PHY 113 A General Physics I 11 AM-12:15 P M MWF Olin 101 Plan for Lecture 6:

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

2. PHY 113 C Fall 2013 -- Lecture 6

3. Isaac Newton, English physicist and mathematician (1642—1727) In the absence of a net force, an object remains at constant velocity or at rest. In the presence of a net force F, the motion of an object of mass m is described by the form F=ma. F12 =– F21. http://www.newton.ac.uk/newton.html PHY 113 C Fall 2013 -- Lecture 6

4. Webassign question from assignment #5 PHY 113 C Fall 2013 -- Lecture 6

5. Webassign question from assignment #5 – continued F1 F2 m PHY 113 C Fall 2013 -- Lecture 6

6. Webassign question from assignment #5 – continued F1 F2 m PHY 113 C Fall 2013 -- Lecture 6

7. Webassign question from Assignment #4 a a T T mg sin q mg PHY 113 C Fall 2013 -- Lecture 6

8. Newton’s second law n T mg PHY 113 C Fall 2013 -- Lecture 6

9. Another example of motion along a frictionless surface n T mg PHY 113 C Fall 2013 -- Lecture 6

10. iclicker exercise: Assuming T>0, how does the suitcase move along surface? It moves at constant velocity. It accelerates. Whether it moves or not depends on magnitude of T. n T mg PHY 113 C Fall 2013 -- Lecture 6

11. In presence of friction force: n T f mg PHY 113 C Fall 2013 -- Lecture 6

12. 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: Normal force between surfaces Material-dependent coefficient Air friction: K and K’ are materials and shape dependent constants PHY 113 C Fall 2013 -- Lecture 6

13. Models of surface friction forces surface friction force fs,max=msn (applied force) Coefficients ms ,mkdepend on the surfaces; usually, ms>mk PHY 113 C Fall 2013 -- Lecture 6

14. PHY 113 C Fall 2013 -- Lecture 6

15. Surface frictionmodels Static friction case: F-fs = 0 if F < msn=msmg Kinetic friction case: if F>msn=msmg , then F-fk=ma (fk= mkmg) PHY 113 C Fall 2013 -- Lecture 6

16. Consider a stationary block on an incline: n f mg cosq mg mg sin q q PHY 113 C Fall 2013 -- Lecture 6

17. Consider a stationary block on an incline: n What happens when f>fs,max? f mg cosq mg mg sin q q PHY 113 C Fall 2013 -- Lecture 6

18. Consider a stationary block on an incline: n What happens when f=fs,max? f mg cosq mg mg sin q q PHY 113 C Fall 2013 -- Lecture 6

19. 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: • There is no net force acting on the box. • There is a net force acting on the box. V (constant) q PHY 113 C Fall 2013 -- Lecture 6

20. Consider a block sliding down an inclined surface; constant velocity case n f=mkn V (constant) mg q PHY 113 C Fall 2013 -- Lecture 6

21. Summary n f mg cosq mg mg sin q q PHY 113 C Fall 2013 -- Lecture 6

22. A block of mass 3 kg is pushed up against a wall by a force P that makes an angle of q=50o with the horizontal. ms=0.25. Determine the possible values for the magnitude of P that allow the block to remain stationary. f N f mg PHY 113 C Fall 2013 -- Lecture 6

23. f N f mg PHY 113 C Fall 2013 -- Lecture 6

24. Models of air friction forces bv mg PHY 113 C Fall 2013 -- Lecture 6

25. Recall: Uniform circular motion: animation from http://mathworld.wolfram.com/UniformCircularMotion.html PHY 113 C Fall 2013 -- Lecture 6

26. Uniform circular motion – continued PHY 113 C Fall 2013 -- Lecture 6

27. Uniform circular motion – continued r In terms of time period T for one cycle: In terms of the frequency f of complete cycles: PHY 113 C Fall 2013 -- Lecture 6

28. Uniform circular motion and Newton’s second law r • iclicker exercise: • For uniform circular motion • Newton’s laws are repealed • There is a force pointing radially outward from the circle • There is a force pointing radially inward to the circle PHY 113 C Fall 2013 -- Lecture 6

29. Example of uniform circular motion: http://earthobservatory.nasa.gov/Features/OrbitsCatalog/page1.php PHY 113 C Fall 2013 -- Lecture 6

30. Example of uniform circular motion: Consider the moon in orbit about the Earth PHY 113 C Fall 2013 -- Lecture 6

31. Example of uniform circular motion: PHY 113 C Fall 2013 -- Lecture 6

32. Example of uniform circular motion: PHY 113 C Fall 2013 -- Lecture 6

33. Curved road continued: PHY 113 C Fall 2013 -- Lecture 6

34. Mass on a swing: • iclicker exercise: • Which of these statements about the tension T in the rope is true? • T is the same for all q. • T is smallest for q=0. • T is largest for q=0. L q T mg PHY 113 C Fall 2013 -- Lecture 6

35. Newton’s law in accelerating train car PHY 113 C Fall 2013 -- Lecture 6

36. Notion of fictitious forces • iclicker question • Fiction is for English class and not for physics class. • The concept of fictitious forces is a bad idea. • 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. PHY 113 C Fall 2013 -- Lecture 6

37. Example of analysis of forces Ferris wheel moving at constant speed v ac ac PHY 113 C Fall 2013 -- Lecture 6

38. 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. PHY 113 C Fall 2013 -- Lecture 6