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Unformatted text preview: Static Equilibrium and Elasticity Chapter 12 Static Equilibrium Equilibrium implies the object is at rest (static) or its center of mass moves with a constant velocity (dynamic) Static equilibrium is a common situation in engineering Principles involved are of particular interest to civil engineers, architects, and mechanical engineers Conditions for Equilibrium The net force equals zero Σ F = 0 If the object is modeled as a particle, then this is the only condition that must be satisfied The net torque equals zero Στ = 0 This is needed if the object cannot be modeled as a particle Torque τ = r x F Use the righthand rule to determine the direction of the torque The tendency of the force to cause a rotation about O depends on F and the moment arm d Rotational Equilibrium Need the angular acceleration of the object to be zero For rotation, Στ = I α For rotational equilibrium, Στ = 0 This must be true for any axis of rotation Static vs. Dynamic Equilibrium In this chapter, we will concentrate on static equilibrium The object will not be moving Dynamic equilibrium is also possible The object would be rotating with a constant angular velocity In either case, the Στ = 0 Equilibrium Equations We will restrict the applications to situations in which all the forces lie in the xy plane These are called coplanar forces since they lie in the same plane There are three resulting equations Σ F x = 0 Σ F y = 0 Στ z = 0 Axis of Rotation for Torque Equation The net torque is about an axis through any point in the xy plane The choice of an axis is arbitrary If an object is in translational equilibrium and the net torque is zero about one axis, then the net torque must be zero about any other axis Center of Gravity All the various gravitational forces acting on all the various mass elements are equivalent to a single gravitational force acting through a single point called the center of gravity (CG) Center of Gravity The torque due to the gravitational force on an object of mass M is the force M g acting at the center of gravity of the object If g is uniform over the object, then the center of gravity of the object coincides with its center of mass If the object is homogeneous and symmetrical, the center of gravity coincides with its geometric center...
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This note was uploaded on 08/22/2010 for the course PHY 2048 taught by Professor Bose during the Summer '08 term at University of Central Florida.
 Summer '08
 bose
 Physics, Mass

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