(6%) Problem 13: Three beads are placed on the vertices of an equilateral triang

Question

(6%) Problem 13: Three beads are placed on the vertices of an equilateral triangle of side d-24 cm-The first bead of mass ml-120 g is placed on the top vertex. The second bead of mass m2 = 55 g is placed on the left vertex. The third bead of mass m3 75 g is placed on the right vertex. Otheexpertta.e 25% Part (a) Write a symbolic equation for the horizontal component of the center of mass relative to the left vertex of the triangle. 25% Part (b) Find the horizontal component of the center of mass relative to the left vertex in centimeters. 25% Part (c) write a symbolic equation for the vertical component of the center of mass relative to the base of the triangle. 25% Part (d) Find the vertical component of the center of mass relative to the base of the triangle, in centimeters. " Grade Summary Deductions Pntential cm

Explanation / Answer

a)

X = (m1 x1 + m2 x2 + m3 x3)/(m1 + m2 + m3)

b)

x2 = 0 , x1 = d/2 = 2.4 /2 = 1.2 cm = 0.012 m, x3 = 2.4 cm = 0.024 m

m1 = 120, m2 = 55 g , m3 = 75 g

X = (120 (1.2) + 55 (0) + 75 (2.4))/(120 + 55 + 75)

X = 1.3 cm

c)

Y = (m1 y1 + m2 y2 + m3 y3)/(m1 + m2 + m3)

d)

y2 = 0 , y1 = d sqrt(3)/2 = 0.87 x 2.4 cm = 2.1 cm, y3 = 0 cm

m1 = 120, m2 = 55 g , m3 = 75 g

Y = (120 (2.1) + 55 (0) + 75 (0))/(120 + 55 + 75)

Y = 1.01 cm

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