How Can I Find the Center of Gravity for a Uniformly Distributed Mass?

[bmandrade]

Homework Statement

i need to find the center of gravity of the attached shape

Homework Equations

i know that in order to find center of gravity i can use the equation $$\Sigma$$m_ix_i$$/$$$$\Sigma$$m_i but for the case it doesn't work becasue i don't have mass of this shape it just says that the mass is uniformly distributed

The Attempt at a Solution

I have no clue how to solve it

 

[PhanthomJay]

Find the centroid of the shape using areas instead of mass. When the mass is uniformly distributed, the results are the same. Or you could just assume a mass density of m per sq.cm, and the m's will cancel, right?

 

[thomate1]

.

I would recommend using the principle of moments to find the center of gravity of the attached shape. This principle states that the sum of the moments of all the forces acting on a body is equal to zero at the point of equilibrium, which is the center of gravity.

To apply this principle, you can divide the shape into smaller, simpler shapes and find the center of gravity for each of them. Then, using the principle of moments, you can find the overall center of gravity for the entire shape.

Another option is to use the concept of symmetry. If the shape is symmetrical, the center of gravity will be located at the point of symmetry. This can help simplify the calculation process.

Additionally, if you know the dimensions and material properties of the shape, you can use the equations for moments and centroids to find the center of gravity.

In summary, while the equation \Sigmamixi/\Sigmami may not be applicable in this case, there are other methods and principles that can be used to find the center of gravity of the attached shape.