(a) Explanation Given information: The total mass of the uniform rod is m . The impulsive force is F Δ t . The length of rod CB is 2 a . The length of rod CD and AB is a . Calculation: Show the free body diagram of the rod as Figure (1). Apply the principle of impulse and momentum and consider the impulsive forces alone. Take the horizontal forces by considering x axis components as follows: m v ¯ x = 0 v ¯ x = 0 Here, m is the mass and v ¯ x is the velocity after impact in the x direction. The velocity before impact is zero. Assume the forces acting towards the right are taken as positive. Take the vertical forces by considering y axis components as follows: T ( Δ t ) = m v ¯ y Here, T ( Δ t ) is the force acting at B due to the suspended uniform rod and v ¯ y is the velocity after impact in y direction. The velocity of the rod after impact in the y direction is zero. Forces acting in the upward direction are positive. Substitute 0 for v ¯ y . T ( Δ t ) = m ( 0 ) = 0 Take the forces by considering the z axis components as follows: − F ( Δ t ) = m v ¯ z Here, F ( Δ t ) is the impulse at D and v ¯ z is the velocity in the z direction. Forces acting downwards are taken as positive (b) To determine Find the angular velocity ( ω ) of the rod.

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 18.1, Problem 18.23P

(a)

To determine

Find the velocity (v¯) of the mass center of the rod.

(b)

To determine

Find the angular velocity (ω) of the rod.

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Chapter 18.1, Problem 18.22P

Chapter 18.1, Problem 18.24P

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Chapter 18 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 18.1 - A thin, homogeneous disk of mass m and radius r...Ch. 18.1 - Prob. 18.2P Ch. 18.1 - 18.3 Two uniform rods AB and CE, each of weight 3...Ch. 18.1 - A homogeneous disk of weight W = 6 lb rotates at...Ch. 18.1 - Prob. 18.5P Ch. 18.1 - A solid rectangular parallelepiped of mass m has a...Ch. 18.1 - Prob. 18.8P Ch. 18.1 - Determine the angular momentum HD of the disk of...Ch. 18.1 - Prob. 18.10P Ch. 18.1 - Prob. 18.11P

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Find the velocity ( v ¯ ) of the mass center of the rod.

Solution Summary: The author explains the principle of impulse and momentum and considers the impulsive forces alone.