Sample Problem 9-1

Three particles of masses = 1.2 kg, = 2.5 kg, and = 3.4 kg form an equilateral triangle of edge length a = 140 cm. Where is the center of mass of this three-particle system?

SOLUTION: A Key Idea to get us started is that we are dealing with particles instead of an extended solid body, so we can use Eq. 9-5 to locate their center of mass. The particles are in the plane of the equilateral triangle, so We need only the first two equations. A second Key Idea is that we can simplify the calculations by choosing the .rand у axes so that one of the particles is located at the origin

and the x axis coincides with one of the triangle's sides (Fig. 9-3). The three particles then have the following coordinates:

The total mass M of the system is 7.1 kg.

From Eq. 9-5, the coordinates of the center of mass are

;