4pointseBookPrintReferencesCheck my workCheck My Work button is now disabledItem 9A 5.00 kg mass is located at (1.0 m, 0.00 m, 3.00 m), a 2.00 kg mass is located at (0.00 m, 3.00 m, −2.00 m), and a 3.00 kg mass is located at (−1.0 m , −2.00 m , 0.00 m). The center of gravity of the system of masses is

The center of gravity of a system of masses is calculated by finding the weighted average of the positions of the masses. The weights in this case are the masses themselves.

The x-coordinate of the center of gravity (x_cg) is given by:

x_cg = (m1x1 + m2x2 + m3*x3) / (m1 + m2 + m3)

Substituting the given values:

x_cg = (5.00 kg * 1.0 m + 2.00 kg * 0.00 m + 3.00 kg * -1.0 m) / (5.00 kg + 2.00 kg + 3.00 kg) x_cg = (5.00 kg - 3.00 kg) / 10.00 kg x_cg = 0.20 m

Similarly, the y-coordinate of the center of gravity (y_cg) is given by:

y_cg = (m1y1 + m2y2 + m3*y3) / (m1 + m2 + m3)

Substituting the given values:

y_cg = (5.00 kg * 0.00 m + 2.00 kg * 3.00 m + 3.00 kg * -2.00 m) / (5.00 kg + 2.00 kg + 3.00 kg) y_cg = (6.00 kg - 6.00 kg) / 10.00 kg y_cg = 0.00 m

Finally, the z-coordinate of the center of gravity (z_cg) is given by:

z_cg = (m1z1 + m2z2 + m3*z3) / (m1 + m2 + m3)

Substituting the given values:

z_cg = (5.00 kg * 3.00 m + 2.00 kg * -2.00 m + 3.00 kg * 0.00 m) / (5.00 kg + 2.00 kg + 3.00 kg) z_cg = (15.00 kg - 4.00 kg) / 10.00 kg z_cg = 1.10 m

So, the center of gravity of the system of masses is at (0.20 m, 0.00 m, 1.10 m).