Explanation Given information: The mass of the bar AB and BC is m = 3 kg . The length of the bar AB and BC is L = 500 mm . The magnitude of horizontal force P = 20 N . The load is applied at C , b = L = 500 mm . Calculation: Consider the acceleration due to gravity as g = 9.81 m / s 2 . Calculate the mass moment of inertia ( I ¯ ) as shown below. I ¯ = 1 12 m L 2 Substitute 3 kg for m and 500 mm for L . I ¯ = 1 12 × 3 kg × ( 500 mm × 1 m 1 , 000 mm ) 2 = 0.0625 kg ⋅ m 2 Sketch the Free Body Diagram of the bar as shown in Figure 1. Refer to Figure 1. The angular acceleration of the bar AB as α A B and α B C is the angular acceleration of the bar BC . The acceleration of bar AB is a ¯ A B = L 2 α A B . The acceleration of bar at B is a B = L α A B . Calculate the acceleration of the bar BC ( a ¯ B C ) as shown below. a ¯ B C = a B + L 2 α B C Substitute L α A B for a B . a ¯ B C = L α A B + L 2 α B C Sketch the Free Body Diagram of the bar BC as shown in Figure 2. Refer to Figure 2. Apply the Equilibrium of moment about B as shown below. ∑ M B = I G α + m a d P L = I ¯ α B C + m a ¯ B C × L 2 Substitute L α A B + L 2 α B C for a ¯ B C . P L = I ¯ α B C + m ( L α A B + L 2 α B C ) L 2 Substitute 20 N for P , 500 mm for L , 0.0625 kg ⋅ m 2 for I ¯ , and 3 kg for m . 20 N × ( 500 mm × 1 m 1 , 000 mm ) = [ ( 0.0625 kg ⋅ m 2 ) α B C + 3 kg 2 × ( 500 mm × 1 m 1 , 000 mm ) 2 ( α A B + 1 2 α B C ) ] 10 = 0.0625 α B C + 0.375 α A B + 0.1875 α B C 0.375 α A B + 0.25 α B C − 10 = 0 (1) Apply the Equilibrium of forces along x direction as shown below. ∑ F x = m a x P − B x = m a ¯ B C Substitute L α A B + L 2 α B C for a ¯ B C . P − B x = m ( L α A B + L 2 α B C ) = m L ( α A B + 1 2 α B C ) Substitute 20 N for P , 500 mm for L , and 3 kg for m

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 16.2, Problem 16.149P

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Find the angular acceleration of each bar.

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Chapter 16.2, Problem 16.148P

Chapter 16.2, Problem 16.150P

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Vector Mechanics for Engineers: Statics and Dynamics

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Find the angular acceleration of each bar.

Solution Summary: The author calculates the angular acceleration of each bar. The mass of the bar AB and BC is m=3kg.

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Find the angular acceleration of each bar.

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Chapter 16 Solutions