Dry Friction Static vs. Kinetic Angles

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1 Outline: Types of Friction Dry Friction Static vs. Kinetic Angles Applications of Friction 1

2 Contacting surfaces typically support normal and tangential forces Friction is a tangential force Friction occurs whenever there is a tendency for one surface to slide along another Friction opposes this tendency 2

3 Friction occurs when any two objects are in contact Some case we try to minimize friction (to minimize energy loss) Bearings, fluid flow etc. Some cases we try to maximize friction Brakes We rely on friction to walk 3

4 Dry (Coulomb friction) Friction force is tangential to surfaces of contact Friction occurs before sliding and during sliding Friction opposes direction of motion Fluid Adjacent layers of fluid (liquid or gas) move at different velocities Depends on velocity gradients and viscosity Internal Function of deformation and elasticity 4

5 If the box is in static equilibrium, then P=F As P increases, F increases, until force P becomes high enough to overcome static friction. Static friction must be determined from a free body diagram because it depends on P. Kinetic friction is constant for all values of P. 5

6 Object is NOT sliding Friction is determined by FBD and equations of equilibrium Maximum value of static friction is F max = μ s N When F = F max motion is IMPENDING When 0 < F s μ s N object is in equilibrium 6

7 Object is slding and generally object is NOT in equilibrium (P>F k ) Friction force is constant and determined by: F max = μ s N Object could in equilibrium (only happens if it is already moving Generally, μ k < μ s 7

8 The resultant contact force is R acting at an angle When the friction is a maximum N (impending motion) then the angle is also at a maximum F tan s max s N φ R F 8

9 F f = 0 for smooth sufaces F N = normal force F f µ s F N for no motion; µ s = coefficient of static friction F f = µ s F N for impending motion (about to slide) F f = µ k F N for motion; µ k = coefficient of kinetic friction F f opposes direction of impending motion 9

10 Consider pushing (with force P) on a uniform crate of weight W that sits on a rough surface. As P increases the crate will slip or tip. If the μ s is large then the normal force with shift to the corner (x = b/2) and the crate will tip over. So, apply N at some unknown distance from the centre line and solve for x. x F N 10

11 Assume it is in equilibrium not moving, acceleration = 0 Treat friction as an unknown & solve from FBD If F solved > s N, then the friction required to maintain static equilibrium is larger than the maximum friction available the object slides 11

12 A 100 N force acts as shown on a 300 N block placed on an inclined plane. The coefficients of friction between the block and the plane are μ s = 0.25 and μ k = Determine whether the block is in equilibrium. 100 N

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15 ANSWER: Since F max < F required for equilibrium, the block slides & is not in equilibrium. 15

16 It is observed that when the bed of a dump truck is raised to an angle of 25 o the vending machines begin to slide off the bed. Determine the coefficient of static friction between them and the surface of the truck. 0.3 m 0.3 m G 25 o 0.5 m 16

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22 The coefficients of friction are s = 0.40 and k = 0.30 between all surfaces of contact. Determine the force P for which motion of the 30 kg block is impending if cable AB is attached as shown. 22

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27 The movable bracket shown may be placed at any height on the m diameter pipe. If the coefficient of static friction between the pipe and the bracket is 0.25, determine the minimum distance x at which the load W can be supported. Neglect the weight of the bracket m m 27

28 Beam AB is subjected to a uniform load of 200 N/m and is supported at B by post BC. Determine the minimum force P required to pull the post out from under the beam if the coefficients of static friction are B = 0.2 and C = 0.5. Neglect the weight of the members and the thickness of the post. A 4 m 0.75 m 0.25 m B C 28

29 Given: See diagram for forces and dimensions A 4 m B Find: Maximum P to pull post BC 0.75 m B 0.25 m C 29

30 CASE 1: Post Pulls B only CASE 2: Post Pulls C only C needed for equilibrium is 240 μ C Nc then case 1 is valid. Since Fc for equilibrium is greater than Fc max = CASE 1 doesn t happen. 30

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32 The uniform rod having a weight W and length l is supported at its ends A and B, where the coefficient of static friction is s. Determine the greatest angle q so the rod does not slip. Neglect the thickness of the rod. 32