Explanation Given information : The weight of disk A ( W ) is 20 lb. The angle ( θ 1 ) for both the springs when they are un-stretched is 90 ° . The stiffness of spring ( k ) is 16 lb / ft . The length of each bar ( l ) is 1.25 ft. Explanation : Show the free body diagram of the spring system with the frame as in Figure (1). Using Figure (1), Determine the potential function. V = V e + V g = 1 2 k x 2 − W y = 1 2 k ( 2 l − 2 l sin θ ) 2 − W ( 2 l cos θ ) (I) Here, the elastic potential energy is V e , the gravitational potential energy is V g , the elongated distance of the spring is x , and the coordinate measured from a fixed datum located at the unstretched length of the spring is y . Formula used: sin 2 θ = 2 sin θ cos θ . Conclusion : Substitute 16 lb / ft for k , 1.25 ft for l , and 20 lb for W in Equation (I). V = 1 2 × 16 ( 2 × 1.25 − 2 × 1.25 sin θ ) 2 − 20 ( 2 × 1.25 cos θ ) = 8 ( 6.25 + 6.25 sin 2 θ − 12.5 sin θ ) − 50 cos θ = 50 + 50 sin 2 θ − 100 sin θ − 50 cos θ (II) Differentiate Equation (II) with respect to θ . d V d θ = 100 sin θ cos θ − 100 cos θ + 50 sin θ (III) Equilibrium requires d V d θ = 0 . Equation (III) can be written as, 100 sin θ cos θ − 100 cos θ + 50 sin θ = 0 (IV) Solve Equation (IV) using a trial and error method. Trial 1: Substitute 32 ° for θ in Equation (IV)

INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)

14th Edition

ISBN: 9780133918922

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 11.7, Problem 8RP

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The angle θ for equilibrium and to investigate the stability of the mechanism.

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Chapter 11.7, Problem 7RP

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The weight of the uniform bar AB is W. The stiffness of the ideal spring attached to B is k and the spring is unstreched when theta= 80 degree.if W=kL the bar has three equilibrium position in the range of 0

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1- Determine equilibrium the angle 9 for and investigate the stability of the mechanism in this position. The spring has a stiffness of k = 1.5 kN/m and is unstretched when 8 = 90°. The block A has a mass of 40 kg as shown in Fig.1. Neglect the mass of the links. quin 450 mm

Chapter 11 Solutions

INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)

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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The angle θ for equilibrium and to investigate the stability of the mechanism.

Solution Summary: The author shows the free body diagram of the spring system with the frame as in Figure (1).

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The angle θ for equilibrium and to investigate the stability of the mechanism.

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Chapter 11 Solutions