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 18, Problem 18.147RP
To determine

The distance of weight from disc B to balance the system dynamically.

The distance of weight from disc C to balance the system dynamically.

Expert Solution & Answer
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Answer to Problem 18.147RP

The distance of weight from disc B to balance the system dynamically is 254in.

The distance of weight from disc C to balance the system dynamically is 258in.

Explanation of Solution

Write the expression for the force.

F=mrω2

Here, the mass is m, the speed is ω and the radius is r.

Write the expression for the force on disk A.

FA=mrAω2

Here, the radius of disc A is rA.

Write the expression for the force on disk B.

FB=mrBω2

Here, the radius of disc B is rB and the balancing mass is m.

Write the expression for the force on disk C.

FC=mrCω2

Here, the radius of disc C is rC.

Write the expression for the sum of effective forces.

FA+FB+FC=0 ...... (I)

Here, the force on the rotor is A is FA, the force on the rotor is B is FB, the force on the rotor is C is FC.

Write the expression for the moment balance.

aFA+bFB+cFC=0 ...... (II)

Conclusion:

Substitute mrAω2 for FA, mrBω2 for FB and mrCω2 for FC in Equation (I).

mrAω2+mrBω2+mrCω2=0 ...... (III)

Substitute mrAω2 for FA, mrBω2 for FB and mrCω2 for FC in Equation (I).

amrAω2+bmrBω2+cmrCω2=0 ...... (IV)

Substitute 14in for rA, 25lb for m and 2lb for m.

(25lb×14in)ω2+(2lb×rB)ω2+(2lb×rC)ω2=0rB+rC=25lb2lb(14in)rB+rC=3.125in ...... (V)

Substitute 4in for a, 10in for b, 16in for c, 14in for rA, 25lb for m and 2lb for m .in Equation (IV).

4in×25lb×14in×ω2+10in×2lb×rBω2+16in×2lb×rCω2=025lbin2ω2+20lbin2rBω2+32lbin2rCω2=010rB+16rC=12.5in ...... (VI)

Solve Equation (V) and Equation (VI).

rC=258in

rB=254in

The distance of weight from disc B to balance the system dynamically is 254in.

The distance of weight from disc C to balance the system dynamically is 258in.

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Chapter 18 Solutions

Vector Mechanics for Engineers: Dynamics

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