Distance Between Center Of Masses

[Warmacblu]

Homework Statement

A circular hole of diameter 26.4 cm is cut out of a uniform square of sheet metal having sides 52.8 cm.

Note - The circle is located at the top right of the square.

What is the distance between the center of mass and the center of the square?

Homework Equations

x_cm = E(m_nx_n) / Em_n

The Attempt at a Solution

I don't really know where to start this one. Do I have to solve for the center off mass for the uncut square then the circle and subtract the two values?

 

[Andrew Mason]

Try looking at this as a square with a circle of negative mass superimposed on it.

AM

 

[Warmacblu]

Try looking at this as a square with a circle of negative mass superimposed on it.

AM

I understand the concept of a square with a circle of negative mass but I don't really know how to approach the problem. I think I should find the center of mass of the square and then the center of mass for the circle and subtract the two values. The center of mass on the square will be somewhere in the bottom left corner.

 

[Andrew Mason]

I understand the concept of a square with a circle of negative mass but I don't really know how to approach the problem. I think I should find the center of mass of the square and then the center of mass for the circle and subtract the two values. The center of mass on the square will be somewhere in the bottom left corner.

You can treat the square and the circle as a point masses located at their respective centres of mass. You can use symmetry to determine where the centres of mass of the circle and square are located. Then is it is just a matter of applying the definition of centre of mass to find the centre of mass of those two combined masses (using the centre of the square as the origin):

(1) $$R = \frac{\sum m_ir_i}{\sum m_i} = \frac{(M_cR_c + M_s x 0)}{M_c + M_s}$$

AM