Explanation Given information: Mass of rod = 4 kg, mR Mass of tube = 6 kg, mT Initial angular velocity ω 1 = 5 rad/sec Length of tube and rod = 800 mm = 0.8 m Concept: Angular momentum principle Conservation of energy Moment of inertia. Calculation: Moment of inertia , For tube I T = 1 12 m T l 2 = 6 × 0.8 2 12 = 0.32 kg.m 2 For rod I R = 1 12 m R l 2 = 4 × 0.8 2 12 = 0.2133 kg m 2 As per kinematics, ( v θ ) T = r T ω = l ω 2 ( v θ ) R = r R ω = ( l 2 + x ) ω ( v r ) T = v r Taking angular momentum about point o, H o = m T r T ( v θ ) T + I T ω + m R r R ( v θ ) R I R ω = ( 6 × l 2 × l ω 2 ) + 1.6 + [ 4 × ( l 2 + x ) ( l 2 + x ) ω ] + 1.0665 H o = ( 3 2 l 2 ω ) + 2.6665 + [ 4 ( l 2 + x ) 2 ω ] + 1.0665 Now, kinetic energy in assembly, T = 1 2 m T ( v θ ) 2 T + 1 2 I T ω 2 + 1 2 m R ( v θ ) 2 R + 1 2 m R v r 2 + 1 2 I R ω 2 = 3 ( l ω 2 ) 2 + 4 + 2 ( l 2 + x ) 2 ω 2 + 2 v r 2 + 2

12th Edition

ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

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Chapter 17.2, Problem 17.88P

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To calculate the speed of rod when distance x= 400 mm as per given figure.RodAB slides within the tube. Initially, entire rod is within the tube and is released with no velocity and angular velocity of assembly is 5 rad/s.

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Chapter 17.2, Problem 17.87P

Chapter 17.2, Problem 17.89P

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To calculate the speed of rod when distance x = 400 mm as per given figure.RodAB slides within the tube. Initially, entire rod is within the tube and is released with no velocity and angular velocity of assembly is 5 rad/s.

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To calculate the speed of rod when distance x= 400 mm as per given figure.RodAB slides within the tube. Initially, entire rod is within the tube and is released with no velocity and angular velocity of assembly is 5 rad/s.

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Chapter 17 Solutions