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J-dizzal
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Homework Statement
Find the coordinates of the centroid of the uniform area.
Homework Equations
equations for centroid coordinates at the top of my paper.
(2/3k)(58.1)Dr. Courtney said:How does k go from the denominator to the numerator of your integrals as you are evaluating them?
Nathanael said:In one of your steps you basically said ##\sqrt{\frac{y}{k}} =\frac{1}{k}\sqrt{y}##
Also Dr. Courtney's point still stands... it's not 2/3k it's 2/(3k)
Wouldnt it be easier to integrate with respect to y, because of the shaded region is above the curve.Nathanael said:38.7/k is still not right. It should be 38.7/√k
When you find the x-coordinate of the centroid, you should be integrating with respect to x.
The "dA" in the formula ##\bar x=\frac{1}{A}\int xdA## is the area of the thin strip between x and x+dx.
##\bar x=\frac{1}{A}\int xdA##Nathanael said:It's not about what is easier, it's simply wrong.
When you integrate with respect to y, you are taking horizontal strips of area, right? Well when you find the x-coordinate of the centroid you want to take vertical strips of area. The reason for this is that you want to take strips of area which all have the same x-value, and then multiply them by that x-value. You just can't do this when you integrate w.r.t. y.
kx2dx is the area under the curve. Try to figure out a way to find the area above the curve.J-dizzal said:##\bar x=\frac{1}{A}\int xdA##
= ##1/2 \int kx^3dx## does this look ok?
The centroid of a uniform shape is the point at which the shape would balance if it were placed on a pin or support at that point.
The centroid of a uniform shape is calculated by finding the average of the coordinates of all the points that make up the shape.
The centroid represents the center of mass or center of gravity of the shape. It is the point where the entire weight of the shape can be considered to act.
No, the centroid will always be located within the boundaries of the shape. It may lie on the edge of the shape if the shape is not symmetrical.
The centroid is used in engineering and design to determine the stability and balance of structures and objects. It is also used in calculating moments of inertia and in the design of structures with equal weight distribution.