Assignment 9 solution 2009

Assignment 9 solution 2009 - PROBLEM 16.25 A 10-kg uniform...

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Unformatted text preview: PROBLEM 16.25 A 10-kg uniform disk is placed in contact with an inclined surface and a constant 11 N m couple M is applied as shown. The weight of the link AB is negligible. Knowing that the coefficient of kinetic friction at D is 0.4, determine ( a ) the angular acceleration of the disk, ( b ) the force in the link AB . SOLUTION Free-body diagram: 2 2 1 mr I = 10 cos60 cos30 4 : o o =- + = + g N N . a m F y y ( 29 81 9 10 cos60 cos30 4 o o =- + . N N . N 90 115 . N = ( a ) ( 29 ( 29( 29 2 225 10 2 1 225 4 11 : . . N . I M B =- = + rad/s 247 2 . = 247 2 . = rad/s ( b ) sin60 sin30 4 : o o =- + = + N N . F a m F AB x x N 19 77 . F AB = 19 77 . AB = F N (compression) N F = k N = 0.4 N 10 g F AB = I PROBLEM 16.67 A uniform sphere of radius r and mass m is placed with no initial velocity on a belt that moves to the right with a constant velocity v 1 . Denoting by k the coefficient of kinetic friction between the sphere and the belt, determine ( a ) the time t 1 at which the sphere will start rolling without sliding, ( b ) the linear and angular velocities of the sphere at time t 1 . SOLUTION Free-body diagram: 2 5 2 mr I = : =- = + mg N a m F y y mg N = a m N a m F k x x = = + : g a k = I r N I M k G = = + : 2 5 2 mr r mg k = r g k 2 5 = Kinematics: gt t a v k = = + (1) t r g t k 2 5 = = + (2) N = C G r F = k N mg C G I a m C = Point of contact with belt r v v C + = + r t r g gt k k...
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This note was uploaded on 12/17/2011 for the course CIVE 281 taught by Professor Prof.v.h.chu during the Spring '10 term at McGill.

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Assignment 9 solution 2009 - PROBLEM 16.25 A 10-kg uniform...

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