Chapter5-Equilirbium of Rigid Body (three dimension )

# Chapter5-Equilirbium of Rigid Body (three dimension ) -...

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Unformatted text preview: PCS211 – Physics II: Mechanics Equilibrium of a Rigid Body Lectures 13-14 (Chapter 5) Dr. Marina Milner-Bolotin [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 two-force and three-force 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 2-D 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 5-1). PCS211 – Physics II: Mechanics Equations of Equilibrium in 2-D (Section 5-3) 4 A body is subjected to a system of forces that lie in the x-y plane. When in equilibrium, the net force and net moment acting on the body are zero (as discussed earlier in Section 5.1). This 2-D 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 2-D equilibrium problems. ; ; = = = ∑ ∑ ∑ z y x M F F PCS211 – Physics II: Mechanics Strategy for Solving 2-D 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 (E-of-E) 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 Two-force Members and Three-force Members (Section 5-4) 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 13-1: 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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Chapter5-Equilirbium of Rigid Body (three dimension ) -...

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