Explanation Given information: The magnitude of the force P is 30 lb. The radius of the inner circle is b = 3 in . . The distance the points A and B from origin is a = 4 in . . The radius of the gear is r = 6 in . . The spring constant is k = 5 lb/in . . The spring is undeformed when θ = 0 ° . Calculation: Show the free-body diagram of the gear arrangement as in Figure 1. Find the elongation s when the spring is undeformed as follows s = a sin θ + a sin θ = 2 a sin θ Find the potential energy ( V ) using the relation; V = V s + V g = 1 2 k s 2 + P ( − b θ ) = 1 2 k ( 2 a sin θ ) 2 − P b θ = 2 k a 2 ( sin θ ) 2 − P b θ Differentiate the equation; d V d θ = 4 k a 2 sin θ cos θ − P b = 2 k a 2 sin 2 θ − P b (1) Differentiate the Equation (1). d 2 V d θ 2 = 4 k a 2 cos 2 θ (2) Equate the Equation (1) to zero for equilibrium. d V d θ = 0 2 k a 2 sin 2 θ − P b = 0 sin 2 θ = P b 2 k a 2 Substitute 30 lb for P , 3 in

12th Edition

ISBN: 9781259977268

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek

Publisher: McGraw-Hill Education

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Chapter 10.2, Problem 10.81P

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Find three values of θ corresponding to equilibrium and check whether the equilibrium is stable, unstable, or neutral.

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Chapter 10.2, Problem 10.80P

Chapter 10.2, Problem 10.82P

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Chapter 10 Solutions

Vector Mechanics for Engineers: Statics

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Find three values of θ corresponding to equilibrium and check whether the equilibrium is stable, unstable, or neutral.

Solution Summary: The author shows the free-body diagram of the gear arrangement as in Figure 1.

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Find three values of θ corresponding to equilibrium and check whether the equilibrium is stable, unstable, or neutral.

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Chapter 10 Solutions