Explanation Given information : The mass of each link ( m ) is 5 kg. The spring constant ( k ) value is 400 kN / m . The unstretched length of the spring ( l 0 ) is 0.3 m. Show the free body diagram of the spring system as in Figure (1). Using Figure (1), Virtual displacement: Write the position coordinate about point B . x B = l A B sin θ (I) Here, the length of the point AB is l A B . Write the position coordinate about point D . x D = 2 l sin θ − l A B sin θ (II) Here, the total length of the link is l . Write the position coordinate about the center of the link. y G = l 2 cos θ (III) Determine the weight of each of the links. W = m g (IV) Here, the acceleration due to gravity is g . Determine the spring force. F s p = k x = k ( 2 l B C sin θ − l 0 ) (V) Here, the spring constant is k , the displacement of the spring from its equilibrium position is x , and the length of point BC is l B C . Virtual work equation: Write the virtual work equation to determine the magnitude of force. δ U = 0 F s p δ x B − F s p δ x D − 2 W δ y G = 0 (VI) Conclusion : Differentiate Equation (I) with respect to θ . δ x B δ θ = l A B cos θ δ x B = l A B cos θ δ θ Substitute 0.1 m for l A B . δ x B = 0.1 cos θ δ θ Differentiate Equation (II) with respect to θ . δ x D δ θ = 2 l cos θ − l A B cos θ δ x D = ( 2 l cos θ − l A B cos θ ) δ θ Substitute 0.7 m for l and 0.1 m for l A B . δ x D = ( 2 × 0.7 × cos θ − 0.1 cos θ ) δ θ = 1.3 cos θ δ θ Differentiate Equation (III) with respect to θ . δ y G δ θ = − l 2 sin θ δ y G = − l 2 sin θ δ θ Substitute 0.7 m for l . δ y G = − 0.7 2 sin θ δ θ = − 0.35 sin θ δ θ Substitute 5 kg for m and 9.81 m / s 2 for g in Equation (IV). W = 5 × 9.81 = 49

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

14th Edition

ISBN: 9780133918922

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

Basic Thermodynamic Processes

The word 'thermodynamics' can be divided into two words, 'thermo' and 'dynamics'. The word thermo deals with the heat and thermal phenomenon, whereas dynamics deals with forces or external agent that drives the heat flow or aids in the motion of heat.

Videos

Question

Chapter 11.7, Problem 5RP

To determine

The angle θ for equilibrium.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.7, Problem 4RP

Chapter 11.7, Problem 6RP

Students have asked these similar questions

If the mass of the flowerpot is 65 kg, calculate the tension generated in every cable for equilibrium. Assume r = 1.5 m and z = 2 m. C+2m 3 m - 6 m

Determine the ratio P/Q of the forces that are required to maintain equilibrium of the mechanism for an arbitrary angle 0. Neglect the weight of the mechanism.

Determine the magnitude of the force P required to hold the 300-kg crate in equilibrium

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

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The angle θ for equilibrium.

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

Concept explainers

Videos

The angle θ for equilibrium.

Want to see the full answer?

Chapter 11 Solutions