Lesson_4.4_Printable

# Lesson_4.4_Printable - Equilibrium of Rigid Bodies...

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Equilibrium of Rigid Bodies Equilibrium is a state of balance. In order that an object may be in equilibrium, all the forces acting on it must be balanced. F net = 0 This can be summarized as: F y = 0 F x = 0 F z = 0 But F net = 0 is not enough to keep an object in equilibrium. Consider two equal and opposite forces F acting on the object on the right. These forces are balanced because F y = 0 But the object is not in equilibrium because these forces produce a net torque on the object. Another necessary condition for equilibrium is τ net = 0 F F τ = 0 1

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Consider forces F 1 and F 2 acting at points A and B of an object trying to produce rotation on it about an axis passing through C. The rotation produced by F 1 about C is counterclockwise We call this a counterclockwise torque. The rotation produced by F 2 about C is clockwise. We call this a clockwise torque. F 2 B C A F 1 Axis of rotation. For convenience we take a counterclockwise torque as positive and a clockwise torque as negative. The torque of F 1 about C is CA · F 1 . (This is positive because it is counterclockwise) The torque of F 2 about C is -CB · F 2 . (This is negative because it is clockwise τ = CA · F 1 – CB · F 2 This should be zero for rotational equilibrium. 2
Torque of a couple A couple is formed by two equal and opposite parallel forces on an object so that their points of applications are different F 1 and F 2 acting on the rod AB have equal magnitudes, F 1 = - F 2 We find the torque of these forces about an axis through A The torque of F 1 about A = 0 · F 1 = 0 (F 1 passes through A) F 2 B C A F 1 The torque of F 2 about A = AB · F 2 (counterclockwise) τ about A = 0 + AB·F 2 = AB·F 2 . Now we take the torque of these two forces about B The torque of F 1 about B = BA · F 1 . (counterclockwise) τ about B = BA·F 1 + 0 The torque of F 2 about B = 0·F 2 = 0 (F 2 passes through B) Torque of a couple is the product of one of the forces and the perpendicular distance between the forces . = BA·F1 = AB·F 2 (F 1 = F 2 in magnitude) 3

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Solving problems using equilibrium conditions To solve problems using conditions of equilibrium, we use the following steps: 1. Identify the point or object in equilibrium 2. Draw vectors to represent all the forces acting on the object 3. Resolve the force vectors into x- and y-components 4. Mark all the distances
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## This note was uploaded on 05/01/2011 for the course PHY 2048 taught by Professor George during the Fall '10 term at Edison State College.

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Lesson_4.4_Printable - Equilibrium of Rigid Bodies...

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