(a) Show that the rate of change of the free-fall acceleration with vertical position near the Earth's surface is dg 2GM 3--5 dr RE³ This rate of change with position is called a gradient. (b) Assuming his small in comparison to the radius of the Earth, show that the difference in free-fall acceleration between two points separated by vertical distance h is |Agl = 2GMEh RE 3 (c) Evaluate this difference for h = 41.25 m, a typical height for a fifteen-story building. (Enter your answer in m/s².) m/s²

(a) Show that the rate of change of the free-fall acceleration with vertical position near the Earth's surface is dg 2GM 3--5 dr RE³ This rate of change with position is called a gradient. (b) Assuming his small in comparison to the radius of the Earth, show that the difference in free-fall acceleration between two points separated by vertical distance h is |Agl = 2GMEh RE 3 (c) Evaluate this difference for h = 41.25 m, a typical height for a fifteen-story building. (Enter your answer in m/s².) m/s²

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter10: Motion In A Noninertial Reference Frame

Section: Chapter Questions

Problem 10.20P: Calculate the effective gravitational field vector g at Earths surface at the poles and the equator....

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