Explanation Given: The relative velocity of the man with respect to moving reference is v m / O = 5 ft/s . The relative acceleration of the man with respect to moving reference is a m / O = 2 ft/s 2 . The constant angular velocity of the swing bridge (moving reference)is Ω = 0.5 rad/s . The displacement of the man along negative y − a x i s is d = 10 ft . Write the formula for velocity of the point C measured from the x , y , z reference. v m = v O + Ω × r m / O + ( v m / O ) x y z (I) Here, v m velocity vector of man measured from the X , Y , Z reference, v O is the velocity vector of the origin O measured from the X , Y , Z reference, ( v m / O ) x y z is the velocity vector of man with respect to origin O measured by an observer attached to the rotating x , y , z reference, Ω is the angular velocity of the x , y , z reference measured from the X , Y , Z reference and r m / O is the position vector of the man with respect to origin O . Write the formula for acceleration of the man measured from the x , y , z reference a m = a O + Ω ˙ × r m / O + Ω × ( Ω × r m / O ) + 2 Ω × ( v m / O ) x y z + ( a m / O ) x y z (II) Here, a m is the acceleration vector of man measured from the X , Y , Z reference, a O is the acceleration vector of the origin measured from the X , Y , Z reference, ( v m / O ) x y z , ( a m / O ) x y z is the velocity and acceleration vector of the man with respect to origin O measured by an observer attached to the rotating x , y , z reference, Ω ˙ is the angular acceleration due to the rotation of x , y , z reference, Ω is the angular velocity of the x , y , z reference measured from the X , Y , Z reference and r m / O is the position vector of the man with respect to origin O . Conclusion: Refer Figure (1). Consider the swing bridge as the moving reference x y z . Here, the moving reference doesn’t have displacement, it revolves along z − a x i s . The linear velocity and acceleration of the moving reference x y z becomes zero. v O = 0 a O = 0 The vector coordinate of angular velocity of the moving reference x y z is Ω = 0.5 k Since, the moving reference x y z revolves with constant speed. Hence the angular acceleration becomes zero. Ω ˙ = 0 Refer Figure (1). Consider the man. Write the position vector ( r m / O ) directed from origin to man. r m / O = 0 i − 10 j = − 10 j Refer Figure (1). The vector coordinate for the relative velocity of the man with respect to moving reference is ( v m / O ) x y z = − 5 j . Since, the man runs with constant speed. Hence the acceleration becomes zero The vector coordinate for the relative acceleration of the man with respect to moving reference is ( a m / O ) x y z = − 2 j

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 16.8, Problem 132P

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The velocity and acceleration of the man $A$ at the instant of $d=10 ft$ .

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Chapter 16.8, Problem 131P

Chapter 16.8, Problem 133P

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Engineering Mechanics: Statics & Dynamics (14th Edition)

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