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Work, Energy, and Power 14–56. A gear with a mass moment of inertia of 0.45 kg⋅m2 has a kinetic energy of rotation of 21 joules. What is its speed of rotation in rpm? 14–63. Wheel A in Figure...

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Work, Energy, and Powe
14–56.
A gear with a mass moment of inertia of 0.45 kg⋅m2 has a kinetic energy of rotation of 21 joules. What is its speed of rotation in rpm?
14–63.
Wheel A in Figure P14–63 weighs 200 lb and has a radius of gyration of 2 ft. If the system is initially at rest, determine the angular velocity of A after B has dropped 8 ft
14–64.
Masses A and B in Figure P14–64 are fastened together by a belt over pulley D. (Assume no slipping of the belt.) The mass moment of inertia of pulley D is 15 kg⋅m2. How far does mass B drop before reaching a velocity of 2 m/s? The system is initially at rest.
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15–43.
Disc A in Figure P15–43 (IC = 8 kg ⋅ m2), while rotating at 100 rpm, is lowered onto disc B (IC = 10.5 kg ⋅ m2), causing the latter to rotate from rest. Assume no slipping and determine the angular velocity of B.
Answered Same Day Feb 23, 2023

Solution

Baljit answered on Feb 23 2023
39 Votes
Work, Energy, and Powe
14–56.
A gear with a mass moment of inertia of 0.45 kg⋅m2 has a kinetic energy of rotation of 21 joules. What is its speed of rotation in rpm?
Answer:-
Given
Mass of Inertia ,IC= 0.45 kg⋅m2
Kinetic Energy of rotation, KE=21J
Now we know that
Kinetic Energy of Rotation is
So speed of rotation
=
66 rad/s
Now
So speed of rotation is 92.246 rpm.
14–63.
Wheel A in Figure P14–63 weighs 200 lb and has a radius of gyration of 2 ft. If the system is initially at rest, determine the angular velocity of A after B has dropped 8 ft
Answer:-
Given
Let v ft/s is velocity of B after it dropped 8 ft.
So the angular velocity is
Here r is radius of wheel i.e 3 ft.
So
Now radius of Gyration is k=2ft
So it moment of inertia
Now Weight of wheel W=200 l
So mass of wheel
So
Moment of inertia
Potential Energy loss of B
Kinetic Energy KEB
Now Kinetic Energy gain of A is
Conservation of energy requires that loss of potential energy of B should be converted into kinetic energy gain of B and A.
So
Angular velocity of A is
So the Angular velocity of A is clockwise.
14–64.
Masses A and B in Figure P14–64 are fastened together by a belt over pulley D. (Assume no slipping of the belt.) The mass moment of inertia of pulley D is 15 kg⋅m2. How far does mass B drop before reaching a velocity of...
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