Explanation Given information : The weight of the each link ( W ) is 20 lb. The stiffness of the spring ( k ) value is 50 lb / ft . The angle when the spring is un-stretched ( θ 1 ) is 0 ° . Show the free body diagram of the spring system as in Figure (1). Using Figure (1), Virtual displacement: Write the horizontal position coordinate about center of the link. x = l x sin θ (I) Here, the horizontal length of the link is l x . Write the vertical position coordinate about the link. y 1 = l y 2 cos θ (II) Here, the horizontal length of the link is l y . Write the position coordinate about the center of the link. y 2 = l y cos θ (III) Determine the spring force. F s = k Δ x = k l y 2 sin θ (IV) Virtual work equation: Write the virtual work equation to determine the magnitude of force. δ U = 0 − W δ y 2 − 2 W δ y 1 − F s δ x = 0 (V) Conclusion : Differentiate the Equation (I) with respect to θ . δ x δ θ = l x 2 cos θ δ x = l x 2 cos θ δ θ Substitute 4 ft for l x . δ x = 4 2 cos θ δ θ = 2 cos θ δ θ Differentiate the Equation (II) with respect to θ . δ y 1 δ θ = l y 2 sin θ δ y 1 = − l y 2 sin θ δ θ Substitute 4 ft for l y . δ y 1 = − 4 2 sin θ δ θ = − 2 sin θ δ θ Differentiate the Equation (III) with respect to θ . δ y 2 δ θ = − l y sin θ δ y 2 = − l y sin θ δ θ Substitute 4 ft for l y

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ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 11.3, Problem 8P

To determine

The angle θ for equilibrium.

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Chapter 11.3, Problem 7P

Chapter 11.3, Problem 9P

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Chapter 11 Solutions

Engineering Mechanics: Statics

Ch. 11.3 - Each link has a mass of 20 kg.Ch. 11.3 - Determine the magnitude of force P required to...Ch. 11.3 - Determine the angle for equilibrium. The spring...Ch. 11.3 - Determine the angle for equilibrium. The spring...Ch. 11.3 - Prob. 5FP Ch. 11.3 - Determine the angle for equilibrium. The spring...Ch. 11.3 - Each of the four links has a length L and is pin...Ch. 11.3 - The lamp weighs 10 lb.Ch. 11.3 - Prob. 3P Ch. 11.3 - Prob. 4P

Ch. 11.3 - Prob. 5P Ch. 11.3 - Prob. 6P Ch. 11.3 - It vertical forces P1 = P2 = 30 lb act at C and E...Ch. 11.3 - Prob. 8P Ch. 11.3 - if the uniform inks AB and CD each weigh 10 lb....Ch. 11.3 - Prob. 10P Ch. 11.3 - Prob. 11P Ch. 11.3 - Prob. 12P Ch. 11.3 - Prob. 13P Ch. 11.3 - Prob. 14P Ch. 11.3 - Prob. 15P Ch. 11.3 - Prob. 16P Ch. 11.3 - Prob. 17P Ch. 11.3 - Prob. 18P Ch. 11.3 - Prob. 19P Ch. 11.3 - The lever is in balance when the load and block...Ch. 11.3 - If the load F weighs 20 lb and the block G weighs...Ch. 11.3 - Determine the force in the hydraulic cylinder...Ch. 11.3 - Determine the horizontal compressive force F...Ch. 11.3 - Prob. 24P Ch. 11.3 - Prob. 25P Ch. 11.7 - Prob. 26P Ch. 11.7 - If the potential function for a conservative...Ch. 11.7 - Prob. 28P Ch. 11.7 - Determine the equilibrium positions and...Ch. 11.7 - Prob. 30P Ch. 11.7 - Prob. 31P Ch. 11.7 - Determine the angle for equilibrium when a weight...Ch. 11.7 - Prob. 33P Ch. 11.7 - Prob. 34P Ch. 11.7 - Prob. 35P Ch. 11.7 - The bars each have a mass of 3 Kg one the...Ch. 11.7 - Prob. 37P Ch. 11.7 - Prob. 38P Ch. 11.7 - Prob. 39P Ch. 11.7 - It is unstretched when the rod assembly is in the...Ch. 11.7 - Prob. 41P Ch. 11.7 - Determine the weight W2, that is on the pan in...Ch. 11.7 - Prob. 43P Ch. 11.7 - Determine the steepest grade along which it can...Ch. 11.7 - Prob. 45P Ch. 11.7 - Prob. 46P Ch. 11.7 - Point C is coincident with B when OA is...Ch. 11.7 - If the block has three equal sides of length d,...Ch. 11.7 - Prob. 49P Ch. 11.7 - Prob. 50RP Ch. 11.7 - Prob. 51RP Ch. 11.7 - Prob. 52RP Ch. 11.7 - Prob. 53RP Ch. 11.7 - Prob. 54RP Ch. 11.7 - Prob. 55RP Ch. 11.7 - Prob. 56RP Ch. 11.7 - Prob. 57RP Ch. 11.7 - Prob. 58RP Ch. 11.7 - If both spring DE and BC are unstretched when =...Ch. 11.7 - Prob. 60RP Ch. 11.7 - Prob. 61RP Ch. 11.7 - Determine the horizontal force P required to hold...

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