Classical Mechanics Free-Body Diagrams and Forces

Transkript

1 Classical Mechanics ree-body Diaras and orces a) Main points b) Relevant Equations c) Hoework Hints Mechanics Lecture 5, Slide

2 Inventory of orces Weiht Noral orce Tension Gravitational Sprins Mechanics Lecture 5, Slide

3 Main Points Mechanics Lecture 5, Slide 3

4 Main Points Mechanics Lecture 5, Slide 4

5 Main Points Mechanics Lecture 5, Slide 5

6 Mechanics Lecture 5, Slide 6

7 Two Strins Mechanics Lecture 5, Slide 7

8 Two Strins Mechanics Lecture 5, Slide 8

9 Two Strins Mechanics Lecture 5, Slide 9

10 Two Strins Mechanics Lecture 5, Slide 0

11 T T tanθ T L R L y T T R R x y T T R R y x / tanθ / tanθ Mechanics Lecture 5, Slide

12 Hanin asses sprin k x k sprin x x Mechanics Lecture 5, Slide

13 Hanin asses sprin, ( + + 3) Mechanics Lecture 5, Slide 3

14 Hanin asses x k k sprin 3 ( )( 3, 3 3 a) sprin + Mechanics Lecture 5, Slide 4

15 Hanin asses x sprin ( + + 3)( + a) k k Acceleration in sae direction as velocity??? Mechanics Lecture 5, Slide 5

16 Hanin asses sprin + ) ( + 3 sprin ) ( + 3 sprin 3 ( 3) x sprin k x >? > x? x? x sprin ( )( a) k k Reeber a<0 Mechanics Lecture 5, Slide 6

17 Hanin Masses x k ( )( k sprin ) Mechanics Lecture 5, Slide 7

18 Hanin Masses ( sprin 3 3) Mechanics Lecture 5, Slide 8

19 Hanin Masses x k ( 3)( k sprin + ) ( + + )( 3 sprin, + a ) Mechanics Lecture 5, Slide 9

20 Hanin Masses x sprin ) k ( 3 )( + a k net a a net net3 3 a net a Mechanics Lecture 5, Slide 0

21 Loop-the-loop v N a ( ac + ) ( + R ) Mechanics Lecture 5, Slide

22 Loop-the-loop ) ( R v a N c ) ( ) ( R v a N c R v a a c botto R v a a c side R v a a c top Mechanics Lecture 5, Slide

23 Loop-the-loop N top 0 0 ( a c ) v ( R in ) v R v in in R Mechanics Lecture 5, Slide 3

24 Pulley a net W + Mechanics Lecture 5, Slide 4

25 Pulley W a net + ) ( ) ( ) ( ) ( ) ( T a T T a T a T net Mechanics Lecture 5, Slide 5

26 Pulley cos a net + θ + cos cos cos cos 0 a net θ θ θ Mechanics Lecture 5, Slide 6

27 Pulley cos a net + θ + + cos cos sin T T θ θ θ Mechanics Lecture 5, Slide 7

28 Tennis Ball v T ( ac + ) ( + R ) Mechanics Lecture 5, Slide 8

29 Tennis Ball R v a T c ) ( ) ( R v a T c ) ( ) ( 0 R v a T c R v R v in in Mechanics Lecture 5, Slide 9

30 Satellite G r G r ars satellite arscenter satellite Carefully read!! r r arscenter satellite rars +.5 rars. 5 ars R Mechanics Lecture 5, Slide 30

31 a rav c G r v R rav v v v a c r rav sat rav sat r r G rav sat r G r ars r ars sat r sat Be careful what value you use for r!!! Should be distance between centers of ass of the two objects Mechanics Lecture 5, Slide 3

32 d πr t t d / v πr 3/ πr / / G r ( G ) ars ars Mechanics Lecture 5, Slide 3

33 Enter Question Text A. B. C. 0% 0% 0% Mechanics Lecture 5, Slide 33

34 Enter Question Text A. Twice the oriinal radius B. our ties the oriinal radius C. Eiht ties the oriinal radius T πr T T T ' ' ' R R 8T R R 3/ ' 3/ 3/ T T ' / /3 ( G ) ' R R ars 3/ /3 ( 8 ) 4 0% 0% 0% Mechanics Lecture 5, Slide 34

35 r G v ars Mechanics Lecture 5, Slide 35

36 G ars r satellite a satellite satellite G r ars Mechanics Lecture 5, Slide 36

37 Mechanics Lecture 5, Slide 37

38 Mechanics Lecture 5, Slide 38

39 Mechanics Lecture 5, Slide 39

40 Mechanics Lecture 5, Slide 40

41 Mechanics Lecture 5, Slide 4

42 Mechanics Lecture 5, Slide 4

43 Mechanics Lecture 5, Slide 43

44 Mechanics Lecture 5, Slide 44

45 Mechanics Lecture 5, Slide 45

46 Mechanics Lecture 5, Slide 46

47 Mechanics Lecture 5, Slide 47

48 Mechanics Lecture 5, Slide 48

49 Mechanics Lecture 5, Slide 49

50 Mechanics Lecture 5, Slide 50

51 Mechanics Lecture 5, Slide 5