ENGR-36_Lec-21_Flat-Friction.pptx 1 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engineering 36 Chp08: Flat Friction

ENGR-36_Lec-21_Flat-Friction.pptx 2 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics 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

ENGR-36_Lec-21_Flat-Friction.pptx 3 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics 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

ENGR-36_Lec-21_Flat-Friction.pptx 4 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics 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

ENGR-36_Lec-21_Flat-Friction.pptx 5 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics 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

ENGR-36_Lec-21_Flat-Friction.pptx 6 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Coefficient of Friction cont.2  Experiments Also Show that the MAXIMUM Resisting Force Just Prior to Break Away, F m, is LINEAR With The Normal Contact Force, N The Constant of (Linear) Proportionality is Called the Coefficient of STATIC Friction and is Defined by

ENGR-36_Lec-21_Flat-Friction.pptx 7 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Coefficient of Friction cont.3  Similarly After Break- Away, The Coefficient of Friction Under Moving, or KINETIC, Conditions  Thus if µ s or µ k is Known, These Friction Forces Can Be Calculated a-Priori  NOTE: Before Break- Away the Fiction Force Does NOT = F m Before Impending Motion

ENGR-36_Lec-21_Flat-Friction.pptx 8 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Rigid Body Friction  The Actions of Friction Forces Divide into 4 Distinct Cases 1.NO Lateral Forces to Generate Resisting Tangential Forces → NO Friction Forces (Fig.a) 2.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

ENGR-36_Lec-21_Flat-Friction.pptx 9 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics R.B. Friction cont.  The Actions of Friction Forces Divide into 4 Distinct Cases 3.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 4.The body Slides under the action of the applied forces (Fig.d)  The equations of Static equilibrium no Longer Apply. (Kinetic case)

ENGR-36_Lec-21_Flat-Friction.pptx 10 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Angle of Friction  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  Apply Equilibrium Analysis  Summing Forces:

ENGR-36_Lec-21_Flat-Friction.pptx 11 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Angle of Friction cont.  Thus The CoEfficient of 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  Reducing The Angle to Where Motion Stops Defines the Kinetic Coefficient of Friction  For Angles of Inclination, , Greater than  s The Body Slides per μ k and  So the block accelerates per Newton’s Eqn

ENGR-36_Lec-21_Flat-Friction.pptx 12 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Angle of Friction – 4 Cases  The Angle of Friction Also Divides into 4 Cases 1.Angle of Inclination,  = 0 → NO Friction (Fig.a) 2.  <  s → Below BreakAway so the The block is in not motion and friction force is not overcome (Fig.b)

ENGR-36_Lec-21_Flat-Friction.pptx 13 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Angle of Friction – 4 Cases cont.  The Angle of Friction Also Divides into 4 Cases 3.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

ENGR-36_Lec-21_Flat-Friction.pptx 14 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Angle of Friction – cont.2  The Angle of Friction Also Divides into 4 Cases 4.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 be Considered in this STATICs Course.  You’ll Take up This Subject in The DYNAMICS Course at The Transfer Institution

ENGR-36_Lec-21_Flat-Friction.pptx 15 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics ME104 UCB

ENGR-36_Lec-21_Flat-Friction.pptx 16 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Classes of Friction Problems  Static Force Problems Involving Friction Tend to Divide into Three Classes I.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. II.All applied forces are given and the motion is known to be impending; need to determine the value of the COEFFICIENT OF STATIC FRICTION. III.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

ENGR-36_Lec-21_Flat-Friction.pptx 17 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example: Class I  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 µ s = 0.25 and µ k = 0.2.  Determine whether or not the block is in equilibrium and find the value of the friction force.  Check Equilibrium Determine the Value of the Force REQUIRED for Equilibrium. Assuming That Friction Directly Opposes Sliding, Draw the F.B.D.

ENGR-36_Lec-21_Flat-Friction.pptx 18 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example: Class I cont.  For the F.B.D. Write Eqns of Equilibrium  Thus To Maintain Equilibrium. the Friction Forces MUST Add 80lb to the Existing 100lb Push  Now Given µ s, Find MAX possible Value for F  Since The Block Can Only Generate 60lbs of Frictional Resistance When it Needs 80lbs, The Block WILL SLIDE

ENGR-36_Lec-21_Flat-Friction.pptx 19 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example: Class I cont.2  To Find The ACTUAL Value for the Friction Force, Note that the Block is in Kinetic motion (Sliding) so µ k Applies  Note that the Forces are UNBALANCED. The Block will Accelerate Downward due to the Net Lateral Force of 32lbs ( )  The Actual Situation Displayed in Diagram at Right

ENGR-36_Lec-21_Flat-Friction.pptx 20 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example – Class III  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.  Determine a)the conditions for which the crate is on the verge of sliding b)the conditions under which the crate will tip about point A

ENGR-36_Lec-21_Flat-Friction.pptx 21 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example – Class III cont  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.  From The FBD the Eqns of Equilibrium Including the Friction Force F:

ENGR-36_Lec-21_Flat-Friction.pptx 22 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example – Class III cont.2  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 ∑M A =0  If the crate is on the verge of sliding F=µ s N where µ s is the coefficient of static friction.

ENGR-36_Lec-21_Flat-Friction.pptx 23 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example – Class III cont.3  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 ∑M A = 0:

ENGR-36_Lec-21_Flat-Friction.pptx 24 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example – Class III cont.5  Which will Happen FIRST; Tipping or Sliding?  Note that tipping will occur before sliding, provided that P sliding > P tipping. So if P increases until some Sort of motion occurs Tipping will occur BEFORE Sliding by:

ENGR-36_Lec-21_Flat-Friction.pptx 25 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example – Class III cont.6  Run The Numbers. Make Some Realistic Assumptions b = 3 feet h = 5 feet W = 300 lb µ s = 0.5 for Wood on ConCrete /cgi-bin/atdl.dll/fm/ /apph.pdf

ENGR-36_Lec-21_Flat-Friction.pptx 26 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example – Class III cont.  ReCall the Tipping Criteria  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

ENGR-36_Lec-21_Flat-Friction.pptx 27 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics CoEffs of Friction

ENGR-36_Lec-21_Flat-Friction.pptx 28 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics WhiteBoard Work Let’s Work This Nice Problem  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 µA = 15% and µB 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.

ENGR-36_Lec-21_Flat-Friction.pptx 29 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE Registered Electrical & Mechanical Engineer Engineering 36 Appendix

ENGR-36_Lec-21_Flat-Friction.pptx 30 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics

ENGR-36_Lec-21_Flat-Friction.pptx 31 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Fun with Friction

ENGR-36_Lec-21_Flat-Friction.pptx 32 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Measure Coeff ofDynamic Friction  Use concept of Spring- Mass Damped Harmonic Motion as studied in Physics and Engineering- 25

ENGR-36_Lec-21_Flat-Friction.pptx 33 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics

ENGR-36_Lec-21_Flat-Friction.pptx 34 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics

ENGR-36_Lec-21_Flat-Friction.pptx 35 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics

ENGR-36_Lec-21_Flat-Friction.pptx 36 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics

ENGR-36_Lec-21_Flat-Friction.pptx 37 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics

ENGR-36_Lec-21_Flat-Friction.pptx 38 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics 3 kN 5 m 7 m