Explanation Given: The length of the telescopic boom A B , l = 60 ft . The angle formed by the boom, θ = 60 ° . The angular velocity of the boom A B , ω A B = 0.02 rad / s . The angular acceleration of the boom A B , α A B = 0.01 rad / s 2 . The constant speed of the boom, v = 0.5 ft / s . Show the free body diagram of the x y z rotating frame attached to boom A B as in Figure (1). Show the magnitude of velocity v B as in Figure (2). Show the magnitude of acceleration a B as in Figure (3). Conclusion: Refer Figure (1) , The x y z rotating references frame is at point A and coincide with the X Y fixed reference frame, thus write the motion of x y frame with respect to X Y frame. v A = a A = 0 ω A B = − 0.02 k rad / s α A B = − 0.01 k rad / s 2 Write the motion of point B with respect to x y z rotating reference frame. r B / A = 60 j ft ( v r e l ) x y z = 0.5 j ft / s ( a r e l ) x y z = 0 Here, relative distance between point A and B is r B / A , relative velocity and acceleration with respect to x y z frame is ( v r e l ) x y z and ( a r e l ) x y z respectively. Apply the relative velocity equation. v B = v A + ω A B × r B / A + ( v r e l ) x y z (I) Substitute 0 for v A , − 0.02 k rad / s for ω A B , 60 j ft for r B / A and 0.5 j ft / s for ( v r e l ) x y z in Equation (I). v B = 0 + ( − 0.02 k ) × ( 60 j ) + 0.5 j = { 1.2 i + 0.5 j } ft / s [ − k × j = i ] (II) Refer Figure (2) , Express the magnitude of velocity v B using Equation (II). υ B = ( v B i ) 2 + ( v B j ) 2 (III) Substitute 1

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 16.8, Problem 130P

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The magnitudes of the velocity υB and acceleration aB of point B .

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Chapter 16.8, Problem 129P

Chapter 16.8, Problem 131P

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The magnitudes of the velocity υ B and acceleration a B of point B .

Solution Summary: The author shows the free body diagram of the xyz rotating frame attached to a telescopic boom.

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The magnitudes of the velocity υB and acceleration aB of point B .

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