# Center of mass problem?

1. Oct 15, 2013

### vac

1. The problem statement, all variables and given/known data

http://img9.imageshack.us/img9/2866/siyx.png [Broken]

2. Relevant equations
Where is the COM of the figure? (width = 8, height = 8)

3. The attempt at a solution
area of triangle: 0.5(8*8) = 32
32 - (pi(0.52) - (2.5*1) - (2.5*0.5) = 27.4646

I don't have an axes to locate the center of mass. How do I solve a problem like this?
Thanks.

Last edited by a moderator: May 6, 2017
2. Oct 15, 2013

### Enigman

Equation for center of mass?
(equate it with c.o.m. in terms of - c.o.m. of whole triangle, c.o.m. circle, c.o.m. rectangle 1, c.o.m. rectangle 2.)

3. Oct 15, 2013

### vac

Can you please elaborate more or give me an example.

4. Oct 15, 2013

### Enigman

What is the formula for center of mass?

5. Oct 15, 2013

### Staff: Mentor

Are there any vertical placement measurements for the cutouts? How do we know how high the circle is positioned, or rectangles? How long are the rectangles?

6. Oct 15, 2013

### vac

All I know is this formula: Mcmx = (m1x1 + m2x2 ... mnxn)/(m1+m2...mn) where x can be x,y, or z.
It does not help me that much in this problem.

7. Oct 15, 2013

### vac

Yes I listed above.

A of circle = pi * 0.5^2
A of rectangle = 2.5*1
A of rectangle = 2.5*0.5

8. Oct 15, 2013

### Staff: Mentor

Okay, but how high are these items from the bottom of the triangle? Their exact placement matters.

And it appears to me from the diagram that the two rectangular cutouts are the same width, so why are you giving one as 2.5*1 and the other 2.5*0.5?

9. Oct 15, 2013

### Enigman

Okay, vector format would have been better but we can work with this. Just need to work out x and y coordinates separately.
1. Can you find out CM of the figure without any holes (geometrically)?
2. Can you find out the individual CM of the shapes that fit into the holes (geometrically)?
3. Can you after all this express the actual CM in terms of these? (Think in terms of the formula.)
Note that you will need all the values specifying their placement....like gneill just said.

10. Oct 15, 2013

### vac

I don't have the exact placement for the cutouts.
I am positive that the two rectangular cutouts are not the same. I agree with you that they look somewhat same size (the height is the same), but the with is for one is 1 and for the other is 0.5. You can verify that from the diagram provided above.

11. Oct 15, 2013

### vac

[*]Can you find out CM of the figure without any holes (geometrically)? I think it is (x,y) should be (4,4) right?
[*]Can you find out the individual CM of the shapes that fit into the holes (geometrically)?
rectangle one is (0.5, 1.25)
rectangle tow is (0.25, 1.25)
[*]Can you after all this express the actual CM in terms of these? (Think in terms of the formula.)
I don't know?

12. Oct 15, 2013

### Enigman

mmm...I think 0.5 is the height at which rectangles are.
2.5 the length is given horizontally too, besides the question can't be solved if we don't know height we can't solve for CM...

13. Oct 15, 2013

### Enigman

Where is your origin? It should be same for all figures.
And the first one's wrong...

14. Oct 15, 2013

### vac

I took each piece and put it bottom left corner (x,y) (0,0) origin.

15. Oct 15, 2013

### Staff: Mentor

You should have listened to Gneill, so I'll say it again. You can't do this problem if you don't know how far above the base of the triangle the centers of the rectangular cutouts and the center of the circular cutout are located. Secondly, the two rectangular cutouts are identical. When the figure says "centered from both sides," it means that the figure is symmetrical about the vertical centerline of the triangle. You misread the figure when you thought that the base of one of those rectangles is 0.5. Look at the figure again. Both triangles have a base of 1.0, as required if the figure is symmetric.

16. Oct 15, 2013

### Staff: Mentor

A question for vac: Were you given just the figure and a ruler to work with? In other words, are you expected to take your own measurements directly from the figure?

17. Oct 15, 2013

### Staff: Mentor

It doesn't seem like this could be the case. The figure implies that the altitude and base of the triangle are both 8 units. Yet, the figure as drawn looks like an equilateral triangle. So the figure could not be to scale.

Chet

18. Oct 15, 2013

### Staff: Mentor

I agree that the diagram is not very accurate. I find that if I cut and paste it into a drawing program and scale it so that the base is as close as I can estimate it to 8 cm, then the height of the triangle is just short of 8 cm: About 0.37 cm short. So about 5% off. Mind you, the circular cutout as drawn is then considerably bigger than a 0.5 cm radius indicated.

I think we need more details about the actual problem statement as it was presented to the OP.