Problem: An 800 g steel plate has the shape of the isosceles triangle shown in figure P12.53. What are the x-and y- coordinates of the center of mass?

FREE Expert Solution

The first thing is to divide the triangle into vertical strips of width dx and mass dm. Let's consider one strip, whose center is at a distance x-from the origin.

Area of the triangle is given by:

A = (1/2)bh = (1/2)(20 × 10-2)(30 × 102) = 0.03 m2 

Let the length of the small strip be l.

The area of this strip is expressed as:

dA = l·dx

The mass of the strip/the element is:

dm = (M/A)dA = (800 × 10-3/0.03)ldx = 26.67 l·dx kg/m2 

From proteries of similar triangles:

l/20 = x/30

l = (20/30)x = (2/3)x

Substituting to the expression of dm:

dm = (26.67)(2/3)x dx

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Problem Details

An 800 g steel plate has the shape of the isosceles triangle shown in figure P12.53. What are the x-and y- coordinates of the center of mass?

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Our tutors have indicated that to solve this problem you will need to apply the Center of Mass By Integration concept. If you need more Center of Mass By Integration practice, you can also practice Center of Mass By Integration practice problems.