The mass and coordinates of three objects are given below: m1 = 6.0 kg at (0.0, 0.0) m, m2 = 1.5 kg at (0.0, 4.1) m, and m3 = 4.0 kg at (1.9, 0.0) m. Determine where we should place a fourth object with a mass m4 = 7.9 kg so that the center of gravity of the four-object arrangement will be at (0.0, 0.0) m

The location of the center of gravity of the fourth mass is .

Explanation:

Vectorially speaking, the center of gravity with respect to origin (), measured in meters, is defined by the following formula:

(1)

Where:

, , , - Masses of the objects, measured in kilograms.

, , , - Location of the center of mass of each object with respect to origin, measured in meters.

If we know that , , , , , , and , then the equation is reduced into this:

The location of the center of gravity of the fourth mass is .

unlike poles attract