College Physics- Center of Mass?

Question

The objects in the figure below are constructed of uniform wire bent into the shapes shown (Figure 1) . Each peice has a length of 0.15 .

There are two objects that we need to figure out the x- and y-coordinates of the center of mass of the object . Assume the origin to be at the bottom left point.

Help please

1. the first object is like a l_l the wires are connected in this exact shape.

2. is the shape of L

3. is an equilateral triangle.

Remember each side is 0.15m .. help me please

Answer 1

1. On axis of symmetry midway between vertical wires and 0.05 m above bottom wire.

2. Along a 45 degree from the corner of the L. 0.0375 m to the right of and 0.0375 m above the corner.

3. At the center of the triangle. (The center of symnmetry where the angle bisectors intersect.)

Answer 2

Yes but how do we go about this.

Let me show you what I did for l_l

Answer 3

r(C) = Σ{r(i) •m(i)}/Σm(i)
Assume the origin to be at the bottom left point and the mass of each part is ’m’

1. X(C) ={ 0+(L/2)+L}m/3m = L/2
Y(C) = { (L/2) +0+(L/2)}m/3m = L/3
C= (L/2; L/3) = (0.075;0.05).

2. X(C) ={ 0+(L/2)}m/2m = L/4
Y(C) = { (L/2) +0}m/2m = L/4
C= (L/4; L/4) = (0.0375;0.0375).

3. X(C) ={ L/2•cos60°)+(L/2)+(L- L/2•cos60°)}m/3m = L/2
Y(C) = { (L/2•sin60°) +0+(L/2•sin60°))}m/3m = 0.29L
C= (L/2; L/3) = (0.075;0.0435).