A-Three 90.4 gram masses are connected in a triangular shape by massless rigid w

Question

A-Three 90.4 gram masses are connected in a triangular shape by massless rigid wires as shown in the first image (which is not drawn to scale). The coordinates of each mass are given in centimeters. Find the x and y coordinates of the center of mass of the triangular object.

ng leaming Three 90.4 qram masses are connected in a triangular shape by massless rigid wires as shown in the first image (which is not drawn to scale), The coordinates of each mass are given in centimeters. Find the x and y coordinates of the center of mass of the triangular object Gr De Pc (13.2, 165) 2 (17.3, 13.4) Yc Number Number Yc cmi cm e m (0,0) + x 5) (0, 43.6) (0,43.6) (2 Th Two more 90.4 gram masses are connected by a straight piece of wire and affixed to the original configuration as shown. Find the x and y coordinates of the new center of mass of the combined object 3 or Number Number c m c m CAT 140:-43 6)

Explanation / Answer

(A)
X cordinate of C.O.M = (m1x1 + m2x2 + m3x3)/(m1+m2+m3)
X cordinate of C.O.M = 90.4 * (x1 + x2 + x3 ) / (3 * 90.4)
X cordinate of C.O.M = (x1 + x2 + x3 )/ 3
X cordinate of C.O.M = (0 + 17.3 + 13.2) / 3
X cordinate of C.O.M = 10.17 cm

Similarly -
Y cordinate of C.O.M = (y1 + y2 + y3 )/ 3
Y cordinate of C.O.M = (0 + 13.4 + 16.5) / 3
Y cordinate of C.O.M = 9.97 cm

(B)
Now,
We can say we have Three masses,
M = m1+m2+m3 = 3*90.4 g @ (10.17, 9.97)
m4 = m5 = 90.4 g

New Cordinates of C.O.M =

X cordinate of C.O.M = (Mx + m4x4 + m5x5)/(M+m4+m5)
X cordinate of C.O.M = 90.4 * (3*x + x4 + x5 ) / (3 * 90.4 + 2 * 90.4)
X cordinate of C.O.M = (3*x + x4 + x5 )/ 5
X cordinate of C.O.M = (3*10.17 + 0 + 0) / 5
X cordinate of C.O.M = 6.1 cm

Similarly -
Y cordinate of C.O.M = (3*y + y4 + y5 )/ 5
Y cordinate of C.O.M = (3*9.97 + 43.6 - 43.6) / 5
Y cordinate of C.O.M = 5.982 cm

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