Explanation Given information: The mass of the compressor is 25 0 kg , the spring constant for the soil is 8 0 × 1 0 6 N / m , the density of the concrete is 24 0 0 kg / m 3 , the dimension of the block is 1.5 m × 1 .5 m , and the speed of the compressor is 2 0 0 0 rpm . Expression for the force transmitted to the ground. P = 0 .25 m r ω f 2 ...... (I) Here, the mass of the compressor is m , radius of the rotor of the compressor is r , and the speed of the compressor is ω f . Expression for the maximum amplitude of the vertical motion. P = m r ω f 2 ( ω f ω n ) 2 − 1 ...... (II) Here, the natural frequency of the system is ω n . Calculation: Substitute 0 .25 m r ω f 2 for P in Equation (II). 0 .25 m r ω f 2 = m r ω f 2 ( ω f ω n ) 2 − 1 ( ω f ω n ) 2 = 5 ω n = ω f 5 ...... (III) Substitute 2 0 0 0 rpm for ω f in Equation (III). ω n = 2 0 0 0 rpm 5 = 2 0 0 0 rpm × 0 .1 0 5 rad / s 1 rpm 5 = 93.19 rad / s Expression for the mass of the block and compressor

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 19, Problem 19.167RP

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The depth that will reduce the force transmitted to the ground.

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Chapter 19, Problem 19.166RP

Chapter 19, Problem 19.168RP

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Chapter 19 Solutions

Vector Mechanics for Engineers: Dynamics

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - A particle moves in simple harmonic motion....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 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - A 10-Ib block A rests on a 40-Ib plate B that is...Ch. 19.1 - A 5-kg fragile glass vase is surrounded by packing...

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The depth that will reduce the force transmitted to the ground.

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Chapter 19 Solutions