• Support PF! Buy your school textbooks, materials and every day products Here!

Center of mass problem?

  • Thread starter vac
  • Start date
  • #1
vac
28
0

Homework Statement



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

Uploaded with ImageShack.us

Homework Equations


Where is the COM of the figure? (width = 8, height = 8)


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:

Answers and Replies

  • #2
662
307
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
vac
28
0
Can you please elaborate more or give me an example.
 
  • #4
662
307
What is the formula for center of mass?
 
  • #5
gneill
Mentor
20,793
2,773
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
vac
28
0
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
vac
28
0
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?
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
gneill
Mentor
20,793
2,773
Yes I listed above.

A of circle = pi * 0.5^2
A of rectangle = 2.5*1
A of rectangle = 2.5*0.5
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
662
307
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.
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
vac
28
0
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?
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
vac
28
0
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.
[*]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
662
307
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
662
307
  1. Can you find out CM of the figure without any holes (geometrically)?
    I think it is (x,y) should be (4,4) right?
  2. Can you find out the individual CM of the shapes that fit into the holes (geometrically)?
  3. rectangle one is (0.5, 1.25)
  4. rectangle tow is (0.25, 1.25)
  5. Can you after all this express the actual CM in terms of these? (Think in terms of the formula.)
  6. I don't know?
Where is your origin? It should be same for all figures.
And the first one's wrong...
 
  • #14
vac
28
0
I took each piece and put it bottom left corner (x,y) (0,0) origin.
 
  • #15
20,131
4,208
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
gneill
Mentor
20,793
2,773
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
20,131
4,208
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?
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
gneill
Mentor
20,793
2,773
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
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.
 

Related Threads on Center of mass problem?

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
12
Views
3K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
9
Views
5K
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
14
Views
3K
  • Last Post
Replies
2
Views
5K
Top