Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley PowerPoint ® Lecture prepared by Richard Wolfson 12 Static Equilibrium Richard Wolfson Slide 12-1 Essential University Physics

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley In this lecture you’ll learn To describe the conditions necessary for static equilibrium To calculate forces and torques needed to ensure that a system is in static equilibrium To determine whether or not an equilibrium is stable Slide 12-2

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Conditions for static equilibrium A system in static equilibrium undergoes neither rotational nor linear acceleration. If it’s at rest, it remains at rest. The conditions for static equilibrium are No net force: No net torque: Torques can be evaluated about any convenient point: A drawbridge of length L and the forces acting on it. Choosing the pivot point at the lower left leaves two forces that contribute torques: Slide 12-3

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question The figure shows three pairs of forces acting on an object. Which pair, acting as the only forces on the object, results in static equilibrium? A.Force pair B.Force pair C.Force pair Slide 12-4

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Center of gravity The gravitational forces acting on all parts of an object exert a torque on the object. These forces act like a single force, equal to the object’s weight, acting at a point called the center of gravity. In a uniform gravitational field, the center of gravity coincides with the center of mass. Gravitational force due to a single mass element produces a torque about O: Finding the center of gravity The dancer is in static equilibrium. Which point is her center of gravity? Slide 12-5

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question The dancer in the figure is balanced; that is, she is in static equilibrium. Which of the three lettered points could be her center of gravity? A. Point A B. Point B C.Point C Slide 12-6

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Problem solving strategy: Static equilibrium Slide 12-7

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Example: A leaning ladder At what angle will the ladder slip? The ladder and the forces on itForces in both directions sum to zero: The torques are all perpendicular to the plane of the page, so there’s only one torque equation: Solve the three equations to get Slide 12-8

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question The figure shows a person in static equilibrium leaning against a wall. Which one of the following must be true? A. There must be a frictional force at the wall, but not necessarily at the floor. B. There must be a frictional force at the floor, but not necessarily at the wall. C.There must be frictional forces at both wall and floor. Slide 12-9

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Stability An equilibrium is stable if a slight disturbance from equilibrium results in forces and/or torques that tend to restore the equilibrium. An equilibrium is unstable if a slight disturbance causes the system to move away from the original equilibrium. Cone on its base is stable Cone on its tip is unstable Slide 12-10

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Kinds of stability Unstable equilibrium: disturbed ball will leave original equilibrium Neutrally stable equilibrium Metastable or conditionally stable equilibrium: ball returns for small disturbances, but not for large ones Stable equilibrium: disturbed ball will return to equilibrium Slide 12-11

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question Which of the labeled points in the figure is in metastable equilibrium? A.Point A B.Point B C.Point C D.Point D E.Point E Slide 12-12

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Conditions for equilibrium and stability To be in equilibrium, there must be zero net force on an object. Therefore the object must be at a maximum or minimum of its potential energy curve: For stable equilibrium, the object must be at a minimum: In two and three dimensions, an object can be stable in one direction but not another: Slide 12-13

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Summary Static equilibrium requires zero net force and zero net torque on a system: A crane in static equilibrium Equilibria can be stable, unstable, neutrally stable, or metastable: Slide 12-14