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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  • #2
How about this: Where is the center of gravity of this triangle, and how far above the base is it?
 

FAQ: Potential Energy of water in a wedge

What is potential energy of water in a wedge?

Potential energy of water in a wedge refers to the amount of energy that is stored in the water when it is held at an elevated position in a wedge-shaped container. This energy is a result of the gravitational pull on the water and can be released when the water is allowed to flow downward.

How is potential energy of water in a wedge calculated?

The potential energy of water in a wedge can be calculated using the formula PE = mgh, where m is the mass of the water, g is the acceleration due to gravity, and h is the height of the water in the wedge. This formula takes into account the gravitational potential energy of the water at a particular height in the wedge.

What factors affect the potential energy of water in a wedge?

The potential energy of water in a wedge is affected by the mass of the water, the height of the water, and the acceleration due to gravity. Additionally, the shape and angle of the wedge can also impact the potential energy of the water as it can affect the height and distribution of the water in the container.

How does the potential energy of water in a wedge compare to other forms of potential energy?

The potential energy of water in a wedge is a form of gravitational potential energy, similar to the potential energy of an object held at a height. However, it is unique in that it is stored in a liquid rather than a solid object. It can also be harnessed and converted into other forms of energy through the use of turbines and other technologies.

What are some real-world applications of potential energy of water in a wedge?

The potential energy of water in a wedge has various real-world applications, such as in hydroelectric power generation. Water is stored at an elevated position in a dam, and its potential energy is used to turn turbines and generate electricity. It is also used in irrigation systems and water transportation, where the potential energy of the water is used to move and transport goods. Additionally, it can be utilized in everyday activities such as filling a water bottle or swimming pool.

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