Explanation Given: The mass of the slender rod ( m r ) is 12 kg. The stiffness of the spring( k ) is 20 N/m . The un-stretched length of spring ( s ) is 1.5 m. The angle of the slender rod in initial position ( θ ) 1 is 60 ° . The angle of the slender rod in final position ( θ ) 2 is 0 ° . The inclined length of the rod AB ( r A B ) is 2 m. The inclined length of the rod BC ( r B / I C ) is 2 m. The radius of the IC ( r C / I C ) is 1 m. Kinetic energy: Show the kinematics diagram of rod BC at the final positionas in Figure (1). Refer to Figure (1), The IC is located at C, therefore ( v C ) 2 = 0 . For rod BC: Find the velocity at B [ ( v B ) 2 ] . ( v B ) 2 = ( ω B C ) 2 r B / I C Substitute 2 m for r B / I C . ( v B ) 2 = ( ω B C ) 2 ( 2 ) (I) Find the velocity at mass center [ ( v G ) 2 ] . ( v G ) 2 = ( ω B C ) 2 r C / I C Substitute 1 m for r C / I C . ( v G ) 2 = ( ω B C ) 2 ( 1 ) For rod AB: Find the velocity at B [ ( v B ) 2 ] . ( v B ) 2 = ( ω A B ) 2 r A B Substitute 2 m for r A B . ( v B ) 2 = ( ω A B ) 2 ( 2 ) (II) Equate Equation (I) and (II). ( ω B C ) 2 ( 2 ) = ( ω A B ) 2 ( 2 ) ( ω B C ) 2 = ( ω A B ) 2 Determine the kinematic energy at final position ( T 2 ) using the relation. T 2 = 1 2 I A ( ω A B ) 2 2 + 1 2 I G ( ω B C ) 2 2 + 1 2 m r ( v G ) 2 2 = 1 2 ( 1 3 × m r × ( r A B ) 2 ) ( ω A B ) 2 2 + 1 2 ( 1 12 × m r × ( r B / I C ) 2 ) ( ω B C ) 2 2 + 1 2 m r ( v G ) 2 2 (III) Conclusion: Substitute 12 kg for m r , 2 m for r A B , ( ω B C ) 2 for ( ω A B ) 2 , 2 m for ( r B / I C ) , and ( ω B C ) 2 ( 1 ) for ( v G ) 2 in Equation (III). T 2 = 1 2 ( 1 3 × 12 × ( 2 ) 2 ) ( ω B C ) 2 2 + 1 2 ( 1 12 × 12 × ( 2 ) 2 ) ( ω B C ) 2 2 + 1 2 × 12 × ( ( ω B C ) 2 ( 1 ) ) 2 2 = 8 ( ω B C ) 2 2 + 2 ( ω B C ) 2 2 + 6 ( ω B C ) 2 2 = 16 ( ω B C ) 2 2 Potential energy: Show the reference to the datum set as in Figure (2). Determine the initial gravitational potential energy ( V g ) 1 using the relation

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

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Chapter 18.5, Problem 52P

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The angular velocity of rod BC (ωBC)2 .

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Chapter 18.5, Problem 51P

Chapter 18.5, Problem 53P

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Chapter 18 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

Ch. 18.4 - Determine the kinetic energy of the 100-kg object.Ch. 18.4 - The 80-kg wheel has a radius of gyration about its...Ch. 18.4 - The uniform 50-lb slender rod is subjected to a...Ch. 18.4 - The uniform 50-kg slender rod is at rest m the...Ch. 18.4 - The 50-kg wheel is subjected to a force of 50 N....Ch. 18.4 - If the uniform 30-kg slender rod starts from rest...Ch. 18.4 - The 20-kg wheel has a radius of gyration about its...Ch. 18.4 - At a given instant the body of mass m has an...Ch. 18.4 - The wheel is made from a 5-kg thin ring and two...Ch. 18.4 - The wheel is made from a 5-kg thin ring and two...

Ch. 18.4 - A force of P = 60 N is applied to the cable, which...Ch. 18.4 - A force of P = 20 N is applied to the cable, which...Ch. 18.4 - A force of P = 20 N is applied to the cable, which...Ch. 18.4 - The double pulley consists of two parts that are...Ch. 18.4 - The double pulley cons1sts of two parts that are...Ch. 18.4 - Prob. 9P Ch. 18.4 - The spool has a mass of 40 kg and a radius of...Ch. 18.4 - Prob. 11P Ch. 18.4 - Determine the velocity of the 50-kg cylinder after...Ch. 18.4 - The 10-kg uniform slender rod is suspended at rest...Ch. 18.4 - Prob. 14P Ch. 18.4 - The pendulum consists of a 10-kg uniform disk and...Ch. 18.4 - A motor supplies a constant torque M = 6 kNm to...Ch. 18.4 - The center O of the thin ring of mass m is given...Ch. 18.4 - Prob. 18P Ch. 18.4 - Prob. 19P Ch. 18.4 - If P = 200 N and the 15-kg uniform slender rod...Ch. 18.4 - A yo-yo has a weight of 0.3 lb and a radius of...Ch. 18.4 - Prob. 22P Ch. 18.4 - Prob. 23P Ch. 18.4 - Prob. 24P Ch. 18.4 - The 30-kg disk is originally at rest, and the...Ch. 18.4 - Two wheels of negligible weight are mounted at...Ch. 18.4 - Prob. 27P Ch. 18.4 - The 10-kg rod AB is pin connected at A and...Ch. 18.4 - The 10-lb sphere starts from rest at = 0 and...Ch. 18.4 - Motor M exerts a constant force of P = 750 Non the...Ch. 18.4 - Prob. 31P Ch. 18.4 - The linkage consists of two 6-kg rods AB and CD...Ch. 18.4 - The two 2-kg gears A and B are attached to the...Ch. 18.4 - The linkage consists of two 8-lb rods AB and CD...Ch. 18.4 - The linkage consists of two 8-lb rods AB and CD...Ch. 18.5 - F187. If the 30-kg disk is released from rest when...Ch. 18.5 - The 50-kg reel has a radius of gyration about its...Ch. 18.5 - The 60-kg rod OA is released from rest when = 0....Ch. 18.5 - Prob. 10FP Ch. 18.5 - The 30-kg rod is released from rest when = 45....Ch. 18.5 - Prob. 12FP Ch. 18.5 - Prob. 36P Ch. 18.5 - Prob. 37P Ch. 18.5 - An automobile tire has a mass of 7 kg and radius...Ch. 18.5 - The spool has a mass of 20 kg and a radius of...Ch. 18.5 - The spool has o mass of 20 kg and a radius of...Ch. 18.5 - A uniform ladder having a weight of 30 lb is...Ch. 18.5 - Prob. 44P Ch. 18.5 - The 12-kg slender rod is attached to a spring,...Ch. 18.5 - Prob. 46P Ch. 18.5 - The 40-kg wheel has a radius of gyration about its...Ch. 18.5 - The assembly consists of two 10-kg bars which are...Ch. 18.5 - The assembly consists of two 10-kg bars which are...Ch. 18.5 - The compound disk pulley consists of a hub and...Ch. 18.5 - Prob. 51P Ch. 18.5 - Prob. 52P Ch. 18.5 - The two 12-kg slender rods are pin connected and...Ch. 18.5 - If the 250-lb block is released from rest when the...Ch. 18.5 - The slender 15-kg bar is initially at rest and...Ch. 18.5 - If the chain is released from rest from the...Ch. 18.5 - Prob. 57P Ch. 18.5 - Prob. 58P Ch. 18.5 - The slender 6-kg bar AB is horizontal and at rest...Ch. 18.5 - Prob. 60P Ch. 18.5 - Prob. 61P Ch. 18.5 - The 50-lb wheel has a radius of gyration about its...Ch. 18.5 - The system consists of 60-lb and 20-lb blocks A...Ch. 18.5 - The door is made from one piece, whose ends move...Ch. 18.5 - Prob. 65P Ch. 18.5 - Prob. 66P Ch. 18.5 - Prob. 67P Ch. 18.5 - The system consists of a 30-kg disk A, 12-kg...Ch. 18.5 - The pendulum of the Charpy impact machine has a...Ch. 18.5 - Prob. 2RP Ch. 18.5 - The drum has a mass of 50 kg and a radius of...Ch. 18.5 - The spool has a mass of 60 Kg and a radius of...Ch. 18.5 - Prob. 5RP Ch. 18.5 - At the Instant shown, the 50-lb bar rotates...Ch. 18.5 - Prob. 7RP Ch. 18.5 - Prob. 8RP

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EVERYTHING on Axial Loading Normal Stress in 10 MINUTES - Mechanics of Materials; Author: Less Boring Lectures;https://www.youtube.com/watch?v=jQ-fNqZWrNg;License: Standard YouTube License, CC-BY

The angular velocity of rod BC ( ω B C ) 2 .

Solution Summary: The author shows the kinematics diagram of rod BC at the final position in Figure (1).

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The angular velocity of rod BC (ωBC)2 .

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Chapter 18 Solutions