Explanation Show the free-body diagram of the system as in Figure 1. Find the vertical displacement ( y E ) at E using the relation. y E = l cos θ Integrate the equation; δ y E = − l sin θ δ θ Find the unstretched length ( x ) of the spring using the relation. x = 2 l sin θ + 2 l sin θ = 4 l sin θ Differentiate the equation; δ x = 4 l cos θ δ θ Find the spring force F using the equation. F = k ( x − 2 l ) Here, the spring constant is k . Substitute 4 l sin θ for x . F = k ( 4 l sin θ − 2 l ) Use the principle of virtual work; δ U = 0 P δ y E − F δ x = 0 Substitute − l sin θ δ θ for δ y E , k ( 4 l sin θ − 2 l ) for F , and 4 l cos θ δ θ for δ x

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ISBN: 9781259977244

Author: BEER

Publisher: MCG

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Free Body Diagram

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freed…

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Chapter 10.1, Problem 10.29P

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Show the equation in P, θ, l, and k that must be satisfied when the system is in equilibrium.

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Chapter 10.1, Problem 10.28P

Chapter 10.1, Problem 10.30P

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Chapter 10 Solutions

Vector Mechanics for Engineers: Statics

Ch. 10.1 - Determine the vertical force P that must be...Ch. 10.1 - Determine the horizontal force P that must be...Ch. 10.1 - Prob. 10.3P Ch. 10.1 - 10.3 and 10.4 Determine the couple M that must be...Ch. 10.1 - A spring of constant 15 kN/m connects points C and...Ch. 10.1 - A spring of constant 15 kN/m connects points C and...Ch. 10.1 - The two-bar linkage shown is supported by a pin...Ch. 10.1 - Determine the weight W that balances the 10-lb...Ch. 10.1 - Prob. 10.9P Ch. 10.1 - Prob. 10.10P

Ch. 10.1 - Prob. 10.11P Ch. 10.1 - Knowing that the line of action of the force Q...Ch. 10.1 - Solve Prob. 10.12 assuming that the force P...Ch. 10.1 - The mechanism shown is acted upon by the force P....Ch. 10.1 - Prob. 10.15P Ch. 10.1 - 10.15 and 10.16 Derive an expression for the...Ch. 10.1 - A uniform rod AB with length l and weight W is...Ch. 10.1 - The pin at C is attached to member BCD and can...Ch. 10.1 - For the linkage shown, determine the couple M...Ch. 10.1 - For the linkage shown, determine the force...Ch. 10.1 - A 4-kN force P is applied as shown to the piston...Ch. 10.1 - A couple M with a magnitude of 100 Nm isapplied as...Ch. 10.1 - Rod AB is attached to a block at A that can...Ch. 10.1 - Solve Prob. 10.23, assuming that the 800-N force...Ch. 10.1 - Prob. 10.25P Ch. 10.1 - Determine the value of corresponding to...Ch. 10.1 - Prob. 10.27P Ch. 10.1 - Determine the value of corresponding to...Ch. 10.1 - Prob. 10.29P Ch. 10.1 - Two rods AC and CE are connected by a pin at Cand...Ch. 10.1 - 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Show the equation in P , θ , l , and k that must be satisfied when the system is in equilibrium.

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Chapter 10 Solutions