Explanation Given information: The weight of the bundle ( w b ) is 20 lb. The rotating weight including bundle weight ( W ) is 40 lb. The radius of the washer basket ( e ) is 9 inch. The spring constant ( k ) is 70 lb/ft. The damping ratio ( c c c ) is 0.05. The speed of the drum ( N ) is 250 rpm. The acceleration due to gravity ( g ) is 32.2 ft/s 2 . Calculation: Calculate the forced circular frequency ( ω f ) using the formula: ω f = 2 π N 60 Substitute 250 rpm for N . ω f = 2 π ( 250 ) 60 = 26.18 rad/s Calculate the mass of the rotating machine ( m ) using the formula: m = W g Substitute 40 lb for W and 32.2 ft/s 2 for g . m = 40 32.2 = 1.24224 lb ⋅ s 2 /ft Calculate the mass of the bundle ( w b ) using the formula: m b = w b g Substitute 20 lb for w b and 32.2 ft/s 2 for g . m b = 20 32.2 = 0.62112 lb ⋅ s 2 /ft Calculate the natural circular frequency ( ω n ) of the machine using the formula: ω n = k m Substitute 70 lb/ft for k and 1.24224 lb ⋅ s 2 /ft for m . ω n = 70 1.24224 lb ⋅ s 2 /ft = 7.5067 rad/s Calculate the critical damping coefficient ( c c ) using the formula: c c = 2 k m Substitute 70 lb/ft for k and 1.24224 lb ⋅ s 2 /ft for m . c c = 2 70 ( 1.24224 ) = 18.650 lb ⋅ s/ft Calculate the damping coefficient ( c ) from the damping ratio using the relation: Damping ratio = c c c Substitute 0.05 for damping ratio and 18.650 lb ⋅ s/ft for c c . 0.05 = c 18.650 c = 18.650 ( 0.05 ) c = 0.9325 lb ⋅ s/ft Calculate the unbalance force ( P m ) of the machine using the formula: P m = m b e ω f 2 Substitute 0.62112 lb ⋅ s 2 /ft for m b , 9 in. for e , and 26.18 rad/s for ω f . P m = 0.62112 × ( 9 in . × 1ft 12in . ) × ( 26.18 ) 2 = 319.28 lb Calculate the amplitude of vibration ( x m ) of the washing machine using the formula: x m = P m ( k − m ω f 2 ) 2 + ( c ω f ) 2 Substitute 319.28 lb for P m , 70 lb/ft for k , 1.24224 lb ⋅ s 2 /ft for m , 0

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 19.5, Problem 19.149P

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The amplitude of the motion (xm) and the magnitude of the force (Fm) transmitted to the sides of the washing machine.

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Chapter 19.5, Problem 19.148P

Chapter 19.5, Problem 19.150P

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Chapter 19 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.2P Ch. 19.1 - Prob. 19.3P Ch. 19.1 - Prob. 19.4P Ch. 19.1 - Prob. 19.5P Ch. 19.1 - Prob. 19.6P Ch. 19.1 - Prob. 19.7P Ch. 19.1 - Prob. 19.8P Ch. 19.1 - Prob. 19.9P Ch. 19.1 - Prob. 19.10P

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The amplitude of the motion ( x m ) and the magnitude of the force ( F m ) transmitted to the sides of the washing machine.

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The amplitude of the motion (xm) and the magnitude of the force (Fm) transmitted to the sides of the washing machine.

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