1. 5 Additional Applications of Newton’s Laws Friction Drag Forces Motion Along a Curved Path The Center of Mass Hk: 31, 43, 53, 57, 67, 81, 91, 101.

2. Friction Surface Force opposing relative motion Component of Contact Force (other component is the Normal Force) Characterized by coefficients (mu) Static (varies 0 to max) Kinetic (~ constant) Rolling (~ one tenth of kinetic)

3. Surface Dependence of Friction

4. Normal Force Dependence of Friction Contact area ~ to Normal Force Frictional Force ~ Normal Force Summary: Two factors affect frictional force; Surface composition Normal Force /

5. 5 Equations for Friction

6. 6 Example Friction Ex. 10kg block. F N = weight = mg = 98N. Static coef. = 0.50; Kinetic coef. = 0.30.

7. Block at rest. Draw a Force Diagram for the block.

8. Three boxes are pushed by force F with v > 0 along a horizontal surface with  k = 0.291. F=26N 3kg 5kg 2kg fkfk

9. Derive the Angle of Repose relation: Maximum angle block remains at rest:

10. Atwood with Friction. m1=1kg m2=2kg. Kinetic friction = 0.5.

11. Drag Forces

12. Motion Along a Curved Path Force required turn and to change speed Coordinates usually used are F/B (tangential) and L/R (radial) Sum forces tangential = mass x tangential acceleration Sum forces L/R (radial centripetal) = mass x centripetal acceleration /

13. What is the fastest speed the car can go without sliding? Assume the car has m = 1200kg and  s = 0.92.

14. A block loops the loop. Which force diagram is correct for when it passed point D?

15. Center of Mass Definition

16. Center of Mass Acceleration

17. Center of Mass when Net External Force is Zero Zero Net Force implies center of mass acceleration is also zero. So if CM originally at rest, it remains at rest. If CM moving, its velocity remains same. Example: two people standing on ice push off one another /

18. Ex. Center of Mass. A 100kg person walks 6 feet forward in a 50kg canoe. How far did he move relative to the shore?

19. Summary Friction depends on Surface Composition and Normal Force Drag Force vary with speed Force required to move along curved path even at constant speed Center of Mass stays same when only internal forces operate

20. Can you stop in time? Buggy rolls. You slide.

21. Given m = 75kg, M = 20kg, D = 3.5m, vo =1.1m/s. What frictional coefficient is needed? Insert values, determine a x.

22. Diagramming Refresher:

23. Accelerating with F2WD. Stopping with 4W Disc-Brakes

24. A 3kg box at rest on level surface with  s = 0.55. What is the largest F acting 60° below horizontal for which the box remains at rest? fs (60° is close to maximum angle)

25. v pc v pg Relative vs. Absolute Velocity

26. Which force diagram applies to the object at Point B?

27. Which force diagram applies to the object at Point C?

28. Assume mass = 1.2kg and radius = 45cm. If speed at Point D is 3.6m/s, what is the size of the normal force acting at Point D? -cen +cen

29. Q. Assume mass = 1.2kg and radius = 45cm. If speed at Point B is 5.1m/s, what is the size of the normal force acting at Point B? +cen -cen

30. Net Given: T = 50N,  = 30°, r = 1m Find: mg and v.

31. The speed is now 6.5m/s and r = 1.0m. Angle, tension, mass? Net For example, if m = 1.0kg, then T = 42.3N.

32. Q. The speed of a mass on a string of length L is 6.5m/s. The radius r = 2.0m. Find angle, tension, mass, and L. Net For example, if m = 1.0kg, then T = 23.9N.

33. Practice Q: What is F such that 0.5kg block stays at rest if all surfaces are frictionless?

34. Banked Turn:

36. Modified Atwood Machine with friction. Let m1 = 2kg, m2 = 3kg,  = 30°, sliding friction coeff. 0.44 Objects are in CW motion.

37. Q. Recalculate last problem with m1 = 6kg m2 = 1kg. (All else remaining the same)

38. Practice Q: Find the variable relationships.

40. Figures

55. Q. Assume the car has m = 1200kg and  s = 0.92. How large is the frictional force if v = 15m/s?

56. 5-3 Drag Forces

57. Drag Forces Can be approximated as, F drag = bv n where b and n are constants

58. Example: Air drag, n = 2. If b = 25N/(m/s) 2, at what speed would the object be resisted by 10N? At what speed would the same object be resisted by 30N?

59. Drag force grows quickly with v: Terminal Velocity: Reached when drag force equals weight force