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Analyzing Equilibrium Problems Involving Dry Friction in Mechanics

This lecture focuses on the analysis of equilibrium problems involving rigid bodies subjected to dry friction forces. Key concepts include identifying unknowns in frictional scenarios, creating Free Body Diagrams (FBDs), and applying equilibrium equations. The lecture outlines various classes of friction problems, such as equilibrium of known geometries and impending motion at contact points. Examples, such as determining the minimum angle for a leaning bar and the forces required to initiate movement of a ladder, provide practical insights into tackling friction-related mechanics challenges.

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Analyzing Equilibrium Problems Involving Dry Friction in Mechanics

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  1. ENGI 1313 Mechanics I Lecture 37: Analysis of Equilibrium Problems with Dry Friction

  2. Lecture 37 Objective • to illustrate the equilibrium analysis of rigid bodies subjected to dry friction force by example

  3. Equilibrium and Frictional Forces • Analysis Steps • FBD • Assume frictional force to be an unknown • Do not assume Fs = sN 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. W W Class of Friction Problems • 1. Equilibrium • Geometry and dimensions are known • Draw FBD • # Unknowns = # Equilibrium Equations • Solve for reaction forces • No motion, if

  5. Class of Friction Problems (cont.) • 2. Impending Motion at All Contact Points • # Unknowns = # Equilibrium Equations + # Friction Equations • Impending Motion • Motion

  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 • Equations? • 3 Equilibrium Equations • 2 Friction Equations

  7. Class of Friction Problems (cont.) • 3. Impending Motion at Some Contact Points • # Unknowns < # Equilibrium Equations + # Friction Equationsor • # Unknowns < # Equilibrium Equations + # Equations for Tipping • May have to evaluate both scenarios • If so, governing case has minimum requirements

  8. Class of Friction Problems (cont.) • 3. Impending Motion at Some Contact Points • Find horizontal force (P) to cause movement. • FBD • # Unknowns? • 7 • Equations • Find minimum P or

  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. Example 37-01 (cont.) • FBD • # Unknowns? • 4 • Equilibrium Equations? • 3 • Assumptions? • Tipping occurs NB W FA NA

  11. Example 37-01 (cont.) • Analysis W FA NA

  12. Example 37-01 (cont.) • Check Tipping Assumption •  Tipping occurs W FA NA

  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. Example 37-02 (cont.) P • FBD • Assume Slipping Occurs 3 ft 3 4 4 ft W = 100lb Fs x N

  15. Example 37-02 (cont.) P • For Slipping 3 ft 3 4 4 ft W = 100 lb Fs x N

  16. Example 37-02 (cont.) P • Check x •  Slipping 3 ft 3 4 4 ft W = 100 lb O Fs x N

  17. Example 37-02 (cont.) P • Assume Tipping Occurs 3 ft 3 4 4 ft W = 100 lb Fs N

  18. Example 37-02 (cont.) P • Check Fs •  Slipping • Calculate minimum P based on slipping condition 3 ft 3 4 4 ft W = 100 lb Fs N

  19. References • Hibbeler (2007) • http://wps.prenhall.com/esm_hibbeler_engmech_1

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