Find m1's coordinates using center of mass equation | Extended Object"

[dgx]

1. The coordinates of the center of mass for the extended object shown in the figure are (L/4, −L/5). What are the coordinates of m1? (Assume m1 = 7 kg, m2 = 3 kg, and m3 = 5 kg. Use any variable or symbol stated above as necessary.)



2.



3. I too the centroid cordinates and substracted them from each corresponding x and y value in each coordinate. Then, distributed the mass to each corresponding coordinate...ie 7(x,y) = (7x,7y), then solved for x and y. My answer was (L/7, -21L/10). But its wrong. Anybody have any insight?

 

[ap123]

Hello dgx!
Can you upload the diagram for us?

 

[dgx]

http://www.tiikoni.com/tis/view/?id=b95408f

http://www.tiikoni.com/tis/view/?id=b95408f

thanks

 

[ap123]

Use the definition of the centre of mass.
You will get 1 equation for the x-direction and 1 for the y-direction.
Each of these equations will only have 1 unknown.

If you post your working we can see what you did.

 

[Nickie]

I would first like to clarify that the coordinates given in the problem statement are the coordinates of the center of mass for the extended object, not the centroid. The center of mass and centroid are not necessarily the same point for an extended object.

To find the coordinates of m1, we can use the center of mass equation:

x = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3)

y = (m1y1 + m2y2 + m3y3) / (m1 + m2 + m3)

Substituting the given values, we get:

x = (7*L/4 + 3*L/2 + 5*L/4) / (7 + 3 + 5) = (15*L/4) / 15 = L/4

y = (-7*L/5 + 3*L/5 + 5*L/5) / (7 + 3 + 5) = L/5

Therefore, the coordinates of m1 are (L/4, L/5).

I am not sure how you arrived at your answer of (L/7, -21L/10), but it seems like there may have been a mistake in your calculations. I hope this explanation helps.