1. 2009 Physics 2111 Fundamentals of Physics Chapter 6 1 Fundamentals of Physics Chapter 6 Force & Motion - II 1.Friction 2.Properties of friction 3.The Drag Force & Terminal Speed 4.Uniform Circular Motion & Force Review & Summary Questions Exercises & Problems

2. 2009 Physics 2111 Fundamentals of Physics Chapter 6 2 Friction Force An increasing pull, F, is applied to the object. An object at rest on a surface: The object is not accelerated because an equal and opposite friction force arises between the object and the surface: The friction force is a “passive force” in that it only arises when F is applied. No friction force here!

3. 2009 Physics 2111 Fundamentals of Physics Chapter 6 3 Friction Force Eventually the object will be accelerated when the pull is greater than the friction force between the object and the surface:

4. 2009 Physics 2111 Fundamentals of Physics Chapter 6 4 The Friction Force f S = static friction force f K = kinetic friction force not moving accelerating It’s easier to keep an object sliding than it is to get the sliding started.

5. 2009 Physics 2111 Fundamentals of Physics Chapter 6 5 The Friction Force Two surfaces in contact: Microscopic “cold welding” occurs. Molecular bonding occurs at points of contact. The friction force is complicated and details are not completely understood!

6. 2009 Physics 2111 Fundamentals of Physics Chapter 6 6 Properties of Friction Experimentally, it is found that the friction force depends on how strongly the surfaces are pressed together; i.e. the Normal Force, N. Experimentally, the friction force is also found not to depend on the surface area!  k only weakly depends on the speed.  S = coefficient of static friction  k = coefficient of kinetic friction

7. 2009 Physics 2111 Fundamentals of Physics Chapter 6 7 Checkpoint 2 applied forces: As F 2 increases, but before the box begins to slide, what happens to; a)Magnitude of frictional force on the box b)Magnitude of the normal force on the box from the floor c)The maximum value of the static frictional force on the box

8. 2009 Physics 2111 Fundamentals of Physics Chapter 6 8 Example: Block on an Inclined Plane with Friction Free-Body Diagram: Apply Newton’s 2 nd Law:  is increased until the block is about to slide. Friction Force:

9. 2009 Physics 2111 Fundamentals of Physics Chapter 6 9 Friction and inclined plane http://lectureonline.cl.msu.edu/~mmp/kap4/cd095a.htm http://lectureonline.cl.msu.edu/~mmp/applist/si/plane.htm

10. 2009 Physics 2111 Fundamentals of Physics Chapter 6 10 Sample Problem Wheels locked If it took 290m to stop  k = 0.60 How fast when wheels locked?

11. 2009 Physics 2111 Fundamentals of Physics Chapter 6 11 Sample Problem M = 75 kg Constant velocity, level surface  k = 0.10  = 42 0 What is T ?

12. 2009 Physics 2111 Fundamentals of Physics Chapter 6 12 Sample Problem Coin of mass m at angle  “verge of sliding” at 13 0” what is  s

13. 2009 Physics 2111 Fundamentals of Physics Chapter 6 13 Problem mg N f m = 2.5 kg Friction Force = ? P = 8, 10, 12 Newtons

14. 2009 Physics 2111 Fundamentals of Physics Chapter 6 14 Problem Both Boxes: Green Box: Wheaties Cheerios F = 12N

15. 2009 Physics 2111 Fundamentals of Physics Chapter 6 15 Problem Three blocks released from rest a = 1.5 m/s 2 If M = 2.0 kg, what is magnitude of frictional force

16. 2009 Physics 2111 Fundamentals of Physics Chapter 6 16 Friction makes your car move! The velocity of the point on the tire in contact with the road is zero relative to the ground. static friction v

17. 2009 Physics 2111 Fundamentals of Physics Chapter 6 17 The Drag Force & Terminal Velocity Drag Force is generated when moving through a fluid.  C  = drag coefficient  = air density  A = effective cross sectional area  v = relative speed For air: For an object freely falling in air: Terminal velocity occurs when v has grown to the point where D equals F g :

18. 2009 Physics 2111 Fundamentals of Physics Chapter 6 18 Uniform Circular Motion Centripetal Force accelerates a body by changing the direction of a body’s velocity without changing the body’s speed. A force, T, must be exerted on the puck in order for it to execute uniform circular motion. What provides the centripetal force on the moon in order for it to execute uniform circular motion? If one cuts the string, what direction does the puck fly off in?

19. 2009 Physics 2111 Fundamentals of Physics Chapter 6 19 Sample Problem If  s = 0.40 R = 2.1 m What is the minimum speed v that the rider and cylinder for the rider not to fall?

20. 2009 Physics 2111 Fundamentals of Physics Chapter 6 20 Sample Problem Stock car mass m = 1600 kg v = 20 m/s R = 190 m Value of  to be “verge of sliding”

21. 2009 Physics 2111 Fundamentals of Physics Chapter 6 21 Sample Problem 6-11 Can’t always count on friction, so you BANK mass m v = 20 m/s R = 190 m What bank angle  makes reliance on friction unnecessary

22. 2009 Physics 2111 Fundamentals of Physics Chapter 6 22 What speed keeps M at rest?

23. 2009 Physics 2111 Fundamentals of Physics Chapter 6 23 http://www.walter-fendt.de/ph11e/carousel.htm Carousel Applet:

24. 2009 Physics 2111 Fundamentals of Physics Chapter 6 24 Swinging a pail of water in a vertical circle: Normal force of the pail on the water Weight of the water Velocity of the water Free-Body Diagrams:

25. 2009 Physics 2111 Fundamentals of Physics Chapter 6 25 How slowly can one swing the pail of water without spilling? Normal force of the pail on the water Weight of the water Velocity of the water Free-Body Diagram: a At the top, F p cannot be upwards: Water is about to lose contact with the pail (i.e. spill).

26. 2009 Physics 2111 Fundamentals of Physics Chapter 6 26 Sample Problem 6-7 R = 2.7 m What is the least speed that Diavolo can have at the top of the loop and still make contact with the loop

27. 2009 Physics 2111 Fundamentals of Physics Chapter 6 27 Problem 6-64 Leave the road @ what speed? About to leave the road when N = 0.