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Unformatted text preview: PCS211 – Physics II: Mechanics Equilibrium of a Rigid Body Lectures 1314 (Chapter 5) Dr. Marina MilnerBolotin [email protected] Check Blackboard for course web site! PCS211 – Physics II: Mechanics Part I: Lecture 13 – Equations of Equilibrium and 2 & 3 Force Members Goals: You will be able to recognize twoforce and threeforce members. You will learn how to apply equations of equilibrium to solve for unknowns in the cases mentioned above. 2 PCS211 – Physics II: Mechanics Review: Support Reactions in 2D 3 As a general rule, if a support prevents translation of a body in a given direction, then a force is developed on the body in the opposite direction. Similarly, if rotation is prevented, a couple moment is exerted on the body. A few examples are shown above. Other support reactions are given in your textbook (in Table 51). PCS211 – Physics II: Mechanics Equations of Equilibrium in 2D (Section 53) 4 A body is subjected to a system of forces that lie in the xy plane. When in equilibrium, the net force and net moment acting on the body are zero (as discussed earlier in Section 5.1). This 2D condition can be represented by the three scalar equations: x y F 1 F 2 F 3 F 4 O Note that these equations are the ones most commonly used for solving 2D equilibrium problems. ; ; = = = ∑ ∑ ∑ z y x M F F PCS211 – Physics II: Mechanics Strategy for Solving 2D Equilibrium Problems 5 1. If not given, establish a suitable x  y coordinate system. 1. Draw a FBD of the object under analysis. 2. Apply the three equations of equilibrium (EofE) to solve for the unknowns. ; ; = = = ∑ ∑ ∑ z y x M F F PCS211 – Physics II: Mechanics Important Notes 6 1. If we have more unknowns than the number of independent equations, then we have a statically indeterminate situation. We cannot solve these problems using just statics. 2. The order in which we apply equations may affect the simplicity of the solution. For example, if we have two unknown vertical forces and one unknown horizontal force, then solving ∑ F X = O first allows us to find the horizontal unknown quickly. 3. If the answer for an unknown comes out as a negative number, then the sense (direction) of the unknown force is opposite to that assumed when starting the problem. PCS211 – Physics II: Mechanics Twoforce Members and Threeforce Members (Section 54) 7 The solution to some equilibrium problems can be simplified if we recognize members that are subjected to forces at only two points (e.g., at points A and B). If we apply the equations of equilibrium to such a member, we can quickly determine that the resultant forces at A and B must be equal in magnitude and act in the opposite directions along the line joining points A and B. PCS211 – Physics II: Mechanics Example 131: Problem Solving 8 Given : Weight of the boom = 125 lb, the center of mass is at G, and the load = 600 lb....
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 Winter '09
 juan
 mechanics, Force, FBD

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