The x and y coordinates in meters of the center of mass of the three-particle system shown below are:
A) 0, 0
B) 1.3 m, 1.7 m
C) 1.4 m, 1.9 m
D) 1.9 m, 2.5 m
E) 1.4 m, 2.5 m

Question

The x and y coordinates in meters of the center of mass of the three-particle system shown below are: 
A) 0, 0 
B) 1.3 m, 1.7 m 
C) 1.4 m, 1.9 m 
D) 1.9 m, 2.5 m 
E) 1.4 m, 2.5 m

Quizplus · Accepted Answer

We can find the x-coordinate of the center of mass by taking the weighted average of the x-coordinates of each particle, where the weights are the masses of the particles:

x-center of mass = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3)

Plugging in the values from the diagram, we get:

x-center of mass = ((2 kg)(1 m) + (3 kg)(2 m) + (1 kg)(2.8 m)) / (2 kg + 3 kg + 1 kg) = 1.4 m

We can do the same thing to find the y-coordinate:

y-center of mass = (m1y1 + m2y2 + m3y3) / (m1 + m2 + m3)

Plugging in the values from the diagram, we get:

y-center of mass = ((2 kg)(1.5 m) + (3 kg)(0.5 m) + (1 kg)(2.5 m)) / (2 kg + 3 kg + 1 kg) = 1.9 m

Therefore, the coordinates of the center of mass are (1.4 m, 1.9 m), which corresponds to choice C).

The X and Y Coordinates in Meters of the Center