Vector Mechanics for Engineers: Dynamics
Vector Mechanics for Engineers: Dynamics
11th Edition
ISBN: 9780077687342
Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
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Chapter 17, Problem 17.135RP

A uniform disk, initially at rest and of constant thickness, is placed in contact with the belt shown, which moves at a constant speed v = 80 ft/s. Knowing that the coefficient of kinetic friction between the disk and the belt is 0.15, determine (a) the number of revolutions executed by the disk before it reaches a constant angular velocity, (b) the time required for the disk to reach that constant angular velocity.

  Chapter 17, Problem 17.135RP, A uniform disk, initially at rest and of constant thickness, is placed in contact with the belt

Expert Solution
Check Mark
To determine

(a)

The number of revolutions executed by the disk before it reaches a constant angular velocity.

Answer to Problem 17.135RP

Disk will take 106.7 revolutions before it reaches to constant angular velocity.

Explanation of Solution

Given:

Velocity of disk V=80ft/sec,μK=0.15

Concept used:

Principle of work and energy.

Calculation:

Vector Mechanics for Engineers: Dynamics, Chapter 17, Problem 17.135RP , additional homework tip  1

Angular velocity, ω=vr

Moment of inertia =I=12mr2

Kinetic Friction ff=μKN=0.15N

Summation of forces at y-direction,

fy=Ncos250ffsin250mg=0mg=(cos250μKsin250)Nff=0.15×0.1863mg=0.1779mg.

Work was done

=W=ffrθ=0.1779mgrθ

Applying the principle of work and energy,

W=T2T1T1=0T2=Iω222=mv240.1779mgrθ=mv24θ=8024×0.1779×32.2×(512)θ=670.34radians=106.7revolutions

Conclusion:

We can calculate the number of rotations done by disk before reaching constant angular velocity are 106.7 rotations.

Expert Solution
Check Mark
To determine

(b)

The time taken by disk to reach the constant angular velocity.

Answer to Problem 17.135RP

The time required for the disk to reach the constant angular velocity is 6.98 sec.

Explanation of Solution

Given:

Velocity of disk V=80ft/sec,μK=0.15

Concept used:

Principle of impulse and momentum.

Calculation:

According to impulse momentum principle.

Vector Mechanics for Engineers: Dynamics, Chapter 17, Problem 17.135RP , additional homework tip  2

Taking moments about A,

fftr=Iω2t=Iω2ffr=mr2×v2×0.1779m×g×r2=802×0.1779×32.2t=6.98

Conclusion:

Thus, the time taken by disk to reach a constant angular velocity is 6.98 sec by using the impulse-momentum principle.

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Chapter 17 Solutions

Vector Mechanics for Engineers: Dynamics

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