(13%) Problem 3: Three beads are placed on the vertices of an equilateral triang

Question

(13%) Problem 3: Three beads are placed on the vertices of an equilateral triangle of side d = 3.3 cm. The first bead of mass m1 = 145 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- 85 g is placed on the right vertex. im ©theexpertta.com 25% Part (a) write a symbolic equation for the horizontal component of the center of mass relative to the left vertex of the triangle Grade Summary Kom- 0% 100% Submissions Attempts remaining: 3 detailed view per attempt) 123 0 DELCLEAR Submit I give up! Hints: 5% deduction per hint. Hints remaining: 2 Feedback: 5% deduction per feedback.

Explanation / Answer

a)

x1 = d/2 , x2 = 0 , x3 = d

X-coordinate of center of mass is given as

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

b)

X = (0.145 (0.033/2) + (0.055) (0) + (0.085) (0.033)) /(0.145 + 0.055 + 0.085)

X = 0.018 m = 1.8 cm

c)

y1 = d Sin60   , y2 = 0 , y3 = 0

Y-coordinate of center of mass is given as

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

Y = (m1 d Sin60 + m2 (0) + m3 (0) )/ (m1 + m2 + m3 ) = m1 d Sin60 / (m1 + m2 + m3 )

d)

Y = m1 d Sin60 / (m1 + m2 + m3 ) = 0.145 (0.033) Sin60 / (0.145 + 0.055 + 0.085) = 0.015 m = 1.5 cm

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