Explanation Given information : The mass of the bar ( m ) is 50 kg. The spring constant ( k ) value is 600 kN / m . The given angle when the spring is un-stretched ( θ ) is 60 ° . Explanation : Show the free body diagram of the bar resting on the wall as in Figure (1). Observation: From Figure (1), the independent coordinate θ undergoes a positive displacement δ θ and only the weight of the bar ( W ) and spring force ( F s p ) do work. The weight of the rod ( W ) and spring force ( F s p ) do negative work, when points A and center of the bar ( G ) undergo positive virtual displacements δ x A and δ y G . Virtual displacement: Write the position coordinate about point A . x A = l cos θ (I) Here, the length of the bar is l . Write the position coordinate about the center of the bar. y G = l 2 sin θ (II) Determine the weight of the bar. W = m g (III) Here, the acceleration due to gravity is g . Determine the spring force. F s p = k x = k l ( cos θ − cos θ 1 ) (IV) Here, the spring constant is k and the displacement of the spring from its equilibrium position is x . Virtual work equation: Write the virtual work equation to determine the magnitude of force. δ U = 0 − F s p δ x A − W δ y G = 0 (V) Conclusion : Differentiate Equation (I) with respect to θ . δ x A δ θ = − l sin θ δ x A = − l sin θ δ θ Substitute 5 m for l . δ x A = − 5 sin θ δ θ Differentiate Equation (II) with respect to θ . δ y G δ θ = l 2 cos θ δ y G = l 2 cos θ δ θ Substitute 5 m for l . δ y G = 5 2 cos θ δ θ = 2.5 cos θ δ θ Substitute 50 kg for m and 9.81 m / s 2 for g in Equation (III). W = 50 × 9.81 = 490.5 kg ⋅ m s 2 × 1 N 1 kg ⋅ m s 2 = 490.5 N Substitute 600 N / m for k , 5 m for l , and 60 ° for θ 1 in Equation (IV)

Engineering Mechanics: Statics and Modified Mastering Engineering with eText and Access Card (14th Edition)

14th Edition

ISBN: 9780134229287

Author: Russell C. Hibbeler

Publisher: PEARSON

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Engineering Mechanics: Statics and Modified Mastering Engineering with eText and Access Card (14th Edition)

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 - The lamp weighs 10 lb.Ch. 11.3 - Each of the four links has a length L and is pin...Ch. 11.3 - Determine the force screw exerts on the cork of...Ch. 11.3 - Determine the disks rotation if the end of the...

Ch. 11.3 - Prob. 5P Ch. 11.3 - Prob. 6P Ch. 11.3 - if the uniform inks AB and CD each weigh 10 lb....Ch. 11.3 - If the unstretched length of the spring is I0,...Ch. 11.3 - It vertical forces P1 = P2 = 30 lb act at C and E...Ch. 11.3 - Prob. 10P Ch. 11.3 - The spring which always remains vertical. Is...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 - Determine the angle for equilibrium. The spring...Ch. 11.3 - Determine the stillness k of the spring for...Ch. 11.3 - Determine the horizontal compressive force F...Ch. 11.3 - Prob. 21P Ch. 11.3 - Prob. 22P 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. 11.7 - Determine the equilibrium positions and...Ch. 11.7 - Prob. 27P Ch. 11.7 - If the potential function for a conservative...Ch. 11.7 - Prob. 29P Ch. 11.7 - Prob. 30P Ch. 11.7 - The rod BD, having negligible weight, passes...Ch. 11.7 - Determine the angle for equilibrium when a weight...Ch. 11.7 - Determine the angle for equilibrium and...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 - The bars each have a mass of 10 kg and the spring...Ch. 11.7 - Determine the required stiffness k of the spring...Ch. 11.7 - It is unstretched when the rod assembly is in the...Ch. 11.7 - Determine the minimum distance d in order for it...Ch. 11.7 - If the spring is unstretched when = 60. Determine...Ch. 11.7 - The contact at A is smooth, end both are pm...Ch. 11.7 - Determine the steepest grade along which it can...Ch. 11.7 - Determine the weight W2, that is on the pan in...Ch. 11.7 - If the rod is supported by a smooth slider block...Ch. 11.7 - Point C is coincident with B when OA is...Ch. 11.7 - Prob. 47P Ch. 11.7 - Prob. 48P Ch. 11.7 - If the block has three equal sides of length d,...Ch. 11.7 - Prob. 1RP Ch. 11.7 - Determine the horizontal force P required to hold...Ch. 11.7 - Prob. 3RP Ch. 11.7 - Prob. 4RP Ch. 11.7 - Prob. 5RP Ch. 11.7 - Prob. 6RP Ch. 11.7 - If both spring DE and BC are unstretched when =...Ch. 11.7 - Prob. 8RP

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Solution Summary: The author shows the free body diagram of the bar resting on the wall as in Figure (1).

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