Question

B Three 82.0 g 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. Mass A is located at (0,0), mass B is at (10.2, 21.5), and mass C is at (16.3, 15.4). Find the x- and y-coordinates of the center of mass of the triangular object. A Xcm= cm Ycm= cm Two more 82.0 g masses are connected by a straight piece of wire and affixed to the original configuration as shown. The coordinates of mass D are (0, -24.7) and the coordinates of mass E are (0,24.7). Find the x- and y-coordinates of the new center of mass of the combined object. B с D Xcm= cm Ycm= cm

Answer 1

Center of mass three object system is given by:

In x-direction

Xcm = (m1x1 + m2x2 + m3x3)/(m1 + m2 + m3)

In y-direction

Ycm = (m1y1 + m2y2 + m3y3)/(m1 + m2 + m3)

Given m1 = m2 = m3 = 82.0 gm = m

m1 = mA = 82.0 g, (x1, y1) = (0, 0)

m2 = mB = 82.0 g, (x2, y2) = (10.2, 21.5)

m3 = mC = 82.0 g, (x3, y3) = (16.3, 15.4)

(Xcm, Ycm) = (?, ?)

Now

Xcm = (m*0 + m*10.2 + m*16.3)/(m + m + m)

Xcm = (0 + 10.2 + 16.3)/3

Xcm = 8.83 cm

Ycm = (m*0 + m*21.5 + m*15.4)/(m + m + m)

Ycm = (0 + 21.5 + 15.4)/3

Ycm = 12.3 cm

So, Xcm = 8.83 cm, Ycm = 12.3 cm

Part B. when two additional masses are added, then

Center of mass five object system is given by:

In x-direction

Xcm = (m1x1 + m2x2 + m3x3 + m4x4 + m5x5)/(m1 + m2 + m3 + m4 + m5)

In y-direction

Ycm = (m1y1 + m2y2 + m3y3 + m4y4 + m5y5)/(m1 + m2 + m3 + m4 + m5)

Given m1 = m2 = m3 = m4 = m5 = 82.0 gm = m

m1 = mA = 82.0 g, (x1, y1) = (0, 0)

m2 = mB = 82.0 g, (x2, y2) = (10.2, 21.5)

m3 = mC = 82.0 g, (x3, y3) = (16.3, 15.4)

m4 = mD = 82.0 g, (x4, y4) = (0, -24.7)

m5 = mE = 82.0 g, (x5, y5) = (0, 24.7)

(Xcm, Ycm) = (?, ?)

Now

Xcm = (m*0 + m*10.2 + m*16.3 + m*0 + m*0)/(m + m + m + m + m)

Xcm = (0 + 10.2 + 16.3 + 0 + 0)/5

Xcm = 5.3 cm

Ycm = (m*0 + m*21.5 + m*15.4 + m*(-24.7) + m*24.7)/(m + m + m + m + m)

Ycm = (0 + 21.5 + 15.4 - 24.7 + 24.7)/5

Ycm = 7.38 cm

So, Xcm = 5.3 cm, Ycm = 7.38 cm

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