Find center of mass of planar quadrilateral

[toforfiltum]

Homework Statement

Consider the planar quadrilateral with vertices (0, 0), (2, 0), (1, 1) and (0, 1). Suppose that it has constant density. What is its center of mass?

Homework Equations

The Attempt at a Solution

Since it has constant density, could I assume that the center of mass would be the same as if I put 4 equal masses on the vertices and calculate the center of mass that way? Like $\bar x= \frac {m_1x_1+...+m_nx_n}{m_1+...m_n}$ and same for $\bar y$?

Thanks!

 

[LCKurtz]

Homework Statement

Consider the planar quadrilateral with vertices (0, 0), (2, 0), (1, 1) and (0, 1). Suppose that it has constant density. What is its center of mass?

Homework Equations

The Attempt at a Solution

Since it has constant density, could I assume that the center of mass would be the same as if I put 4 equal masses on the vertices and calculate the center of mass that way? Like $\bar x= \frac {m_1x_1+...+m_nx_n}{m_1+...m_n}$ and same for $\bar y$?

Thanks!

No. But you could break up the region into two pieces and put the mass of each piece at its center of mass and calculate from there.

 

[toforfiltum]

No. But you could break up the region into two pieces and put the mass of each piece at its center of mass and calculate from there.

How do I find the center of mass of the half piece?

 

[LCKurtz]

How do I find the center of mass of the half piece?

The center of mass of a rectangle is at its center and the center of mass of a triangle is at the intersection of its medians. Or you could just use the standard calculus formulas and calculate the center of mass of the region directly.