1. Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland spkenny@engr.mun.ca ENGI 1313 Mechanics I Lecture 37:Analysis of Equilibrium Problems with Dry Friction

2. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 2 Lecture 37 Objective to illustrate the equilibrium analysis of rigid bodies subjected to dry friction force by example

3. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 3 Equilibrium and Frictional Forces Analysis Steps  FBD Assume frictional force to be an unknown  Do not assume F s =  s N unless impending motion is stated Determine the Number of Unknowns  If more unknowns than equations, assume friction force at some or all contact points  Apply Equilibrium Equations Impending motion or tipping

4. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 4 Class of Friction Problems W W 1. Equilibrium  Geometry and dimensions are known  Draw FBD  # Unknowns = # Equilibrium Equations  Solve for reaction forces  No motion, if

5. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 5 Class of Friction Problems (cont.) 2. Impending Motion at All Contact Points  # Unknowns =# Equilibrium Equations + # Friction Equations  Impending Motion  Motion

6. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 6 Class of Friction Problems (cont.) 2. Impending Motion at All Contact Points  Find the minimum angle (  ) for a 100 N bar to be placed against the wall. FBD Unknowns? 55 Equations?  3 Equilibrium Equations  2 Friction Equations

7. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 7 Class of Friction Problems (cont.) 3. Impending Motion at Some Contact Points  # Unknowns <# Equilibrium Equations + # Friction Equations or  # Unknowns <# Equilibrium Equations + # Equations for Tipping  May have to evaluate both scenarios If so, governing case has minimum requirements

8. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 8 Class of Friction Problems (cont.) 3. Impending Motion at Some Contact Points  Find horizontal force (P) to cause movement. FBD # Unknowns? 77 Equations  Find minimum P or

9. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 9 Example 37-01 A uniform ladder weighs 20 lb. The vertical wall is smooth (no friction). The floor is rough with  s = 0.8. Find the minimum force P needed to move (tip or slide) the ladder.

10. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 10 Example 37-01 (cont.) FBD # Unknowns? 44 Equilibrium Equations? 33 Assumptions?  Tipping occurs W FAFA NANA NBNB

11. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 11 Example 37-01 (cont.) Analysis W FAFA NANA

12. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 12 Example 37-01 (cont.) Check Tipping Assumption  Tipping occurs W FAFA NANA

13. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 13 Example 37-02 Drum weight is 100 lb,  s = 0.5, a = 3 ft and b = 4 ft. Find the smallest magnitude of P that will cause impending motion (tipping or slipping) of the drum.

14. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 14 Example 37-02 (cont.) FBD Assume Slipping Occurs x P 3 4 3 ft 4 ft W = 100lb FsFs N

15. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 15 Example 37-02 (cont.) For Slipping x P 3 4 3 ft 4 ft W = 100 lb FsFs N

16. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 16 Example 37-02 (cont.) Check x  Slipping x P 3 4 3 ft 4 ft FsFs N O W = 100 lb

17. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 17 Example 37-02 (cont.) Assume Tipping Occurs P 3 4 3 ft 4 ft FsFs N W = 100 lb

18. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 18 Example 37-02 (cont.) Check F s  Slipping Calculate minimum P based on slipping condition P 3 4 3 ft 4 ft FsFs N W = 100 lb

19. ENGI 1313 Statics I – Lecture 37© 2007 S. Kenny, Ph.D., P.Eng. 19 References Hibbeler (2007) http://wps.prenhall.com/esm_hibbeler_eng mech_1