# Math Project

Topics: Mathematics, Rotation, Archimedes Pages: 2 (284 words) Published: April 29, 2013
The physics behind a dam

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The Clc πrtes

The Clc πrtes
Marlon Arriaza- Wrote the paper.
Achraf Derdak- Solved the problem, presenter.
Mohammad Elhocheimi- Solved the problem, presenter.
Shan Li- PowerPoint.
Jie Li- PowerPoint.

Set-up
Mathematics explains all aspects of engineering and economics. By calculating the minimum width necessary to hold back the large amounts of water that come with the building of a dam, one can figure out the minimum cost necessary for building it. Problem

You are being paid \$10 million to design a new dam. You decide to make the front Of the dam in the shape of a parabola and the back of the dam (i.e. that will contact the water) vertical. The dam is to be made of concrete with a density of2.50 g/cc, have a height of H = 100 m and retain water that will reach the top of the dam. Find: (a) The width of the dam, w, that will allow the torque of gravity to balance the torque from the pressure of the water behind the dam, using the lower front edge of the dam as the axis of rotation; (b) The value of “a” in the expression that describes the shape of the face of the dam

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Questions
1) What would be the minimum width if the dam was made from gold, which has a density of 19.3g/cc, and height of 50 cm instead of concrete, in order for the pressure of water not to break the dam?

2) If the price of concrete is \$3.50 per square foot, what would be the cost of building the dam from the original problem?

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