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Engineering and Tech / Engineering Mechanics Dynamics (1) 1 14 / Chapter 18 / Problem 18-8

Engineering Mechanics Dynamics (1) 1 | 14th Edition | ISBN: 9780133915389 | Authors: Russell C. Hibbeler

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The double pulley consists of two parts that are attached to one another. It has a

Chapter 18, Problem 18-8

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QUESTION:

The double pulley consists of two parts that are attached to one another. It has a weight of 50 lb and a centroidal radius of gyration of \(k_{O} = 0.6 \ ft\) and is turning with an angular velocity of 20 rad/s clockwise. Determine the angular velocity of the pulley at the instant the 20-lb weight moves 2 ft downward.

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QUESTION:

The double pulley consists of two parts that are attached to one another. It has a weight of 50 lb and a centroidal radius of gyration of \(k_{O} = 0.6 \ ft\) and is turning with an angular velocity of 20 rad/s clockwise. Determine the angular velocity of the pulley at the instant the 20-lb weight moves 2 ft downward.

ANSWER:

Problem 18-8

The double pulley consists of two parts that are attached to one another. It has a weight of 50 lb and a centroidal radius of gyration of kO = 0.6 ft and is turning with an angular velocity of 20 rad>s clockwise. Determine the angular velocity of the pulley at the instant the 20-lb weight moves 2 ft downward.

Step by Step Solution

Step 1 of 4

To determine the kinetic energy of the system, use equation (18-4) for translational, rotational kinetic energy while the pulley rotates and blocks A & B moves in y-direction

Where

is the pulley mass,

is the radius of gyration of the pulley about its center axis, is the mass of block A, and is the mass of block B,

is the angular velocity of the pulley

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