Explanation Given information : The crankshaft subjected to a torque ( M ) is 50 N ⋅ m . The position of the rod ( θ ) is 60 ° . Explanation : Show the free body diagram of the crankshaft as in Figure (1). Using Figure (1), Virtual displacement: Determine the position coordinate about the point A, which is measured from point O . l r = x 2 + l c 2 − 2 x ( l c ) cos θ (I) Here, the length of the rod is l r , the centre-to-centre distance of crankshaft is l c , and the position of the crankshaft is θ . Virtual work equation: Write the virtual work equation to determine the force F . δ U = 0 − F δ x − M δ θ = 0 F δ x = − M δ θ F = − M δ θ δ x (II) Formula used: Write the quadratic equation. x = − b ± b 2 − 4 a c 2 a Conclusion : Differentiate Equation (I) with respect to θ . 0 = 2 x δ x + 2 x ( l c ) sin θ δ θ − 2 δ x ( l c ) cos θ Substitute 100 mm for l c . 0 = { 2 x δ x + 2 x ( 100 mm × 1 m 1 , 000 mm ) sin θ δ θ − 2 δ x ( 100 mm × 1 m 1 , 000 mm ) cos θ } δ x ( 0.2 cos θ − 2 x ) = 0.2 x sin θ δ θ δ x = 0.2 x sin θ ( 0.2 cos θ − 2 x ) δ θ Substitute 400 mm for l r and 100 mm for l c in Equation (I). ( 400 mm × 1 m 1 , 000 mm ) 2 = { x 2 + ( 100 mm × 1 m 1 , 000 mm ) 2 − 2 x ( 100 mm × 1 m 1 , 000 mm ) cos θ } 0.16 = x 2 + 0.01 − 0.2 cos θ x x 2 − 0.2 cos θ x − 0.15 = 0 (III) Solve Equation (III). x = − ( − 0.2 cos θ ) ± ( − 0.2 cos θ ) 2 − 4 ( 1 ) ( − 0

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ISBN: 9780136522409

Author: HIBBELER

Publisher: PEARSON

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It is defined as the energy transfer from one location to another location. The energy will start moving from the energy generation source to the energy applied position to obtain the work output. From this method, a large amount of electric energy moves…

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Chapter 11.3, Problem 21P

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The horizontal compressive force F applied to the piston for equilibrium.

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Chapter 11.3, Problem 20P

Chapter 11.3, Problem 22P

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Chapter 11 Solutions

ENGINEERING MECHANICS

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The horizontal compressive force F applied to the piston for equilibrium.

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The horizontal compressive force F applied to the piston for equilibrium.

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Chapter 11 Solutions