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Engineering and Tech / Engineering Mechanics Dynamics (1) 1 14 / Chapter 18 / Problem R18-5

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

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The gear rack has a mass of 6 kg, and the gears each have

Chapter 18, Problem R18-5

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QUESTION:

The gear rack has a mass of 6 kg, and the gears each have a mass of 4 kg and a radius of gyration of k = 30 mm at their centers. If the rack is originally moving downward at 2 m/s, when s = 0, determine the speed of the rack when s = 600 mm. The gears are free to turn about their centers A and B.

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QUESTION:

The gear rack has a mass of 6 kg, and the gears each have a mass of 4 kg and a radius of gyration of k = 30 mm at their centers. If the rack is originally moving downward at 2 m/s, when s = 0, determine the speed of the rack when s = 600 mm. The gears are free to turn about their centers A and B.

ANSWER:

Problem R18-5

The gear rack has a mass of 6 kg, and the gears each have a mass of 4 kg and a radius of gyration of k = 30 mm at their centers. If the rack is originally moving downward at 2 m/s, when s = 0, determine the speed of the rack when s = 600 mm. The gears are free to turn about their centers A and B.

Step by Step Solution

Step 1 of 3

Let us consider the principle of work and energy between the initial and final states of the system (equation 1)

(1)

We continue to define the initial kinetic energy in terms of the known variables. Note that I is the moment of inertia of either gear about point A or B . Also, note that m is the mass of each gear, while M is the mass of the gear rack.

(2)

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