Three 81.5 gram masses are connected in a triangular shape by massless rigid wir

Question

Three 81.5 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.

Three 81.5 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. (12.2, 21.5) 2 (18.3, 11.4) Number Number cm cm + x (0, 0) 5) (0, 30.1) 2 Two more 81.5 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. Number cm em 4 (0, -30.1)

Explanation / Answer

let,

mass m1=m2=m3= m=81.5g

and

m1 position is (x1, y1)=(0, 0)

m2 position is (x2, y2)=(12.2, 21.5)

m3 position is (x3, y3)=(18.3, 11.4)

x-cordinate of center of mass is,

Xcm=(m1*x1+m2*x2+m3*x3)/(m1+m2+m3)

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

=m((x1+x2+x3)/(3*m)

=(x1+x2+x3)/(3)

=(0+12.2+18.3)/3

=10.17 cm

and

y-cordinate of center of mass is,

ycm=(m1*y1+m2*y2+m3*y3)/(m1+m2+m3)

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

=m((y1+y2+y3)/(3*m)

=(y1+y2+y3)/3

=(0+21.5+11.4)/(3)

=10.97 cm

there,

(Xcm, Ycm) = (10.17cm, 10.97cm)

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