Question

Three point mass particles are located in a plane: 4.27 kg located at the origin, 7.8995 kg at [(5.77 cm),(11.54 cm)], and 2.23321 kg at [(12.117 cm),(0 cm)]. How far is the center of mass of the three particles from the origin? Answer in units of cm.

Answer 1

m₁ = 4.27 kg      x₁ = 0      y₁ = 0

m₂ = 7.8995       x₂ = 5.77    y₂ = 2.23321

m₃ = 2.23321       x₃ = 12.117    y₃ = 0

X-coordinate of center of mass is given as

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

X_cm = (4.27 x 0 + 7.8995 x 5.77 + 2.23321 x 12.117) /(4.27 + 7.8995 + 2.23321)

X_cm = 5.04 cm

Y-coordinate of center of mass is given as

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

Y_cm = (4.27 x 0 + 7.8995 x 2.23321 + 2.23321 x 0) /(4.27 + 7.8995 + 2.23321)

Y_cm = 1.22 cm

distance from origin = sqrt(Xcm² + Ycm²) = sqrt((5.04)² + (1.22)²) = 5.2 cm