(a) Explanation Given information: The mass of the crate is m . The length of an edge of a crate is c . The angular velocity of the crate immediately before B strikes the floor is ω 0 . Calculation: Write the equation of centroidal mass moment of inertia ( I ¯ ) of the crate. I ¯ = 1 12 m ( c 2 + c 2 ) = 1 6 m c 2 Find the radial distance ( r G ) of the crate about the mass center: ( I ¯ ) r G = 1 2 d Here, d is the diagonal length of the crate. r G = 1 2 2 c Sketch the impulse and momentum diagram of crate as shown in Figure (1). Here, v ¯ 0 is the velocity of crate at initial position, B y and B x is the impulsive reaction at cornet B , v ¯ is the velocity of crate at final position, and ω is the angular velocity of crate at final position. Refer Figure (1), Write the equation of initial velocity ( v ¯ 0 ) of the crate using kinematics. v ¯ 0 = r G / A ω 0 Substitute 1 2 2 c for r G / A . v ¯ 0 = ( 1 2 2 c ) ω 0 Write the equation of Final velocity ( v ¯ ) of the crate using kinematics. v ¯ = r G / B ω Substitute 1 2 2 c for r G / B (b) To determine Find the fraction of the kinetic energy of the crate lost during the impact. (c) To determine Find the angle θ through which the crate will rotate after B strikes the floor.

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

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 17.118P

(a)

To determine

Find the angular velocity of the crate immediately after B strikes the floor.

(b)

To determine

Find the fraction of the kinetic energy of the crate lost during the impact.

(c)

To determine

Find the angle θ through which the crate will rotate after B strikes the floor.

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Chapter 17.3, Problem 17.117P

Chapter 17.3, Problem 17.119P

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Find the angular velocity of the crate immediately after B strikes the floor.

Solution Summary: The author calculates the angular velocity of a crate immediately after B strikes the floor. The equation of centroidal mass moment of inertia is written.

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Find the angular velocity of the crate immediately after B strikes the floor.

Find the fraction of the kinetic energy of the crate lost during the impact.

Find the angle θ through which the crate will rotate after B strikes the floor.

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Chapter 17 Solutions