ME 242 Lecture 30 04.17

# Example prob 7311 given cart mass mc rod mass ma

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: mc , Rod mass = ma rod length = 2L , inertia about O = IO Cart applies a moment Mk on rod at O Find: equations of motion for system d A mc g Ry FBD=IRD Rx F mc y FBD=IRD M O mc x Rx O b2 M N1 N2 F + Rx = mc x N + N - m g + R = m 1 2 c y cy b1 A Ry I ma g -Rx- (Ry + ma g) j = ma a A i a A = aO + k r A /O + k ( k r A /O ) ma aA y m a aA x -N1d + N 2 d - M = 0 = i + k Lb1 + k ( k Lb1 ) x 2 = i + Lb 2 - Lb1 x FBD=IRD M Choice of moment equations ma aA y ma aA x M Rx O A b2 b1 Rx O A b2 b1 ma aA y m a aA x -Rx i - (Ry + ma g) j = ma (i + Lb 2 - 2 Lb1 ) x Ry ma g I Ry ma g I -Rx = ma ( + L cos - 2 L sin ) x -Ry - ma g = ma (L sin + 2 L cos ) k M A = IA M O = IA k + r A /O ma a A M O = IO k + r A /O ma aO 2 Moment equation M 6 equations, 6 unknowns F + Rx = mc x N1 + N 2 - mc g + Ry = 0 -N1d + N 2 d - M = 0 -Rx = ma ( + L cos - 2 L sin ) x -Ry - ma g = ma (L sin + 2 L cos ) Rx O A b2 b1 ma aA y ma aA x Ry ma g I x Rx Ry N1 N2 M O IO k + r A /O ma aO = M k - ma gL sin k = IO k + Lb1 ma x i = IO k + Lma sin(90 - )k x = IO k + Lma cos k x M - ma gL sin = IO + Lm a cos x Equations of Motion M - ma gL sin = IO + Lm a cos x F = (ma + mc ) + ma (L cos - 2 L sin ) x A 3...
View Full Document

## This note was uploaded on 09/19/2009 for the course ME 242 taught by Professor Kam during the Spring '06 term at Nevada.

Ask a homework question - tutors are online