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ENGI 1313 Mechanics I Lecture 10: Particle Equilibrium, Free-Body Diagrams and Coplanar Forces

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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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Lecture 10 Objectives to examine and apply Chapter 3 objectives in 2D space

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**2 Equations Solve for at most 2 Unknowns**

Particle Equilibrium F1 F2 F3 V = 0, v +Y +X Newton’s 1st Law – Inertia Particle equilibrium Rest (Static) Constant velocity Scalar components = 0 2 Equations Solve for at most 2 Unknowns

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**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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**Example 10-01 FBD Procedure Draw isolated or “free” outlined shape**

+Y +X FBD Procedure Draw isolated or “free” outlined shape Show all forces Characterize each force Magnitude Sense Direction

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**Comprehension Quiz 10-01 Select the Correct FBD of Particle A**

Answer: D Hibbeler (2007)

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Applications Hibbeler (2007)

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Example 10-01 For the engine in static equilibrium, using a free body diagram, solve for the force magnitudes FAD and FAB. The engine mass is 255 kg.

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**Example 10-01 Draw FBD +Y FAB A = 30 FAD +X W = FAC = mg**

W = (255 kg)(9.806m/s2) = 2.5kN

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**Example 10-01 State Equilibrium Equation +Y +X = 30 FAB**

W = FAC = 2.5kN FAD A State Equilibrium Equation

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Example 10-02 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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**Example 10-02 (cont.) FBD at Point A 600 lb A 25 30 FAC FAB**

2 Equations 2 Unknowns

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**Example 10-03 (cont.) Equilibrium at Point A Rearrange Substitute**

25 600 lb FAB FAC A 30 Equilibrium at Point A Rearrange Substitute

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**Example 10-03 Find the forces in the cables and weight of sack B.**

What point is first selected for the FBD?

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**Example 10-03 (cont.) Unknown force magnitudes at Point C**

FBD at Point E 2 Equations 2 Unknowns

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Example (cont.) Equilibrium at Point E Rearrange Substitute

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Example (cont.) FBD at Point E and Point C

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Example (cont.) Equilibrium at Point C

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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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**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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**Classification of Textbook Problems**

Hibbeler (2007)

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**References Hibbeler (2007)**

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