1. PH 201 Dr. Cecilia Vogel Lecture 10

2. REVIEW  Free Body Diagrams  forces OUTLINE  Friction examples  kinetic, static, max static

3. Friction and Drag  Friction and drag are called “dissipative forces”  Both oppose the relative motion of two things  friction opposes two surfaces sliding against each other  drag opposes a fluid flowing past an object  OFTEN friction and drag slow things down  but not always!  You can use friction between your hand and paper to move paper across table  Wind can blow leaves around due to drag

4. Three Cases of Friction  Static Friction  In general, if surfaces don’t slide.  just big enough to prevent sliding.  must use 2 nd law to find out how big  Maximum Static Friction  Only if surfaces don’t slide, but are on the verge of sliding.  f smax =  s F N  Kinetic Friction  In general, if the surfaces do slide.  f k =  k F N

5. In All 3 Cases  Normal force may or may not be equal to the weight, mg.  Frictional force opposes slipping between surfaces.

6. Example #1  Two 5.0-g coins are on a turntable, which is turning at a rate of 2.0 revolutions per second. One coin is 2.3 cm from the center of rotation, the other is 9.9 cm from the center. The coefficient of kinetic friction between the coins and the turntable is 0.29, and the coefficient of static friction is 0.49.  Find the frictional force on each coin. Note:  k always <  s.  k and  s don’t have units.

7. How to determine if it slips  Find the force needed to hold it in place.  Find the maximum static frictional force.  Compare:  If F needed < f smax, then  does no t slip, and f = f s = F needed.  If F needed > f smax, then  does slip, and f = f k  If F needed = f smax, then  on the verge of slipping, and f = F needed = f smax.

8. Example 1 – F needed  What would it take to hold coin in place?  Apply  F = ma to horizontal motion:  Object: coin  Acceleration: centripetal, Forces: friction  To hold a coin in place:  inner coin:  outer coin:

9. Example 1 -- f smax Does FN = mg in this case? Yes, no slope, no other vertical force, no vertical acceleration

10. Example 1 – Compare Compare: does the force needed to hold coin in place exceed the maximum static frictional force?  For the inner coin:  0.0182 N < 0.0240 N  F needed < f smax  No, inner coin does not slip.  Frictional force is static, and equals F needed  0.0182 N  directed toward center.

11. Example 1 – Compare Compare: does the force needed to hold coin in place exceed the maximum static frictional force?  For the outer coin:  0.0782 N > 0.0240 N  F needed > f smax  Yes, outer coin does slip.  Frictional force is kinetic, and equals  Coin slides out, so frictional force is toward center, initially.

12. Example #2 A 1.0-kg box is sitting on a slope, with a string attached that goes over a pulley, with 2N weight hanging from the string. The slope makes an angle of 10 o with the horizontal. Find the magnitude and direction of frictional force.

13. Example 2 –static  In this question, the object not slipping  so it involves static friction.  which is equal to whatever is needed to keep it from slipping  must apply 2 nd law  Let +x-direction be down slope  What is the direction of friction  always opposite tendency to slip  tension tends to make it slip up, gravity tends to make it slip down, so I’m not sure   GUESS – friction is up the slope

14. Example 2 –force diagram x y weight N f FTFT

15. Example 2 – book slide  If the box is not sliding,  a=0.  x-components: x y weight N f since the answer came out negative, the direction is opposite what we guessed fs=0.30 N DOWN the slope

16. Summary  Frictional Forces  sometimes f =  s F N  sometimes f =  k F N  sometimes f = whatever it takes