Finding center of mass of a right triangle

In summary, to find the center of mass for a triangle with side lengths of 1 and 2 and a total weight of 5kg, you will need to use the formula for the centroid of area. This involves using integrals for each dimension, but for a uniform density and gravitational field, the center of mass will be equal to the centroid of area. These formulas can be found in any statics book or online.
  • #1
vande060
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Homework Statement



Find the center of mass for the following triange:

http://www.ehow.com/how_5132033_calculate-hypotenuse.html

above is a picture of a triangle, it is a right triangle

the side labeled a in the picture is a length of 1 and side b is length of 2, the total weight of the triangle is 5kg.



Homework Equations



a = bh*1/2



The Attempt at a Solution



I don't know much about where to begin, except for that this problem is an integral problem, somehow involving the area of a triangle formula, and the formula for density.
 
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  • #2
Yes, its technically an integral. Actually one integral for each dimension x & y,
but for a uniform density and gravitational field, the center of mass will be equal to the centroid of area. These formulas for a triangle are quite common and should be able to be found in any statics book or online easily.
 

What is the center of mass of a right triangle?

The center of mass of a right triangle is the point where the mass of the triangle is evenly distributed, meaning that the triangle would balance perfectly if placed on a pivot at that point.

How do you find the center of mass of a right triangle?

To find the center of mass of a right triangle, you need to locate the midpoint of each side of the triangle. Then, draw lines connecting the midpoints to the opposite vertices. The intersection of these lines is the center of mass.

Why is it important to find the center of mass of a right triangle?

Finding the center of mass of a right triangle can help determine how the triangle will behave when subjected to external forces, such as when it is rotating or being used as a support structure.

Can the center of mass of a right triangle be outside the triangle?

No, the center of mass of a right triangle will always lie within the triangle. This is because the triangle is a closed shape and all the mass is contained within its boundaries.

How does the center of mass of a right triangle relate to its centroid?

The center of mass and the centroid of a right triangle are the same point. The centroid is the geometric center of the triangle, and the center of mass is the point where the mass is evenly distributed. In a right triangle, these two points coincide.

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