362CHAPTER 12• Static Equilibrium and Elasticity±Balanced Rock in Arches National Park, Utah, is a 3 000 000-kg boulder that has beenin stable equilibrium for several millennia. It had a smaller companion nearby, called “ChipOff the Old Block,” which fell during the winter of 1975. Balanced Rock appeared in an earlyscene of the movie Indiana Jones and the Last Crusade. We will study the conditions underwhich an object is in equilibrium in this chapter. (John W. Jewett, Jr.)Static Equilibrium and ElasticityChapter 12362CHAPTER OUTLINE12.1The Conditions for Equilibrium12.2More on the Center of Gravity12.3Examples of Rigid Objects inStatic Equilibrium12.4Elastic Properties of Solids
363In Chapters 10 and 11 we studied the dynamics of rigid objects. Part of this currentchapter addresses the conditions under which a rigid object is in equilibrium. Theterm equilibriumimplies either that the object is at rest or that its center of massmoves with constant velocity relative to the observer. We deal here only with the for-mer case, in which the object is in static equilibrium. Static equilibrium represents acommon situation in engineering practice, and the principles it involves are ofspecial interest to civil engineers, architects, and mechanical engineers. If you are anengineering student, you will undoubtedly take an advanced course in statics in thefuture.The last section of this chapter deals with how objects deform under load condi-tions. An elasticobject returns to its original shape when the deforming forces are re-moved. Several elastic constants are deﬁned, each corresponding to a different type ofdeformation.12.1The Conditions for EquilibriumIn Chapter 5 we found that one necessary condition for equilibrium is that the netforce acting on an object must be zero. If the object is modeled as a particle, then thisis the only condition that must be satisﬁed for equilibrium. The situation with real (ex-tended) objects is more complex, however, because these objects often cannot be mod-eled as particles. For an extended object to be in static equilibrium, a second conditionmust be satisﬁed. This second condition involves the net torque acting on the ex-tended object.Consider a single force Facting on a rigid object, as shown in Figure 12.1. Theeffect of the force depends on the location of its point of application P. If ris theposition vector of this point relative to O, the torque associated with the force FaboutOis given by Equation 11.1:±±r²FRecall from the discussion of the vector product in Section 11.1 that the vector is per-pendicular to the plane formed by rand F. You can use the right-hand rule to deter-mine the direction of as shown in Figure 11.2. Hence, in Figure 12.1 is directedtoward you out of the page.
This is the end of the preview. Sign up to
access the rest of the document.