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 1.40 m. Following are the values of g at each particle's location: Particle 1: g 7.94 m/s² Particle 2: g 7.87 m/s² Particle 3: g = 7.67 m/s² Particle 4: g 7.48 m/s² Particle 5: g = 7.67 m/s² Particle 6: g 7.87 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 y cog of the center of gravity of the six-particle system. 3 6 SUPPORT

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics
Section: Chapter Questions
Problem 7.5P
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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 1.40 m. Following are the
values of g at each particle's location:
Particle 1: g 7.94 m/s²
Particle 2: g 7.87 m/s²
Particle 3: g = 7.67 m/s²
Particle 4: g 7.48 m/s²
Particle 5: g = 7.67 m/s²
Particle 6: g 7.87 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 y cog of the center of gravity of the six-particle system.
3
6
SUPPORT
Transcribed Image Text: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 1.40 m. Following are the values of g at each particle's location: Particle 1: g 7.94 m/s² Particle 2: g 7.87 m/s² Particle 3: g = 7.67 m/s² Particle 4: g 7.48 m/s² Particle 5: g = 7.67 m/s² Particle 6: g 7.87 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 y cog of the center of gravity of the six-particle system. 3 6 SUPPORT
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