Three heads are placed on the vertices of an equilateral triangle of side d = 2.

Question

Three heads are placed on the vertices of an equilateral triangle of side d = 2.6 cm. The first bead of mass m_1 = 1.30 g is placed on the top vertex. The second head of mass m_2 = 45 g is placed on the left vertex. The third bead of mass m_3 = 75 g is placed on the right vertex. Write a symbolic equation for the horizontal component of the center of mass relative to the left vertex of the triangle. Find the hot octal component of the center of mass relative to the left vertex, in centimeters. Write .a symbolic equation for the vertical component of the center of mass relative to the base of the triangle. Find the vertical component of the center of mass relative to the base of the triangle, in centimeters.

Explanation / Answer

(a)
Horizontal Component = (m2*0 + m1 * d/2 + m3*d)/(m1+m2+m3)

(b)
Substituing Values,
Horizontal Component =  (45*0 + 130 * 2.6/2 + 75*2.6)/(130+45+75)
Horizontal Component = 1.456 cm

(c)
Vertical Distance of m1 = sqrt(d^2 - (d/2)^2) = sqrt(d^2 - d^2/4) = d*sqrt(3)/2 = 0.866 d

Vertical Component = (m2*0 + m1*0.866d + m3*0)/(m1+m2+m3)

(d)
Substituing Values,
Vertical Component = (45*0 + 130*0.866*2.6 + 75*0)/(130+45+75)
Vertical Component = 1.17 cm

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