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Reference Guide

Free Body Diagrams - Reference Guides

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University of Texas - El Paso
Basic Engineering
BE 1101

permachartsTM F r e eB o d yD ia g ra m s Introduction d’Alembert’s Principle •frces that act upon them; the procedure involves 2 stepsembert’s Principle asserts that inertial and centrifugal effects can be treated like a force •Isolate the object or system (i.e.,detach the rigi•This allows Dynamics problems to be analyzed using the principles of Statics •Replace all forces,either real or virtual (see For• Translational inertia acts in the direction opposite to the direction of the acceleration; its magnitude is the quantity ma •off-axis (angled force) vectors into their XY componentsti2nal inertia acts perpendicular to the curvilinear path (i.e.,radially outward) that an object is traveling; its magnitude is mv / Basic Situations & Free Body Diagrams Note: In each situation,the diagram on the left is indicated by the heading of the section (e.g.,WEIGHT ON FRICTIONLESS SURFACE); the diagram on the right is the corresponding Free Body Diagram (see Force & Vector Representations) FREE WEIGHT WEIGHT ON FRICTIONLESS SURFACE •W is a force; therefore,it is a vector •n is the reaction of the floor acting on the stationary weight •This force is due to gravitational interaction between the Earth and the body,which always acts towards the center of the Note: Mass is not a force; it is a property of matter and related to weight by W = mg WEIGHT ON FRICTIONLESS SURFACE WITH HORIZONTAL FORCWEIGHT ON REAL SURFACE WITH ANGLED FORCE • Since the mass is being pushed on a frictionless floor,the only resistance to the acceleration is the inertia (ma) o the mass; it opposes the acceleration • If Px (not shown) matches Rf,then there will be no inertial force (in accordance with Newton’s Second Law) m o • Cables always pull along their line of action at the point of attachmentong their line of action at the point of attachment . s t r a h c a ROLLER CONTACT FRICTIONLESS CONTACT • Roller contacts cannot resist a force parallel to the surface of contact cannot resist a force parallem to the surface of contact •Therefore,any force at this contact must be perpendicular (normal) to the surfacentact must be perpendirular (normal) to the surface e p ROUGH CONTACT OR PIN JOINT WELDED, BOLTED (RIGID) CONNECTION •A swivel or pin joint can resist any linear push or pullhe swivel joint is replaced by a welded,bolted or rigid connection,then the joint can be represented by R (as for the • In two dimensions (2-D),this can be represented by a resultant force with components Rf and Rn orRx and Rymoment) permacharts TM Force Types •There are 2 categories of forces in mechanical analysis (see Force & Vector Representations) B ODY FORCES SURFACE FORCES • Body forces are also known as action-at-a-distance forces • Surface forces are also known as contact forces •They include gravitational,electrical,magnetic,and inertial force•These forces arise from contact between the rigid body and anything it contacts (e.g.,the floor,a cable,a plate to which it is attached with a bolt or pin joint) Note: In Statics and Dynamics,problems are usually limited to grav• Surface forces may be concentrated or distributed inertial forces • Concentrated surface forces can act in compression or tension • Inertial forces are reactions resulting from an acceleration • Compressive forces are represented by conventional arrows that terminate at the point of contact • Translational and rotational inertial forces (identified by d’AlNote:When body forces are concentrated tensile forces,they are represented by conventional arrows that originate at the point of contact expressed by ma and mv (centrifugal force) • Distributed surface forces are usually compressive; therefore,they act perpendicular (normal) to the surface • Body forces are represented by arrows that originate at the cent• However,they can also act tangential to the surface (e.g.,friction) (cg) of the object (rigid body) being analyzed •The arrow points in the direction of the force’s action • Tangential distributed forces are represented by a double-headed arrow indicating that they act along a line Examples: Weight vectors,due to gr
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