1. 9/12/2013PHY 113 C Fall 2013 -- Lecture 61 PHY 113 A General Physics I 11 AM-12:15 PM MWF Olin 101 Plan for Lecture 6: Chapters 5 & 6 – More a pplications of Newton’s laws 1.Friction and other dissipative forces 2.Forces in circular motion

2. 9/12/2013 PHY 113 C Fall 2013 -- Lecture 62

3. 9/12/2013PHY 113 C Fall 2013 -- Lecture 63 Isaac Newton, English physicist and mathematician (1642—1727) http://www.newton.ac.uk/newton.html 1.In the absence of a net force, an object remains at constant velocity or at rest. 2.In the presence of a net force F, the motion of an object of mass m is described by the form F=ma. 3.F 12 =– F 21.

4. 9/12/2013PHY 113 C Fall 2013 -- Lecture 64 Webassign question from assignment #5

5. 9/12/2013PHY 113 C Fall 2013 -- Lecture 65 Webassign question from assignment #5 – continued m F1F1 F2F2

6. 9/12/2013PHY 113 C Fall 2013 -- Lecture 66 Webassign question from assignment #5 – continued m F1F1 F2F2

7. 9/12/2013PHY 113 C Fall 2013 -- Lecture 67 Webassign question from Assignment #4 T T mg mg sin  a a

8. 9/12/2013PHY 113 C Fall 2013 -- Lecture 68 Newton’s second law n mg T

9. 9/12/2013PHY 113 C Fall 2013 -- Lecture 69 mg n T Another example of motion along a frictionless surface

10. 9/12/2013PHY 113 C Fall 2013 -- Lecture 610 mg n T iclicker exercise: Assuming T>0, how does the suitcase move along surface? A.It moves at constant velocity. B.It accelerates. C.Whether it moves or not depends on magnitude of T.

11. 9/12/2013PHY 113 C Fall 2013 -- Lecture 611 In presence of friction force: mg n T f

12. 9/12/2013PHY 113 C Fall 2013 -- Lecture 612 Friction forces The term “friction” is used to describe the category of forces that oppose motion. One example is surface friction which acts on two touching solid objects. Another example is air friction. There are several reasonable models to quantify these phenomena. Surface friction: Material-dependent coefficient Normal force between surfaces Air friction: K and K’ are materials and shape dependent constants

13. 9/12/2013PHY 113 C Fall 2013 -- Lecture 613 Models of surface friction forces (applied force) surface friction force f s,max =  s n Coefficients  s,  k depend on the surfaces; usually,  s >  k

14. 9/12/2013PHY 113 C Fall 2013 -- Lecture 614

15. 9/12/2013PHY 113 C Fall 2013 -- Lecture 615 Surface friction models F-f s = 0 if F <  s n=  s mg if F>  s n=  s mg, then F-f k =ma (f k =  k mg) Static friction case: Kinetic friction case:

16. 9/12/2013PHY 113 C Fall 2013 -- Lecture 616 mg f n  mg sin  mg cos  Consider a stationary block on an incline:

17. 9/12/2013PHY 113 C Fall 2013 -- Lecture 617 mg f n  mg sin  mg cos  Consider a stationary block on an incline: What happens when f>f s,max ?

18. 9/12/2013PHY 113 C Fall 2013 -- Lecture 618 mg f n  mg sin  mg cos  Consider a stationary block on an incline: What happens when f=f s,max ?

19. 9/12/2013PHY 113 C Fall 2013 -- Lecture 619 V (constant) iclicker exercise: Suppose you place a box on an inclined surface as shown in the figure and you notice that the box slides down the incline at constant velocity V. Which of the following best explains the phenomenon: A.There is no net force acting on the box. B.There is a net force acting on the box. 

20. 9/12/2013PHY 113 C Fall 2013 -- Lecture 620 V (constant)  mg n f=  k n Consider a block sliding down an inclined surface; constant velocity case

21. 9/12/2013PHY 113 C Fall 2013 -- Lecture 621 mg f n  mg sin  mg cos  Summary

22. 9/12/2013PHY 113 C Fall 2013 -- Lecture 622 A block of mass 3 kg is pushed up against a wall by a force P that makes an angle of  =50 o with the horizontal.  s =0.25. Determine the possible values for the magnitude of P that allow the block to remain stationary. f mg N f

23. 9/12/2013PHY 113 C Fall 2013 -- Lecture 623 f mg N f

24. 9/12/2013PHY 113 C Fall 2013 -- Lecture 624 Models of air friction forces mg bv

25. 9/12/2013PHY 113 C Fall 2013 -- Lecture 625 Recall: Uniform circular motion: animation from http://mathworld.wolfram.com/UniformCircularMotion.html http://mathworld.wolfram.com/UniformCircularMotion.html

26. 9/12/2013PHY 113 C Fall 2013 -- Lecture 626 Uniform circular motion – continued

27. 9/12/2013PHY 113 C Fall 2013 -- Lecture 627 Uniform circular motion – continued r In terms of time period T for one cycle: In terms of the frequency f of complete cycles:

28. 9/12/2013PHY 113 C Fall 2013 -- Lecture 628 Uniform circular motion and Newton’s second law r iclicker exercise: For uniform circular motion A.Newton’s laws are repealed B.There is a force pointing radially outward from the circle C.There is a force pointing radially inward to the circle

29. 9/12/2013PHY 113 C Fall 2013 -- Lecture 629 http://earthobservatory.nasa.gov/Features/OrbitsCatalog/page1.php Example of uniform circular motion:

30. 9/12/2013PHY 113 C Fall 2013 -- Lecture 630 Example of uniform circular motion: Consider the moon in orbit about the Earth

31. 9/12/2013PHY 113 C Fall 2013 -- Lecture 631 Example of uniform circular motion:

32. 9/12/2013PHY 113 C Fall 2013 -- Lecture 632 Example of uniform circular motion:

33. 9/12/2013PHY 113 C Fall 2013 -- Lecture 633 Curved road continued:

34. 9/12/2013PHY 113 C Fall 2013 -- Lecture 634 Mass on a swing: mg  T iclicker exercise: Which of these statements about the tension T in the rope is true? A.T is the same for all . B.T is smallest for  C.T is largest for  L

35. 9/12/2013PHY 113 C Fall 2013 -- Lecture 635 Newton’s law in accelerating train car

36. 9/12/2013PHY 113 C Fall 2013 -- Lecture 636 Notion of fictitious forces iclicker question A.Fiction is for English class and not for physics class. B.The concept of fictitious forces is a bad idea. C.The concept of fictitious forces is necessary for analyzing certain types of problems. In analyzing motion in an inertial frame of reference, the notion of “fictitious force” does not appear.

37. 9/12/2013PHY 113 C Fall 2013 -- Lecture 637 Example of analysis of forces Ferris wheel moving at constant speed v acac acac

38. 9/12/2013PHY 113 C Fall 2013 -- Lecture 638 Example of analysis of forces Mass moving in vertical circle Analysis similar to Ferris wheel except that the speed v varies and the magnitude of the centripetal acceleration varies accordingly.