Fundamentals of Physics

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

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

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

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

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

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. mS = coefficient of static friction mk = coefficient of kinetic friction Experimentally, the friction force is also found not to depend on the surface area! mk only weakly depends on the speed. Physics 2111 Fundamentals of Physics

7. Checkpoint 2 applied forces: • As F2 increases, but before the box begins to slide, what happens to; • Magnitude of frictional force on the box • Magnitude of the normal force on the box from the floor • The maximum value of the static frictional force on the box Physics 2111 Fundamentals of Physics

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

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

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

11. Sample Problem M = 75 kg Constant velocity, level surface mk = 0.10 f = 420 What is T ? Physics 2111 Fundamentals of Physics

12. Sample Problem Coin of mass m at angle q “verge of sliding” at 130” what is ms Physics 2111 Fundamentals of Physics

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

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

15. Problem Three blocks released from rest a = 1.5 m/s2 If M = 2.0 kg, what is magnitude of frictional force Physics 2111 Fundamentals of Physics

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

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

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. If one cuts the string, what direction does the puck fly off in? What provides the centripetal force on the moon in order for it to execute uniform circular motion? Physics 2111 Fundamentals of Physics

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

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

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 q makes reliance on friction unnecessary Physics 2111 Fundamentals of Physics

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

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

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

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

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 Physics 2111 Fundamentals of Physics

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