A 3.0-kg mass is located at (0.0 m, 8.0 m), and a 1.0-kg mass is located at (12 m, 0.0 m) where (x, y) represents x and y coordinates respectively on x-y plane. You want to add a 4.0-kg mass so that the center of mass (or center of gravity) of the three-mass system will be at the origin. What should be the coordinates of the 3.0-kg mass

The coordinates of the 4.0-kg mass must be .

Explanation:

We have a system formed by three particles with known masses and locations with respect to origin. The location of the center of mass is calculated by means of weighted means. That is:

(Eq. 1)

(Eq. 2)

Where:

, - Coordinates of the center of mass of the system, measured in meters.

, - Coordinates of the i-th particle, measured in meters.

- Mass of the i-th particle, measured in kilograms.

If we know that , , , , , , , and , the location of the 4.0 kg mass is:

The coordinates of the 4.0-kg mass must be .

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