PHYS120 Lecture 19 - riction 19-1 Demonstrations: blocks on planes, scales, to ind coeicients o static and kinetic riction Text: ishbane 5-1, 5-2 Problems: 18, 21, 28, 30, 34 rom Ch. 5 What s important: rictional orces coeicients o static and kinetic riction riction Where objects move in contact with other objects, we know that it may take a constant orce to maintain a constant velocity. E.g., motion o a book on a table Big Book o Stu Applied orce needed to overcome riction riction arises on a microscopic scale because o the roughness o the suraces. Interlocking suraces impede motion All other things being equal, the rictional orce does not depend on the contact area between suraces: w = mg mg Same rictional orce, It depends only on the magnitude o the orce N normal to the surace. N reacts against the weight o the object, and any other orce that may be applied to it normal to the surace. It is only present when a orce attempts to move an object along the surace. 1996 by David Boal, Simon raser University. All rights reserved; urther resale or copying is strictly prohibited.
PHYS120 Lecture 19 - riction 19-2 N ext (external) w = mg As can be seen in the demo, the orce rom static riction looks like: µ s N maximal static riction orce only opposes ext is in opposite direction to ext no ext, no ext The maximum orce o static riction, max, is max = µ s N, where µ s is the coeicient o static riction. The riction orce cannot exceed the applied orce, or else the object would move! What happens when ext > µ s N? Then the object begins to move and the rictional orce drops: µ s N µ k N µ k = coeicient o kinetic riction ext In the class demo, the coeicients o riction are ound or aluminum on wet wood: µ s ~ 0.6 µ k ~ 0.5 1996 by David Boal, Simon raser University. All rights reserved; urther resale or copying is strictly prohibited.
PHYS120 Lecture 19 - riction 19-3 Some typical values or various material combinations: smooth suraces µ static µ kinetic steel on steel glass on glass telon on steel rubber on concrete (dry) rubber on concrete (wet) waxed ski on snow 0.7 0.9 0.04 1.0 0.30 0.1 0.6 0.4 0.04 0.80 0.25 0.05 Note the substantial coeicient o static riction or steel on steel, even though the suraces are smooth. Railways couldn t work without it. Example The coeicient o static riction between a car s tires and a concrete road is 1.0. I 40 % o the car s weight is over the drive wheels, what is the maximum acceleration o the car? w N < s, max = µ N = µ (0.4 mg) But = ma ma = 0.4 µ mg or a = 0.4 µ g = 0.4 1 9.8 = 3.9 m/s2 or no slipping How long would it take or this car to go rom 0 to 100 km/hr = 28 m/s? rom v = at, then t = 28 / 3.9 = 7 seconds. Theoretically, i all o the weight were over the drive wheels, then a = 9.8 m/s 2 and the time or 0 to 100 km/hr would decrease to 28 / 9.8 = 3 seconds. 1996 by David Boal, Simon raser University. All rights reserved; urther resale or copying is strictly prohibited.
PHYS120 Lecture 19 - riction 19-4 Example A block o mass m 1 sits on another block o mass m 2, which in turn sits on a rictionless table. What is the maximum orce that can be applied to m 2 such that m 1 will not slide with respect to m 2? µ m 1 m 2 Solution: µ m 1 m 2 results in an acceleration a o both blocks or < µ m 1 g = (m 1 + m 2 ) a Considering the top block only m 1 : m 1 g N 1 = m 1 g = m 1 a and < µ m 1 g a < µ g < (m 1 + m 2 ) µ g Demonstrations: - pull block with dierent orientations -weigh block to get N -ind µ s ~ 0.6, µ k ~ 0.5 or aluminum on wet wood 1996 by David Boal, Simon raser University. All rights reserved; urther resale or copying is strictly prohibited.
PHYS120 Lecture 19 - riction 19-5 Consider a block on a plane, the active orces being, N and mg. The condition that the block not slide is that = mgsin. The maximum orce o static riction is: mg N In the demo, i µ = 0.6, then = 31 o. θ = µ N = mg sin θ N = mg cos θ µ mg cos θ = mg sin θ µ = tan θ measure θ at slip point, ind µ 1996 by David Boal, Simon raser University. All rights reserved; urther resale or copying is strictly prohibited.