Explanation Given: The angular velocity of the link A B is ω A B = 4 rad/s (counter clockwise). The angular acceleration of the link A B is α A B = 5 rad/s 2 (clockwise). Draw the free body diagram ofsystem as shown in Figure 1. Write the relation between the linear velocity and angular velocity. ω = v r (I) v = ω r (II) Here, ω is the angular velocity, v is the linear velocity and r is the radial distance from the instantaneous center or permanent center to the point where the linear velocity acting on the object. Refer Figure (1). Write the equation of relative velocity of slider C with respect to the end B . v C = v B + ω B C × r C / B (III) Here, v C is the velocity vector of the slider C , v B is the velocity vector of the end B , ω B C is the angular velocity of the link B C and r C / B is the position vector directed from B to C . Refer Figure (1). The end B of the link A B travels in a circular motion of radius r = 7 in . Hence it experience the normal acceleration [ ( a B ) n ] and tangential acceleration [ ( a B ) t ] . Write the formula for acceleration at the end B . a B = − ( a B ) t i − ( a B ) n j = − ( α A B r ) i − ( ω A B 2 r ) j (IV) Write the equation of relative acceleration of slider C with respect to the end B . a C = a B + α B C × r C / B − ω B C 2 r C / B (V) Here, a C is the acceleration vector of the slider C , a B is the acceleration vector of the end B , α B C is the angular acceleration of the link B C , r C / B is the position vector directed from B to C and ω B C is the angular velocity of the link B C . Conclusion: Refer Figure (1a) and Equation (II). Calculate the velocity at B of the link A B . v B = ω A B r Substitute 4 rad/s for ω A B and 2 m for r . v B = 4 rad/s ( 2 m ) = 8 m/s Refer Figure (1b). Express the vector coordinate for all velocity component of the system. The vector coordinate of velocity at C is v C = − ( v C 5 4 ) i − ( v C 3 5 ) j = − ( 0 .8 v C ) i − ( 0.6 v C ) j The vector coordinate of velocity at B is v B = − 8 i + 0 j = ( − 8i ) m/s The vector coordinate of angular velocity of link B C is ω B C = ω B C k (counter clockwise) Refer Figure (1b). Write the position vector ( r C / B ) directed from B to C . r C / B = − 0.5 i − 2 j = ( − 0. 5i − 2 j ) m Calculate the velocity of the slider C . Substitute − ( 0.8 v C ) i − ( 0.6 v C ) j for v C , − 8 i for v B , ω B C k for ω B C and ( − 0.5 i − 2 j ) for r C / B in Equation (III). − ( 0.8 v C ) i − ( 0.6 v C ) j = − 8 i + [ ω B C k × ( − 0.5 i − 2 j ) ] = − 8 i + | i j k 0 0 ω B C − 0.5 − 2 0 | = − 8 i + [ i ( 0 + 2 ω B C ) − j ( 0 + 0

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 16.7, Problem 106P

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The velocity and acceleration of the slider block C .

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Chapter 16.7, Problem 105P

Chapter 16.7, Problem 107P

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Chapter 16 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

Ch. 16.3 - When the gear rotates 20 revolutions, it achieves...Ch. 16.3 - The flywheel rotates with an angular velocity of ...Ch. 16.3 - The flywheel rotates with an angular velocity of (...Ch. 16.3 - The bucket is hoisted by the rope that wraps...Ch. 16.3 - A wheel has an angular acceleration of = (0.5 )...Ch. 16.3 - For a short period of time, the motor turns gear A...Ch. 16.3 - Prob. 1P Ch. 16.3 - The angular acceleration of the disk is defined by...Ch. 16.3 - The disk is originally rotating at 0 = 12 rad/s....Ch. 16.3 - Prob. 4P

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The velocity and acceleration of the slider block C .

Solution Summary: The author illustrates the relationship between the linear velocity and angular velocity of the slider block C.

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