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Problem 15.252

4.5 in. A. B. E. 7.5 in. D. F. Problem 15.252. A drum of radius 4.5 in. is mounted on a cylinder of radius 7.5 in. A cord is wound around the drum, and its extremity E is pulled to the right with a constant velocity of 15 in./s , causing

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Problem 15.252

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  1. 4.5 in A B E 7.5 in D F Problem 15.252 A drum of radius 4.5 in. is mounted on a cylinder of radius 7.5 in. A cord is wound around the drum, and its extremity E is pulled to the right with a constant velocity of 15 in./s, causing the cylinder to roll without sliding on plate F. Knowing that plate F is stationary, determine: (a) the velocity of the center of the cylinder, (b) the acceleration of point D of the cylinder.

  2. Problem 15.252 4.5 in A B E 7.5 in D F C vB B A Solving Problems on Your Own A drum of radius 4.5 in. is mounted on a cylinder of radius 7.5 in. A cord is wound around the drum, and its extremity E is pulled to the right with a constant velocity of 15 in./s, causing the cylinder to roll without sliding on plate F. Knowing that plate F is stationary, determine: (a) the velocity of the center of the cylinder, (b) the acceleration of point D of the cylinder. 1. Determine velocities in a body under general plane motion: Velocities can be determined either by method of instantaneous center of rotation, or by considering the motion of the body as the sum of a translation and a rotation. vA vA w A vB A A vA rB/A = + vB/A B B B vA vB = vA + vB/AvB/A = wxrB/A

  3. Problem 15.252 4.5 in A B E 7.5 in D F Solving Problems on Your Own A drum of radius 4.5 in. is mounted on a cylinder of radius 7.5 in. A cord is wound around the drum, and its extremity E is pulled to the right with a constant velocity of 15 in./s, causing the cylinder to roll without sliding on plate F. Knowing that plate F is stationary, determine: (a) the velocity of the center of the cylinder, (b) the acceleration of point D of the cylinder. 2. Determine accelerations in a body under general plane motion: Draw (a) a plane motion diagram, (b) translation diagram, and (c) rotation diagram. y’ wk A x’ A A aA aA ak aB/A + = (aB/A)n (aB/A)t B B aA aB B (a) (c) (b) aB = aA + aB/AoraB = aA + (aB/A )n + (aB/A ) t

  4. Problem 15.252 Solution 4.5 in A B E 7.5 in D F vA A vE vB B E D F Determine velocities in a body under general plane motion. (a) The velocity of the center of the cylinder (point A). Since disk rolls without sliding vD = 0 vE = vB = 15 in/s vB = (BD) w 15 in/s = (3 in ) w w = 5 rad/s vA = (AD) w = ( 7.5 in )( 5 rad/s ) vA = 37.5 in/s

  5. Problem 15.252 Solution 4.5 in A B E 7.5 in D F w aA = 0 = + A A A (aD)y (aD/A)n D D (aD)x D a = 0 aA = aD = 0 Determine accelerations in a body under general plane motion. (a) The acceleration of point D. aD = aA + (aD/A)n [(aD)x ] + [(aD)y ] = [0 ] + [ 7.5 w2 ] aD = (7.5 in)( 5 rad/s )2aD = 187.5 in/s2

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