Final answer:
The center of mass of an equilateral triangle coincides with the centroid, located at a height of h/3 from the base, where h is the overall height of the triangle and can be calculated using the formula h = (sqrt(3)/2)*s for a triangle of side length s.
Step-by-step explanation:
To find the center of mass of an equilateral triangle, you can consider the symmetrical nature of the shape. In an equilateral triangle, the center of mass will coincide with the centroid, which is found by drawing lines from each vertex to the midpoint of the opposite side. These lines, known as medians, will intersect at the centroid. The centroid divides each median in a 2:1 ratio, with the longer segment adjacent to the vertex.
If we assume that an equilateral triangle has a uniform mass distribution, then the center of mass will be located at the centroid. For a triangle with side length s, the distance from each vertex to the center of mass (which is also the height of the triangle) can be calculated using the formula for the height of an equilateral triangle, which is h = (sqrt(3)/2)*s. Therefore, the center of mass is h/3 from the base along the median.
To solve the problem in Example 12.6, you would place the pivot at the calculated center of mass to show that the net torque about the center of mass is zero, which is consistent with a system in equilibrium.