What Is the Correct Approach to Find the Centroid of a Parabolic Area?

In summary, the problem is to find the centroid of a parabolic area. The solution involves setting up an integral and using the relationship between the point (b,h) and the curve to solve for the centroid coordinates, which are (3/8b, h/2).
  • #1
jesuslovesu
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[SOLVED] Centroid Parabolic area

Homework Statement


http://img227.imageshack.us/img227/7518/slowge9.th.jpg
Find the centroid of the area.

Homework Equations


The Attempt at a Solution



I'm not quite sure what I'm screwing up on this problem, I can do other problems like when y = x^2. I have only shown my work for the x centroid, but I can't seem to get the answer (3/8b). Does anyone see where I messed up, I assume it's somewhere in the integral setup. I think dA = h-y dx is correct.
 
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  • #2
The point (b,h) lies on the curve. Doesn't that suggest something, like a relationship between them, which you can put in the answer?
 
  • #3
Thanks for your reply, I figured it out
 
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1. What is a centroid in relation to a parabolic area?

A centroid is the geometric center of a shape or object. In the case of a parabolic area, it is the point of balance or equilibrium where the shape would balance perfectly on a needle.

2. How is the centroid calculated for a parabolic area?

The centroid of a parabolic area can be calculated using the formula (2a/3h, 8a/15), where a is the length of the semi-major axis and h is the height of the parabola.

3. What is the significance of the centroid in a parabolic area?

The centroid represents the point of balance or equilibrium for the parabolic area. It is also used in engineering and architecture to determine the stability and strength of structures.

4. Can the centroid of a parabolic area be outside of the shape?

No, the centroid will always be located within the boundaries of the parabolic area as it is the point of balance for the shape.

5. How does the centroid of a parabolic area differ from other geometric shapes?

The centroid of a parabolic area is unique in that it is not located at the center of the shape, as is the case with other symmetrical shapes. It is also not always located on the axis of symmetry, making it more challenging to locate without using mathematical formulas.

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