Halliday, Resnick & Walker — Equilibrium and Elasticity: Problem 40

Because g varies so little over the extent of most structures, any structure’s center of gravity effectively coincides with its center of mass. Here is a fictitious example where g varies more significantly. Figure 12-43 shows an array of six particles, each with mass m, fixed to the edge of a rigid structure of negligible mass. The distance between adjacent particles along the edge is 4.00 m. The following table gives the value of g (m/s²) at each particle’s location. Using the coordinate system shown, find (a) the x coordinate \(x_{com}\) and (b) the y coordinate \(y_{com}\) of the center of mass of the six-particle system. Then find (c) the x coordinate \(x_{cog}\) and (d) the y coordinate \(y_{cog}\) of the center of gravity of the six-particle system. Table of g values: Particleg (\(m/s^2\))Particleg (\(m/s^2\)) 18.0047.40 27.8057.60 37.6067.80