Finding center of mass of a right triangle

AI Thread Summary
To find the center of mass of a right triangle with base length 1 and height 2, and a total weight of 5 kg, one can use the area formula for a triangle, A = (1/2) * base * height. The center of mass for a uniform density triangle coincides with its centroid, which can be calculated using standard formulas found in statics resources. Since the triangle is right-angled, the centroid is located at the coordinates (1/3, 1/6) from the right angle vertex. The problem involves integral calculus for more complex shapes, but for this triangle, the centroid provides a straightforward solution. Understanding these concepts is essential for solving similar problems in physics and engineering.
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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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.
 

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