Centre of mass of of an isosceles Triangle

In summary, the conversation discusses a problem involving a uniform triangular lamina with an axis of symmetry at y=4. One of the vertices is given as (2,1) and the x-coordinate of the centre of mass is to be found. The conversation provides a hint to begin with a sketch and to use the formula for finding the centre of mass. It is mentioned that the y-coordinate of the centre of mass will be 4, and the third vertex will lie on y=4. The conversation also mentions the reflection of one vertex on y=4 and finding the x-coordinate of the third vertex.
  • #1
aurao2003
126
0

Homework Statement


Hi
I am really stuck on this problem. It reads as such:
A uniform triangular lamina is isocceles and has the line y= 4 as its axis of symmetry. One of the vertices of the triangle is the point (2,1). Given that the x-co-ordinate of the centre of mass of the lamina is -3, find the co-ordinates of the other two vertices.

I am not sure where to begin. Any hints or guides please?



Homework Equations


Centre of mass = (X1 +x2+X3/3, Y1+Y2+Y3/2)



The Attempt at a Solution

 
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  • #2
Try starting with a sketch.
 
  • #3
vela said:
Try starting with a sketch.
Thanks. I will commence ze sketch!
 
  • #4
the Y-coordinate of COM will be 4, as it will lie on y=4, the axis of symmetry. now proceed. one of the vertices will be the reflection of (2,1) on y=4. the third one will lie on y=4, just find the x coordinate of that.
 
  • #5
supratim1 said:
the Y-coordinate of COM will be 4, as it will lie on y=4, the axis of symmetry. now proceed. one of the vertices will be the reflection of (2,1) on y=4. the third one will lie on y=4, just find the x coordinate of that.
Let me try it. Thanks!
 
  • #6
aurao2003 said:
Let me try it. Thanks!

welcome...so did it work?
 
  • #7
supratim1 said:
welcome...so did it work?
Sorry! I will let you know tonight. I have 5 exams between now and monday. All A2! Cheers!
 
  • #8
ok..all the best!
 

1. What is the formula for finding the centre of mass of an isosceles triangle?

The formula for finding the centre of mass of an isosceles triangle is (1/3)h, where h is the height of the triangle.

2. How is the centre of mass of an isosceles triangle different from that of a regular triangle?

The centre of mass of an isosceles triangle is located on the line of symmetry, while the centre of mass of a regular triangle is located at the intersection of the medians.

3. Can the centre of mass of an isosceles triangle be located outside of the triangle?

No, the centre of mass of an isosceles triangle will always be located within the boundaries of the triangle.

4. How does the location of the centre of mass of an isosceles triangle affect its stability?

The closer the centre of mass is to the base of the triangle, the more stable the triangle will be. If the centre of mass is located too far from the base, the triangle may be more prone to tipping over.

5. Can the centre of mass of an isosceles triangle change?

Yes, the centre of mass of an isosceles triangle can change if the dimensions of the triangle change. For example, if the height or base length of the triangle is altered, the centre of mass will also be affected.

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