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Engineering Mechanics: Statics

Engineering Mechanics: Statics. Chapter 6: Friction. Introduction. Ideal assumption – forces between contacting surfaces act normal to the surfaces Real surfaces – there are tangential forces between contacting surfaces = “Friction forces”

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Engineering Mechanics: Statics

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  1. Engineering Mechanics: Statics Chapter 6: Friction

  2. Introduction Ideal assumption – forces between contacting surfaces act normal to the surfaces Real surfaces – there are tangential forces between contacting surfaces = “Friction forces” Friction force occurs when one contacting surface tends to slide along another. Minimize the effects: bearings, screws, gears, flow of fluids in pipe Maximize the effects: brakes, clutches, belt drives, wedges

  3. Types of Friction Dry friction - unlubricated surfaces in contact under a tendency to slide - friction occurs in the direction opposite to the impending motion - called Coulomb friction   Fluid friction - adjacent layers in a fluid are moving at different velocity Internal friction –solid material under cyclical loading 

  4. Mechanism of Dry Friction Dry Friction • Static friction: Fmax = msN • limiting value for impending motion!!! • Kinetic friction: Fk = mkN

  5. The direction of R is specified by tan a= F/N When the friction force reaches Fmax, the angle areaches a maximum valuefs. Thus, tanfs = ms When slippage is occurring, tanfk = mk The angles fs andfkare called angle of static frictionand angle of kinetic frictionwhich define the limiting direction of the total reaction R for each case. Dry Friction

  6. Cone of Friction • If motion is impending, R must be one element of the cone of static friction • If motion is not impending, R is within the cone. The cone vertex angle is 2fs • If motion occurs, the angle of kinetic friction is applied. The reaction R must lie on the surface of cone of vertex angle 2fk

  7. Types of Friction problems 1. Motion is impending (body about to slip) Fmax = msN 2. Condition of motion is not known –find friction force F from equilibrium equation • If F < Fmax (= msN) – body is in equilibrium and friction force = F • If F = Fmax (= msN) – body is in equilibrium  motion is impending • If F > Fmax (= msN) – impossible  not in equilibrium 3. Relative motion exist Fk = mkN

  8. Sample Problem 6/2 Determine the range of values which the mass m0 may have so that the 100-kg block will neither start moving up the plane nor slip down the plane The coefficient of static friction for the contact surfaces is 0.30

  9. Sample Problem 6/5 The three flat blocks are positioned on the 30 degree incline as shown, and a force P parallel to the incline is applied to the middle block. The upper block is prevented from moving by a wire which attaches it to the fixed support. The coefficient of static friction for each of the three pairs of mating surfaces is shown. Determine the maximum value which P may have before any slipping takes place.

  10. Problem 6/9 The 30-kg homogeneous cylinder of 400-mm diameter rests against the vertical and inclined surfaces as shown. If the coefficient of static friction between the cylinder and the surfaces is 0.30, calculate the applied clockwise couple M which would cause the cylinder to slip.

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