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Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI 1313 Mechanics I Lecture 10:Particle Equilibrium, Free-Body Diagrams and Coplanar Forces

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 2 Chapter 3 Objectives to introduce the concept of the free-body diagram for a particle. to show how to solve particle equilibrium problems using the equations of equilibrium

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 3 Lecture 10 Objectives to examine and apply Chapter 3 objectives in 2D space

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 4 Particle Equilibrium Newton’s 1 st Law – Inertia Particle equilibrium Rest (Static) Constant velocity F1F1 F2F2 F3F3 V = 0, v +Y +X 2 Equations Solve for at most 2 Unknowns Scalar components = 0

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 5 Free-Body Diagram (FBD) What is it? Sketch or diagram illustrating all force vectors acting on a particle (body) Purpose? A visual aid in developing equilibrium equation of motion What is the procedure? Draw isolated or “free” outlined shape Show all forces Characterize each force Magnitude Sense Direction

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 6 Example FBD Procedure Draw isolated or “free” outlined shape Show all forces Characterize each force Magnitude Sense Direction +Y +X

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 7 Comprehension Quiz Select the Correct FBD of Particle A Answer: D Hibbeler (2007)

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 8 Applications Hibbeler (2007)

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 9 Example For the engine in static equilibrium, using a free body diagram, solve for the force magnitudes F AD and F AB. The engine mass is 255 kg.

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 10 Example Draw FBD +Y +X = 30 F AB W = F AC = mg F AD W = (255 kg)(9.806m/s 2 ) = 2.5kN A

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 11 Example State Equilibrium Equation +Y +X = 30 F AB W = F AC = 2.5kN F AD A

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 12 Example The car is towed at a constant speed by the 600 lb force and the angle is 25°. Find the forces in the ropes AB and AC.

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 13 Example (cont.) FBD at Point A 25 600 lb F AB F AC A 30 2 Equations 2 Unknowns

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 14 Example (cont.) Equilibrium at Point A Rearrange Substitute 25 600 lb F AB F AC A 30

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 15 Example Find the forces in the cables and weight of sack B. What point is first selected for the FBD?

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 16 Example (cont.) Unknown force magnitudes at Point C FBD at Point E 2 Equations 2 Unknowns

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 17 Example (cont.) Equilibrium at Point E Rearrange Substitute

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 18 Example (cont.) FBD at Point E and Point C

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 19 Example (cont.) Equilibrium at Point C

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 20 Homework Problem Each cord can sustain a maximum tension of 200 lb. Determine the largest weight of the sack that can be supported. Also, determine θ of cord DC for equilibrium.

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 21 Quiz #2 Examining concepts from Tutorial Problem Set #2 Only approved calculators allowed Any formulae, conversion factors will be provided Ancillary information may also be provided

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 22 Classification of Textbook Problems Hibbeler (2007)

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ENGI 1313 Statics I – Lecture 10© 2007 S. Kenny, Ph.D., P.Eng. 23 References Hibbeler (2007) mech_1

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