Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu

1. Engineering 36 Chp08:Flat Friction Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

2. Outline - Friction • The Laws of Dry Friction • Coefficient of Static Friction • Coefficient of Kinetic (Dynamic) Friction • Angles of Friction • Angle of Static Friction • Angle of Kinetic Friction • Angle of Repose • Wedge & Belt Friction • Self-Locking & Contact-Angle

3. Friction Physics • When Two Bodies in Contact Attempt to Move Laterally (Sideways) Opposing Tangential Forces Develop Between The two bodies • The Tangential Force is Called FRICTION • Friction Forces Caused Primarily by Surface MicroRoughness

4. Coefficient of Friction • Consider the Block of Weight W, Balanced by the Normal Reaction Force N. • A Lateral Push, P, is Applied to the Block, The Push will Be Balanced, Up to a Point, By The Friction Force, F • The Friction Force Rises With P Until The Block Reaches the “Break-Away” Condition and Motion Ensues

5. Coefficient of Friction cont. • After Break-Away, The Block Accelerates per • Experiment Shows That The Resisting Friction Force Follows a General Profile as Noted in Fig.c Below

6. Coefficient of Friction cont.2 • Experiments Also Show that the MAXIMUM Resisting Force Just Prior to Break Away, Fm, is LINEAR With The Normal Contact Force, N • The Constant of (Linear) Proportionality is Called the Coefficient of STATIC Friction and is Defined by

7. Similarly After Break-Away, The Coefficient of Friction Under Moving, or KINETIC, Conditions Coefficient of Friction cont.3 • NOTE: Before Break-Away the Fiction Force Does NOT = Fm • Before Impending Motion • Thus if µs or µk is Known, These Friction Forces Can Be Calculated a-Priori

8. The Actions of Friction Forces Divide into 4 Distinct Cases Rigid Body Friction • NO Lateral Forces to Generate Resisting Tangential Forces → NO Friction Forces (Fig.a) • The applied force tends to move body along the surface of contact but are NOT large enough to set it in motion (Fig.b) • NOT At BreakAway so

9. The Actions of Friction Forces Divide into 4 Distinct Cases R.B. Friction cont. • The applied forces are such that the body is just about to slide, MOTION IS IMPENDING (Fig.c) • The Static Case Where The Friction Equation CAN Be Applied • The body Slides under the action of the applied forces (Fig.d) • The equations of Static equilibrium no Longer Apply. (Kinetic case)

10. Consider the Situation Depicted at Right Block of Mass M Angle of Inclination s Impending Motion Thus Static Equilibrium Applies Anti-Sliding Friction Force Described by Angle of Friction • Summing Forces: • Apply Equilibrium Analysis

11. Thus The CoEfficientof Friction is EASILY Measured with a Simple Inclined Plane Once Motion Begins Experiment Shows That The Angle of Inclination can be REDUCED without Halting the Slide Angle of Friction cont. • For Angles of Inclination, , Greater than sThe Body Slides per μk and • So the block accelerates per Newton’s Eqn • Reducing The Angle to Where Motion Stops Defines the Kinetic Coefficient of Friction

12. The Angle of Friction Also Divides into 4 Cases Angle of Friction – 4 Cases Angle of Inclination,  = 0 → NO Friction (Fig.a)  <s → Below BreakAway so the The block is in not motion and friction force is not overcome (Fig.b)

13. The Angle of Friction Also Divides into 4 Cases Angle of Friction – 4 Cases cont. • With increasing angle of inclination, motion will soon become impending. At that time, the angle between R and the normal will have reached its maximum value s (Fig.c) • The value of the angle of inclination corresponding to impending motion is called the ANGLE OF REPOSE

14. The Angle of Friction Also Divides into 4 Cases Angle of Friction – cont.2 • With Further increases in the angle of inclination, motion occurs and the Resultant force, R, Applied by the Inclined plane on the Body no Longer Balances the Gravity Force (Fig.d). • The Body is not in Equilibrium so This case Will NOT beConsidered in this STATICsCourse. • You’ll Take up This Subjectin The DYNAMICS Courseat The Transfer Institution

15. ME104 Dynamics @ UCB

16. Classes of Friction Problems • Static Force Problems Involving Friction Tend to Divide into Three Classes • All of the applied forces are given and the coefficients of friction are known; need to determine whether the body considered will REMAIN AT REST or SLIDE. • All applied forces are given and the motion is known to be impending; need to determine the value of the COEFFICIENT OF STATIC FRICTION. • The static friction coefficient is known, and it is known that motion is impending in a given direction; need to determine the MAGNITUDE OR DIRECTION OF ONE OF THE APPLIED FORCES

17. Example: Class I • Check Equilibrium • Determine the Value of the Force REQUIRED for Equilibrium. Assuming That Friction Directly Opposes Sliding, Draw the F.B.D. • A 100-lb force acts on a 300-lb block on an inclined plane. The coefficient of friction between the block and the plane are µs = 0.25 and µk= 0.2. • Determine whether or not the block is in equilibrium and find the value of the friction force.

18. Example: Class I cont. • Thus To Maintain Equilibrium. the Friction Forces MUST Add 80lb to the Existing 100lb Push • Now Given µs, Find MAX possible Value for F • For the F.B.D. Write Eqns of Equilibrium • Since The Block Can Only Generate 60lbs of Frictional Resistance When it Needs 80lbs, The Block WILL SLIDE

19. Example: Class I cont.2 • To Find The ACTUAL Value for the Friction Force, Note that the Block is in Kinetic motion (Sliding) so µk Applies • Note that the Forces are UNBALANCED. • The Block will Accelerate Downward due to the Net Lateral Force of 32lbs (180-148) • The Actual Situation Displayed in Diagram at Right

20. A large rectangular shipping crate of height h and width b rests on the floor. A Dock Worker Applies a force P to the Upper-Right Edge of the Crate. Assume that the material in the crate is uniformly distributed so that the weights acts at the Geometric centroid of the crate. Example – Class III • Determine • the conditions for which the crate is on the verge of sliding • the conditions under which the crate will tip about point A

21. Draw a Free-Body-Diagram of the Crate, noting that the Pressure Applied by the Floor Decreases at the Right-Bottom Edge as The Worker Applies a Greater Push. Example – Class III cont • From The FBD the Eqns of Equilibrium Including the Friction Force F:

22. In Equilbrium F = P N = W Substituting These Values in the moment equation Yields The Location for the Application of the Resultant Normal Force. By ∑MA=0 Example – Class III cont.2 • If the crate is on the verge of sliding F=µsNwhere µs is the coefficient of static friction .

23. Now, if the crate is on the verge on tipping it is just about to rotate about point A, so the crate and the floor are in contact ONLY at Point-A. Therefore the Normal-Resultant Application Point has moved to Point-A, and Hence x=0 Setting x to Zero in the Moment Equation Yields the TIPPING Condition of ∑MA = 0: Example – Class III cont.3

24. Which will Happen FIRST; Tipping or Sliding? Note that tipping will occur before sliding, provided that Psliding > Ptipping. So if P increases until some Sort of motion occurs Tipping will occur BEFORE Sliding by: Example – Class III cont.5

25. Run The Numbers. Make Some Realistic Assumptions b = 3 feet h = 5 feet W = 300 lb µs = 0.5 for Wood on ConCrete Example – Class III cont.6 http://www.adtdl.army.mil/cgi-bin/atdl.dll/fm/3-34.343/apph.pdf

26. ReCall the Tipping Criteria Example – Class III cont. • In this case • So Since The Actual Friction Factor of 0.5 EXCEEDS this value, then the Crate WILL, in fact, TIP OVER • Calc The Overturning and Sliding Pushes

27. CoEffsof Friction

28. WhiteBoard Work Let’s WorkThis NiceProblem • Two blocks A and B have a weight of 10 lb and 6 lb, respectively. They are resting on the incline for which the coefficients of static friction are µA = 15% and µB = 25%. Determine the incline angle for which both blocks begin to slide. Also find the required stretch or compression in the connecting spring for this to occur. The spring has a stiffness of k = 2 lb/ft.

29. Engineering 36 Appendix Bruce Mayer, PE Registered Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

31. Fun with Friction

32. Measure Coeff ofDynamic Friction • Use concept of Spring-Mass Damped Harmonic Motion as studied in Physics and Engineering-25

38. 3 kN 3 kN 5 m 7 m 5 m