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more interacting bodies

# more interacting bodies - TAM 210/211 Engineering Mechanics...

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1 Lecture 15 More Interacting Bodies Stephen D. Downing Mechanical Science and Engineering © 2001 - 2008 University of Illinois Board of Trustees, All Rights Reserved TAM 210/211 Engineering Mechanics: Statics TAM 210/211 - Lecture 15 © 2008 Stephen Downing, University of Illinois at Urbana-Champaign, All Rights Reserved 1 of 15 Homework 4.106 Assume cable is horizontal Homework #5 is due on Fri Feb 22nd

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2 TAM 210/211 - Lecture 15 © 2008 Stephen Downing, University of Illinois at Urbana-Champaign, All Rights Reserved 2 of 15 Interacting Bodies Suppose we have the system shown in (a) above. If we wish to draw a FBD of the bar and the pulley the result is shown in B Note: No forces are shown at B between the pulley and the bar because they are internal forces (and would cancel anyway) Here we have 3 forces, 3 unknowns so the solution does exist. = = = = = = N 320 A 0 F N 160 A 0 F N 200 T 0 M Y Y X X A If the body is in equilibrium, each of it’s parts is also in equilibrium TAM 210/211 - Lecture 15 © 2008 Stephen Downing, University of Illinois at Urbana-Champaign, All Rights Reserved 3 of 15 Separate FBDs Hence we can draw FBDs for beam AB and the pulley at B separately as shown We can write separate equilibrium equations for (b) first to solve for T, P X , P Y Then use P X , P Y in (a) to solve for A X , A Y Note: in (a) there are initially 4 unknown forces so we cannot begin with (a)