(a) Explanation The spring is unstretched when θ = 30 ° . Show the free-body diagram of the arrangement as in Figure 1. Find the distance x using the relation; x = l cos θ When the spring is unstretched; θ = 30 ° ; x = x 0 . Substitute x 0 for x and 30 ° for θ . x 0 = l cos 30 ° = 0.866 l Find the distance s using the relation. s = x 0 − x = 0.866 l − l cos θ Find the potential energy ( V ) using the relation; V = V s + V g = 1 2 k s 2 + m g ( − 2 l sin θ ) = 1 2 k ( 0.866 l − l cos θ ) 2 − 2 m g l sin θ = 1 2 k l 2 ( 0.866 − cos θ ) 2 − 2 m g l sin θ Differentiate the equation; d V d θ = k l 2 ( 0 (b) To determine Find the value of θ corresponding to equilibrium and check whether the equilibrium is stable.

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ISBN: 9781260912814

Author: BEER

Publisher: MCG

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Chapter 10.2, Problem 10.78P

(a)

To determine

Find the equation in terms of θ, m, k, and l for equilibrium of bar ABC.

(b)

To determine

Find the value of θ corresponding to equilibrium and check whether the equilibrium is stable.

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Chapter 10.2, Problem 10.77P

Chapter 10.2, Problem 10.79P

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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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Derive an expression for the mechanical...Ch. 10.1 - Denoting the coefficient of static friction...Ch. 10.1 - Knowing that the coefficient of static...Ch. 10.1 - Using the method of virtual work,...Ch. 10.1 - Using the method of virtual work, determine...Ch. 10.1 - Referring to Prob. 10.43 and using the value...Ch. 10.1 - Prob. 10.56P Ch. 10.1 - Prob. 10.57P Ch. 10.1 - Prob. 10.58P Ch. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.29....Ch. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.30....Ch. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.31....Ch. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.32....Ch. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.34....Ch. 10.2 - Prob. 10.64P Ch. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.37....Ch. 10.2 - Prob. 10.66P Ch. 10.2 - Prob. 10.67P Ch. 10.2 - Show that equilibrium is neutral in Prob. 10.7....Ch. 10.2 - Two uniform rods, each with a mass m, areattached...Ch. 10.2 - Two uniform rods, AB and CD, are attached to gears...Ch. 10.2 - 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Find the equation in terms of θ , m , k , and l for equilibrium of bar ABC .

Solution Summary: The author shows the free-body diagram of the arrangement as in Figure 1. Find the distance x using the relation.