Presentation is loading. Please wait.

Presentation is loading. Please wait.

Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI.

Similar presentations


Presentation on theme: "Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI."— Presentation transcript:

1 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

2 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

3 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

4 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

5 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

6 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

7 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)

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

9 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.

10 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

11 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

12 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.

13 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

14 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 

15 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?

16 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

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

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

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

20 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.

21 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

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

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


Download ppt "Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI."

Similar presentations


Ads by Google