To determine The tangential acceleration of point B along its path. The angular acceleration of the bar AB . Explanation Write the expression for the acceleration of point B in terms of acceleration of point A in vector form. a B = a A + α × r B / A − ω 2 r B / A (I) Here, acceleration of point B in vector form is a B , acceleration of point A in vector form is a A , angular acceleration of the bar AB in vector form is α , angular velocity of the bar AB in vector form is ω , position vector of point B with respect to point A is r B / A and unit vectors along x and y -directions are i and j respectively. Conclusion: Show the schematic diagram of the bar AB as in Figure (1). From Figure (1), calculate the angle made by the bar AB . β = sin − 1 ( 0.5 m − ( 0.5 m × sin 30 ° ) 1.2 m ) = 12.02 ° Here, angle made by the bar AB is β . Calculate the position vector of point B with respect to point A . r B / A = ( 1.2 m ) ( − cos β i + sin β j ) = ( 1.2 ) ( − cos β i + sin β j ) m Substitute 12.02 ° for β . r B / A = ( 1.2 ) ( − cos 12.02 ° i + sin 12.02 ° j ) m Write the angular velocity of the bar AB in vector form using right hand rule. ω = ( 3.23 rad / s ) k = 3.23 k rad / s Here, unit vector along z direction is k . Write the angular acceleration of the bar AB in vector form using right hand rule. α = α k Calculate the acceleration of point B . a B = ( a B ) t sin 30 ° i + ( a B ) t cos 30 ° r j × r + v B 2 r ( cos 30 ° i + sin 30 ° j ) = ( a B ) t ( sin 30 ° i − cos 30 ° j ) + v B 2 r ( cos 30 ° i + sin 30 ° j ) (II) Here, tangential acceleration of point B is ( a B ) t , velocity of point B is v B and length of the bar AB is r . Substitute 4.38 m / s for v B and 0.5 m for r in Equation (II). a B = ( a B ) t ( sin 30 ° i − cos 30 ° j ) + ( 4.38 m / s ) 2 0.5 m ( cos 30 ° i + sin 30 ° j ) = ( a B ) t ( sin 30 ° i − cos 30 ° j ) + 33

8th Edition

ISBN: 9781118885840

Author: James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher: WILEY

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Chapter 5.6, Problem 149P

To determine

The tangential acceleration of point B along its path.

The angular acceleration of the bar AB.

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Chapter 5.6, Problem 148P

Chapter 5.6, Problem 150P

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Engineering Mechanics: Dynamics

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The tangential acceleration of point B along its path. The angular acceleration of the bar AB .

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The tangential acceleration of point B along its path. The angular acceleration of the bar AB.

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Chapter 5 Solutions

The tangential acceleration of point B along its path.

The angular acceleration of the bar AB.