Explanation Given information: Neglect the radius of the wheel and the effect of friction. Calculation: Show the free-body diagram of the slender rod AB as in Figure 1. Find the vertical distance ( y A ) using the geometry of the triangle A A ′ C . tan θ = Opposite side Adjacent side = y A a y A = a tan θ = − a tan θ ( Downward ) Differentiate the equation; δ y A = − a cos 2 θ δ θ Find the vertical distance ( y B ) using the geometry of the triangle. y B = l sin θ − y A = l sin θ − a tan θ Differentiate the equation; δ y B = l cos θ δ θ − a cos 2 θ δ θ Use the virtual work principle: δ U = 0 − Q δ y A − P δ y B = 0 Substitute − a cos 2 θ δ θ for δ y A and ( l cos θ δ θ − a cos 2 θ δ θ ) for δ y B

Vector Mechanics for Engineers: Statics, 11th Edition

11th Edition

ISBN: 9780077687304

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek

Publisher: McGraw-Hill Education

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Chapter 10.1, Problem 10.10P

To determine

Express the magnitude Q of the horizontal forces required for equilibrium of the rod.

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Chapter 10.1, Problem 10.9P

Chapter 10.1, Problem 10.11P

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Chapter 10 Solutions

Vector Mechanics for Engineers: Statics, 11th Edition

Ch. 10.1 - 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 - Prob. 10.8P Ch. 10.1 - Prob. 10.9P Ch. 10.1 - Prob. 10.10P

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