Explanation Given information: The distance ( x ) between the slider AB is 60 in . The maximum velocity ( v right ) of slider to the right is 12 in ./s . The maximum velocity ( v left ) of slider to the left is 30 in ./s . The slider accelerates and decelerates ( a right ) at the constant rate to the right is 6 in ./s 2 . The slider accelerates and decelerates ( a left ) at the constant rate to the left is 20 in ./s 2 . Calculation: Calculate the time from right ( t right ) using the relation: t right = v right a right Substitute 12 in ./s for v right and 6 in ./s 2 for a right . t right = 12 6 = 2 sec Calculate the time from right ( t left ) using the relation: t left = v left a left Substitute 30 in ./s for v left and 20 in ./s 2 for a left . t left = 30 20 = 1.5 sec Tabulate the velocity ( v ) corresponding to time ( t ) as in Table (1): t (s) v ( in ./s ) 0 0 2 12 t 1 − 2 12 t 1 0 t 1 + 1.5 -30 t 2 − 1.5 -30 t 2 0 Plot the v-t of the slider as in Figure (1): Calculate the area ( A 1 ) using the relation: A 1 = ( t 1 − t right ) v right Substitute 2 sec for t right and 12 in ./s for v right . A 1 = ( t 1 − 2 ) 12 = 12 t 1 − 24 Calculate the time ( t 1 ) : Equate the A 1 with x . A 1 = x Substitute 12 t 1 − 24 for A 1 and 60 in . for x . ( 12 t 1 − 24 ) = 60 t 1 = ( 60 + 24 ) 12 t 1 = 7 sec Calculate the area ( A 2 ) using the relation: A 2 = ( ( t 2 − t 1 ) − t left ) v left Substitute 1.5 sec for t left , 7 sec for t 1 and 30 in ./s for v left . A 2 = ( ( t 2 − 7 ) − 1.5 ) × 30 Calculate the time ( t 2 ) : Equate the A 2 with x . A 2 = x Substitute ( ( t 2 − 7 ) − 1.5 ) × 30 for A 2 and 60 in . for x

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 11.3, Problem 11.68P

To determine

The time (tcycle) required for the slider to complete a full cycle and the construct the v-t and x-t curves of its motion.

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Chapter 11.3, Problem 11.67P

Chapter 11.3, Problem 11.69P

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Vector Mechanics for Engineers: Statics and Dynamics

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The time ( t cycle ) required for the slider to complete a full cycle and the construct the v-t and x-t curves of its motion.

Solution Summary: The author calculates the time from right (t_cycle) using the relation:.

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The time (tcycle) required for the slider to complete a full cycle and the construct the v-t and x-t curves of its motion.

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Chapter 11 Solutions