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Unformatted text preview: Chapter 12 Equilibrium and Elasticity In this chapter we will define equilibrium and find the conditions needed so that an object is at equilibrium. We will then apply these conditions to a variety of practical engineering problems of static equilibrium. We will also examine how a “rigid” body can be deformed by an external force. In this section we will introduce the following concepts: Stress and strain Young’s modulus (in connection with tension and compression) Shear modulus (in connection with shearing) Bulk modulus (in connection to hydraulic stress) (121) We say that an object is in equilibrium when the following two conditions are satisfied: 1. The linear momentum of the cnter of mass is constant 2. The angular momentum about the cente Equilibrium P L r r r of mass or any other point is a constant Our concern in this chapter is with situtations in which 0 and That is we are interested in objects that are not moving in any way (this include P L = = r r s translational as well as rotational motion) in the reference frame from which we observe them. Such objects are said to be in In chapter 8 we differentiated betwe static en stab equilib le and rium unstable static equilibrium If a body that is in static equilibrium is displaced slightly from this position the forces on it may return it to its old position. In this case we say that the equilibrium is . If the body does not return to its old position then the equilibrium i stable unst s able (122) In chapter 9 we calculated the rate of change for the linear momentum of the center of mass of an object. If The Condi an objec tions of equilibri t is in translational equilibrium u t n m he net dP F dt = r r constant and thus In chapter 11 we analyzed rotational motion and saw that Newton's second law takes the form: For an object in rotational equilibrium we hav e: net net dP P dt dL dt F τ = = → = = r r r r r constant The two requirements for a body to be i...
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This note was uploaded on 02/12/2010 for the course PHY PHY taught by Professor Mueller during the Fall '09 term at University of Florida.
 Fall '09
 MUELLER

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