The x and y coordinates in meters of the center of mass of the three-particle system shown below are:
A) 0 m, 0 m
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 m, 0 m 
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

To find the center of mass, we need to consider the mass and position of each particle. At first, we notice that the triangle formed by the particles is isosceles with the base being the segment between particles A and C. Therefore, the center of mass lies on this base.

To determine the exact position, we need to calculate the weighted average of the x- and y-coordinates of the particles, where the weights are given by the masses. The masses of the particles are not given, so we assume that they are equal.

Let's call the x-coordinate of the center of mass "X" and the y-coordinate "Y". Then we have:

X = (1/3)(2.0 m + 1.0 m + 1.4 m) = 1.4 m
Y = (1/3)(2.0 m + 2.4 m + 1.0 m) = 1.8 m

So the center of mass is at (1.4 m, 1.8 m). The closest answer choice to this is C) 1.4 m, 1.9 m.

The X and Y Coordinates in Meters of the Center