Concept explainers
A drum of 4-in. radius is attached to a disk of 8-in. radius. The disk and drum have a combined weight of 10 Ib and a combined radius of gyration of 6 in. A cord is attached as shown and pulled with a force P of magnitude 5 Ib. Knowing that the coefficients of static and kinetic friction are
(a)
The whether or not disk slides.
Answer to Problem 16.105P
The disk slides.
Explanation of Solution
Given information:
The radius of the drum is
Below figure represent the free body diagram and the kinetic diagram of the drum.
Figure-(1)
Write the expression of acceleration of the drum.
Here, the radius of the disk is
Write the expression of total force applied in the disk and drum.
Here, the combined mass is
Write the expression of generated torque in the disk and drum.
Here, the of inertia of drum is
Write the expression of inertia of the disk and drum.
Here, the combined mass is
Write the expression of combined mass of the disk and drum.
Here, the combined weight of the disk and drum is
Write the expression of moment about point
Here, the effective moment is
Write the expression of moment about point
Here, the radius of the disk is
Write the expression of total effective moment about point
Here, the total force is
Substitute
Substitute
Substitute
Write the expression of force equilibrium equation in
Here, the normal force in
Write the expression of frictional force for static friction.
Here, the coefficient of static friction is
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Here, the friction force is less than the total force, hence the disk slides.
Conclusion:
The disk slides.
(b)
The angular acceleration of the disk
The acceleration of
Answer to Problem 16.105P
The angular acceleration of the disk is
The acceleration of
Explanation of Solution
Write the expression of friction force by considering kinetic friction.
Here, the coefficient of kinetic friction is
Write the expression of total moment about point
Here, the total effective moment is
Write the expression of moment about
Here, the radius of the drum is
Write the expression of total effective moment.
Substitute
Substitute
Write the expression of total force in
Here, the total force is
Substitute
Calculation:
Substitute
Substitute
Substitute
Conclusion:
The angular acceleration of the disk is
The acceleration of
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Chapter 16 Solutions
Vector Mechanics for Engineers: Dynamics
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