PHYS120 Lecture 19 - Friction 19-1

Transcription

1 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 by David Boal, Simon raser University. All rights reserved; urther resale or copying is strictly prohibited.

2 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 ~ by David Boal, Simon raser University. All rights reserved; urther resale or copying is strictly prohibited.

3 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 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 = = 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 by David Boal, Simon raser University. All rights reserved; urther resale or copying is strictly prohibited.

4 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.

5 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.