This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: v C PROBLEM 17.20 A rope is wrapped around a cylinder of radius r and mass m as shown. Knowing that the cylinder is released from rest, determine the velocity of the center of the cylinder after it has moved downward a distance s . SOLUTION Kinematics: Point C is the instantaneous center r v = r v = Energy: Position 1 . At rest. T 1 = 0 Position 2 . Cylinder has fallen through distance s . 2 2 2 2 1 2 1 I v m T + = 2 2 2 2 1 2 1 2 1 + = r v mr v m 2 4 3 v m = Work. mgs U = 2 1 Principle of Work and Energy. 2 2 1 1 T U T = + 2 4 3 v m mgs = + gs v 3 4 2 = = gs 3 4 v PROBLEM 17.22 A halfcylinder of mass m and radius r is released from rest in the position shown. Knowing that the halfcylinder rolls without sliding, determine ( a ) its angular velocity after it has rolled through 90 o , ( b ) the reaction at the horizontal surface at the same instant. [ Hint : Note that GO = 4 r /3 and that, by the parallelaxis theorem, ( 29 2 2 2 1 GO m mr I = .] SOLUTION Kinematics: Point C is the instantaneous center b v =  = 3 4 r r r . 5756 = Energy: Position 1 . T 1 = 0 V 1 = 0 Position 2 . Kinetic energy 2 2 2 2 1 2 1 I v m T + = ( 29 2 2 2 2 3 4 2 1 2 1 5756 2 1  + = r m mr r . m 2 2 3256 mr . = Potential energy ( 29 OG mg V = 2 r mg 3 4 = ( a ) Conservation of energy. 2 2 1 1 V T V T + = + mgr mr . 3 4 3256 2 2 = + r g . 3035 1 2 = r g . 142 1 = v O G C b ( b ) Kinematics: Translation + Rotation about O = Rolling motion Acceleration of C . xcomponent. component....
View
Full
Document
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.
 Spring '10
 Prof.V.H.Chu

Click to edit the document details