(a) Explanation Given information: The acceleration of gravity be expressed as g h . The altitude be expressed as h which is 0.625 mi . The acceleration of gravity above the earth surface be expressed as g 0 . The radius of the earth be expressed as R . Assume the radius of the earth ( R ) is 3960 mi . Calculation: Show the free body diagram of the earth with the forces acting as in Figure (1). Calculate the force ( F ) using the formula: F = G M E m ( h + R ) 2 = G M E m ( h R + 1 ) 2 R 2 = G M E m R 2 ( h R + 1 ) 2 Substitute m g h for F . m g h = G M E m R 2 ( h R + 1 ) 2 g h = G M E R 2 ( h R + 1 ) 2 (1) The altitude ( h ) will be zero at the earth surface. Substitute 0 for h . m g 0 = G M E m R 2 ( 0 R + 1 ) 2 m g 0 = G M E m R 2 1 m g 0 = G M E m R 2 g 0 = G M E R 2 (2) Equate the equation (1) and (2). g h = g 0 Substitute G M E R 2 ( h R + 1 ) 2 for g h and G M E R 2 for g 0 (b) To determine Find the percent error if the weight that an object has on surface of earth’s is used as its weight at an altitude of 625 mi .

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 13.1, Problem 13.37P

(a)

To determine

Find the percent error if the weight that an object has on surface of earth’s is used as its weight at an altitude of 0.625mi.

(b)

To determine

Find the percent error if the weight that an object has on surface of earth’s is used as its weight at an altitude of 625mi.

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Chapter 13.1, Problem 13.36P

Chapter 13.1, Problem 13.38P

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Find the percent error if the weight that an object has on surface of earth’s is used as its weight at an altitude of 0.625 mi .

Solution Summary: The author shows the free body diagram of the earth with the forces acting as in Figure (1).