Question

Three 90.790.7 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)(0,0), mass B is at (10.2,19.5)(10.2,19.5), and mass C is at (17.3,13.4)(17.3,13.4). Find the xx- and yy‑coordinates of the center of mass of the triangular object.

Two more 90.790.7 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,−39.1)(0,−39.1) and the coordinates of mass E are (0,39.1)(0,39.1). Find the xx- and yy‑coordinates of the new center of mass of the combined object.

Answer 1

Mass of each object = m = 90.7 g

Position of mass A = (X₁, Y₁) = (0 , 0) cm

Position of mass B = (X₂ , Y₂) = (10.2 , 19.5) cm

Position of mass C = (X₃ , Y₃) = (17.3 , 13.4) cm

X-coordinate of center of mass of the triangular object = X_cm1

Y-coordinate of center of mass of the triangular object = Y_cm1

X_cm1 = 9.17 cm

Y_cm1 = 10.97 cm

Position of mass D = (X₄ , Y₄) = (0 , -39.1) cm

Position of mass E = (X₅ , Y₅) = (0 , 39.1) cm

X-coordinate of center of mass of the combined object = X_cm2

Y-coordinate of center of mass of the combined object = Y_cm2

X_cm2 = 5.5 cm

Y_cm2 = 6.58 cm

A) Coordinates of the center of mass of the triangular object = (9.17 , 10.17) cm

B) Coordinates of the center of mass of the combined object = (5.5 , 6.58) cm