Because g varies so little over the extent of most structures, any structure\'s
ID: 1644659 • Letter: B
Question
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. The figure 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 2.70 m. Following are the values of g at each particle's location:
Particle 1: g = 8.03 m/s2
Particle 2: g = 7.71 m/s2
Particle 3: g = 7.54 m/s2
Particle 4: g = 7.41 m/s2
Particle 5: g = 7.54 m/s2
Particle 6: g = 7.71 m/s2
Using the coordinate system shown, find (a) the x coordinate xcom and (b) the y coordinate ycom of the center of mass of the six-particle system. Then find (c) the x coordinate xcog and (d)the y coordinate ycog of the center of gravity of the six-particle system.
Explanation / Answer
To get the center of mass, you took the weighted average of m over the points, x_cm = Sum(m_i * x_i) / Sum(m_i) anf for y-coordinate y_cm = Sum(m_i * y_i) / Sum(m_i).
To get the center of gravity also, do a weighted average, but use (m_i g_i) in place of (m_i)
The question can be solved numerically if the picture is visible, which is not in this case.