Chapter5-Rigid Body Diragrams

# Chapter5-Rigid Body Diragrams - Equilibrium of a Rigid Body...

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PCS211 – Physics II: Mechanics Equilibrium of a Rigid Body Lectures 11-12 (Chapter 5) Dr. Marina Milner-Bolotin [email protected] Check Blackboard for course web site!

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PCS211 – Physics II: Mechanics Part I: Lecture 11 – FBD and Equilibrium of a Rigid Body Goals: Review what you already know about FBD (particle case) Expand your FBD knowledge to the rigid body Learn how to identify support reactions Learn to draw relevant FBD for rigid body problems 2
PCS211 – Physics II: Mechanics Questions to Think About! A 200 kg platform is suspended off an oil rig. How do we determine the force reactions at the joints and the forces in the cables? How are the idealized model and the FBD diagram used to do this? Which diagram above is the idealized model? 3

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PCS211 – Physics II: Mechanics More Questions! A steel beam is used to support roof joists. How can we determine the support reactions at A & B? Again, how can we make use of an idealized model and an FBD to answer this question? 4
PCS211 – Physics II: Mechanics Mechanical Systems and FBD All physical bodies are 3-D but we can treat them as 2-D when the forces, they are subjected to, act on a plane. We define a mechanical system as a body or a group of bodies which can be conceptually isolated or independent from all other bodies. Once we decide which body or combination of bodies make up the system then we treat it as a single body isolated from all other bodies. This isolation is accomplished by means of a free- body diagram (FBD) . 5

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PCS211 – Physics II: Mechanics Forces and FBD Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon a particular body in a given situation. If there is more than a body one has to make sure the free-body diagram is for the chosen body. The free-body diagram is the most important step in the solution of problems in Mechanics the force is applied. 6
PCS211 – Physics II: Mechanics Reminder: Characteristics of Forces 1. Forces are vectors. 2. Forces can be applied by direct physical contact or remote action. 3. Forces can be either internal or external to the system. 4. Forces may be either concentrated or distributed . 5. The principle of transmissibility permits the treatment of a force as a sliding vector as far as its external effects on a system are concerned. 7

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PCS211 – Physics II: Mechanics 7 Steps in FBD Construction 1. Choose a system to isolate. It should involve one or more of the desired unknown quantities 2. Draw a diagram that represents the external boundary of the system 3. Identify all external forces that act on the isolated system 4. Show the choice of coordinate axes 5. Represent all forces known by vector arrows indicating the magnitudes (either numerically or symbolically) and directions 1. If the force direction is unknown assign arbitrarily a sense to that force. Subsequent calculations will yield a + value if the direction chosen is correct and a - value if it is the opposite to what you chose.
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