Explanation Given information: The mass of the rod AB is m . The length of the rod AB is L . Calculation: Write the equation of centroidal mass moment of inertia ( I ¯ ) of the rod. I ¯ = 1 12 m L 2 Rod swings to vertical position. Sketch the free body diagram of position 1 and position 2 as shown in Figure (1). Write the equation of velocity ( v ¯ 2 ) of rod at position 2 using kinematics. v ¯ 2 = L 2 ω 2 (1) Here, ω 2 is the angular velocity of rod at position 2. Refer Figure (1). The position 1 is in horizontal. Therefore, the potential energy ( V 1 ) and the kinetic energy ( T 1 ) at position 1 is zero. Find the equation of potential energy ( V 2 ) at position 2. V 2 = − m g L 2 Find the equation of kinetic energy ( T 2 ) at position 2. T 2 = 1 2 m v ¯ 2 2 + 1 2 I ¯ ω ¯ 2 2 Substitute L 2 ω 2 for v ¯ 2 and 1 12 m L 2 for I ¯ . T 2 = 1 2 m ( L 2 ω 2 ) 2 + 1 2 ( 1 12 m L 2 ) ω 2 2 = 1 8 m L 2 ω 2 2 + 1 24 m L 2 ω 2 2 = 1 6 m L 2 ω 2 2 Consider the conservation of energy equation. T 1 + V 1 = T 2 + V 2 Substitute 0 for T 1 , 0 for V 1 , 1 6 m L 2 ω 2 2 for T 2 , and − m g L 2 for V 2 . 0 + 0 = 1 6 m L 2 ω 2 2 − m g L 2 1 6 m L 2 ω 2 2 = m g L 2 1 3 L ω 2 2 = g ω 2 2 = 3 g L ω 2 = 3 g L Find the equation of velocity ( v ¯ 2 ) of rod at position 2 using Equation (1). v ¯ 2 = L 2 ω 2 Substitute 3 g L for ω 2 . v ¯ 2 = L 2 3 g L Find the equation of velocity [ ( v B ) 2 ] of rod at position 2 using kinematics. v B = L ω 2 Substitute 3 g L for ω 2 . ( v B ) 2 = L 3 g L = 3 g L 2 L = 3 g L Consider the impact condition. Find the equation of velocity [ ( v C ) 3 ] at point C at position 3. ( v C ) 3 − L ω 3 = e 3 g L ( v C ) 3 = L ω 3 + e 3 g L (2) Consider the impulse and momentum principle. Sketch the impulse and momentum diagram of the bar as at position 2 and 3 as shown in Figure (2). Write the equation of velocity ( v ¯ 3 ) of rod at position 3 using kinematics

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 17.3, Problem 17.124P

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Find the velocity of rod CD immediately after the impact.

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Chapter 17.3, Problem 17.123P

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Find the velocity of rod CD immediately after the impact.

Solution Summary: The author calculates the velocity of rod CD immediately after the impact using kinematics.

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