Halliday, Resnick & Walker — Equilibrium and Elasticity: Problem Problem_1

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 12.11 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 2.00 m. The following table gives the value of g (m/s²) at each particle’s location. Particle | g (m/s²) | Particle | g (m/s²) --- | --- | --- | --- 1 | 8.00 | 4 | 7.40 2 | 7.80 | 5 | 7.60 3 | 7.60 | 6 | 7.80 Using the coordinate system shown, find (a) the x coordinate \( x_{\text{com}} \) and (b) the y coordinate \( y_{\text{com}} \) of the center of mass of the six‑particle system. Then find (c) the x coordinate \( x_{\text{cog}} \) and (d) the y coordinate \( y_{\text{cog}} \) of the center of gravity of the six-particle system.