(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 The angular velocity ( ω ) of the rod.

12th Edition

ISBN: 9781260663778

Author: BEER

Publisher: MCG

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Chapter 18.1, Problem 18.24P

(a)

To determine

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

(b)

To determine

The angular velocity (ω) of the rod.

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Chapter 18.1, Problem 18.23P

Chapter 18.1, Problem 18.25P

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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.