Center of mass of a triangle

In summary, a 60 cm length of uniform wire with a mass of 60 g is bent into a right triangle. The x- and y-coordinates of the center of mass are calculated to be (8,3.33) using the points of each corner and the average at each point. This is confirmed to be correct.
  • #1
preluderacer
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0

Homework Statement



In the figure, a 60 cm length of uniform wire, of 60 g mass, is bent into a right triangle. The x- and y-coordinates of the center of mass, in cm, are closest to... I am going to explain the picture in my textbook.

The origin is at (0,0). It goes up 10 cm and to the right 24cm. The hyp is 26 cm


The Attempt at a Solution



What I did was get the points of a,b and c of each corner. Then I calculated average at each point. a = (0,0) b = (24,0) c= (0,10). In the x direction I got (0+24+0)/3 = 8 and the y direction I got (0+0+10)/3 = 3.33. So the center of mass is at (8,3.33). Does this look right?
 
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  • #2
Yes, it is correct.

ehild
 

What is the definition of center of mass of a triangle?

The center of mass of a triangle is a point that represents the average location of the mass of the triangle. It is the point at which the triangle would balance if it were suspended at that point.

How is the center of mass of a triangle calculated?

The center of mass of a triangle is calculated by finding the average of the x and y coordinates of the triangle's vertices. This can be done by using the formula x̅ = (x1 + x2 + x3)/3 and ȳ = (y1 + y2 + y3)/3, where (x1,y1), (x2,y2), and (x3,y3) are the coordinates of the vertices.

Why is the center of mass of a triangle important?

The center of mass of a triangle is important because it helps in understanding the stability and balance of the triangle. It also has applications in fields such as engineering, physics, and astronomy.

Does the location of the center of mass affect the stability of a triangle?

Yes, the location of the center of mass affects the stability of a triangle. If the center of mass is located at the base of the triangle, it will be more stable than if it is located towards the top. This is because the lower the center of mass, the less likely the triangle is to topple over.

How does the center of mass of a triangle change with different shapes and sizes?

The center of mass of a triangle changes with different shapes and sizes because it is dependent on the distribution of mass within the triangle. For example, a triangle with a larger base will have a lower center of mass compared to a triangle with a smaller base. Similarly, a triangle with a greater concentration of mass towards one side will have a center of mass closer to that side.

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