Chapter 4: Dynamics. Newton s Laws

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1 Chapter 4: Dynamics Newton s Laws

2 What if we all jumped at once?

3 Newton s 1st Law Objects with mass have Inertia: the tendency to stay at rest (or moving!) The more mass an object has, the more difficult it is to move it (or stop it!) Activity: penny/cardboard

5 LAB P

6 Lab p Write out headings, purpose procedure (choose one of a-h) Observations: Copy out data tables

7 Lab p : choose on of A-H A: Caitlyn/Susan B: Carson C: Lindsay,Miranda D: Hailey/Brett E: Steven^2,Kev,Zach F: Elisabeth/Lalia G: Noah H: Liam/Captain Proton! logger pro file to yourself - lab

8 Newton s 2 nd Law The force necessary to move (or stop) objects depends on: mass ma acceleration F net Ex 1: how much force is necessary to accelerate a 80kg student at 10 m/s 2? m F ma 80kg N net s 2

10 What do we mean net force? Net force is zero if there are no unbalanced forces We usually do not notice forces until they become unbalanced Ex. What are the forces acting on a suction cup?

11 Free Body Diagrams The point of a FBD is to simplify the dynamics involved We only point out the forces acting on the body in question To get to the point, we draw the body as a point! F 1 F 2 The forces are drawn pointing away from the body F 3

12 More than one force? Ex 1: Cody applies a 50 N force to a 2.5kg book to slide it across the table. Find the acceleration if there is a 45 N friction force resisting this motion F net ma F f F a a F 50 N ( 45 N) 5N net 2.0 m 2 m 2.5kg 2.5kg s

13 Ex 2: Find the force necessary to accelerate a 1200 kg rocket at 3.4 m/s 2, if there is a 250 N force of air resistance. F net = ma F a F a +F r = ma F r

14 Exercises p. 81 #1-6

15 Weight Weight is the force of gravity acting on an object F g m Where g is the gravitational field strength at some location in space Near the surface of the earth, each kg of mass has a weight of 9.8 N Ex 1: what is the weight of a 86 kg student? F mg Fg 843N

16 Ex 2 What is the weight of the same student, while carrying a 55N bag of tricks? Fg 843N

17 Ex 3 What is the mass of a student with a weight of 700N? g F m m F g m 700N 9.8N / kg m 71kg

18 Ex 3 What is the weight of the same student in orbit around the earth, where g=9.2m/s 2? 792N

19 Ex 4: What is the weight of the same student on the moon, whose gravitational field strength is 1/6 earth s? 140N

20 Exercises p #1-5 Prep Lab p. 85

21 Percent Difference Comparing two numbers: subtract, then divide Experimental Accepted Accepted

22 Lab p : choose on of A-H A: Caitlyn/Susan B: Carson C: Lindsay,Miranda D: Hailey/Brett E: Steven^2,Kev,Zach F: Elisabeth/Lalia G: Noah H: Liam/Captain Proton! logger pro file to yourself - lab

23 Newton s 3 rd Law For every action there is an equal and opposite reaction When you hit something, it hits back!

Normal Force When an object is in contact with a

Newton s 3rd Law states the surface pushes back

25 Normal Force When an object is in contact with a supporting surface, it pushes down on that surface Newton s 3rd Law states the surface pushes back with an equal and opposite force This is normally (but not always!) equal to the object s weight We sometimes refer to Normal force as the apparent weight

26 Simple case: object at rest Ex 3: What is the normal force acting on the 2.5 kg book resting on your desk? What forces act on the book? Gravity and Normal force Free body diagram Apply 2nd law F N F g Fnet ma 0

27 F g F N 0 F F mg N g F N F 2.5kg 9.8 N 24.5N N kg F g

28 Extended object at rest Ex 3: what is the normal force acting on your book as you lean on it with a 35 N force? What forces act on the book? Gravity, Applied and Normal force Free body diagram Apply 2nd law F g F N F a Fnet ma 0

29 Fnet ma 0 F F F g a N 0 F N F F F N g a F ( 24.5 N) ( 35 N) N F g F a FN 60N

30 Accelerating object Ex 4: find the apparent weight of a 50 kg student accelerating upwards at 3.4 m/s 2 What forces act on the student? Gravity and Normal force Free body diagram Apply 2nd law F N F g Fnet ma

31 F N F g ma F N F g ma F N mg ma F N F N F 660N N F g

32 Accelerating object Ex 4: find the acceleration of a 55 kg student with a normal force of 1300N What forces act on the student? Gravity and Normal force Free body diagram Apply 2nd law F N F g Fnet ma

33 F N F g ma a F N F g m F N 1300N 55( 9.8) a 55 F g a 13.8 m s 2

34 P Do Lab 4-3

35 Friction Once we know normal force, we can calculate friction Friction force can be calculated as normal force times mu F f =μf N But how do we find mu? Lab 3-3 p. 55 F f F N F g F a

36 Friction lab 3-3 Conclusion: find the average value of μ from part 1 Make a statement about what factors affect friction force As always, state sources of error and possible improvements F f F N F g F a

37 ReTest procedure Come in at lunch, do corrections, get help Then book date to come in another lunch to do retest

38 Friction We find friction force is proportional to the Normal force and a stickiness factor (AKA coefficient of friction) F F f N Ex: find the friction force acting on your 25N textbook as it slides across the table if =0.55

39 Applying 2nd law to find Normal force: x y F F f N F net ma F N f F g F N ma F 14N f F F g N 0 F F 25N N g

40 Ex: find the coefficient of friction if it takes a 13 N force to slide your 2.2 kg book along the table at a constant speed. F F f N F F f N (9.8)

41 P. 60 #1-4 Lab p. 55 done!! Exercises

42 Friction on static objects If an object is not moving, forces must be balanced friction force must be equal to the applied horizontal force The maximum static friction force is given by the previous formula, so we have: F f s F N Where s is the coefficient of static friction, and tends to be larger than k for kinetic friction

43 When does static become kinetic? Static friction increases with applied force until it breaks free at this point, it starts moving and kinetic or sliding friction takes over Ex 6: for what applied force if s =0.65 does your textbook start moving? What will the acceleration be?

44 We already have Normal force: x y max F F f N F 25N N max F N f max F 16N f

45 Once it breaks free we have kinetic friction again: x y F 16N a F net ma a F a m F f 16.25N 2.55kg 13.75N a 0.98m s 2

46 Friction Lab Add a column to table 1 for coefficient of friction Do questions #1, 3 (average) & 4 p. 56 Do question #1 p. 58 (#2: sources of error should be done in your conclusion)

47 Universal Gravitation Newton s most original contribution! All objects in the universe exert a gravitational pull on each other But why doesn t the moon fall?

48 Newton realized objects don t fall to the Earth s surface if they have a high enough tangential velocity

49 Universal gravitation: F g =GMm/r 2 Where G is the universal gravitational constant How do we find G? G F g r 2 Mm Weigh the Earth!?

50 Weigh the Earth!

51 Pendulum Method If only we had a large enough mass to get a measurable force Ex 1: Calculate G if you get a N force on a 1.5kg pendulum 150m away from a mountain with a mass of kg G F g r 2 Mm

52 G G F g r 2 Mm N 150m 1.5kg kg 2 G Nm 2 kg 2 G Nm 2 kg 2

53 Cavendish s experiment G To get a more precise measurement of G, he used a torsional pendulum Cavendish was able to get a value of: Nm 2 kg 2

54 Ex 2: What is the Earth s mass if 1kg of mass has a weight of 9.8N? F g GMm r 2 M r 2 F g mg M M N( m) 1kg kg Nm 2 kg 2

55 Ex 3: Find the force of attraction between Kat (54 kg) and Mikael (95 kg) if they sit 4.0 m apart. F g GMm r 2

56 F g GMm r 2 F g Nm 95kg 54kg kg 2 (4.0 m) 2 F g N

57 Start Exercises P. 67 question 6 a) through c) *part (a) consider what happens when we replace r with 2r? GMm GMm F 1 r 2 F 2 2r 2

58 What about g? How does gravitational field strength g fit into all of this?

59 Ex 4: find g at an altitude of 130 km. Careful! F g mg GMm GM mg r 2 g r 2 g 11 Nm kg ( m1.310 m) kg g N kg

60 Ex. 3: find g on the moon. g GM r 2 g 11 Nm kg 6 2 ( m) kg g N kg

61 Ex 4: Find the Sun s gravitational field here g GM r 2 g 11 Nm kg 11 2 ( m) kg g N kg

62 Do you feel lighter? How much difference would a 85kg student feel from noon to midnight? F g mg F g 85kg N kg F 0. 5N g

63 Solve for Mass Ex 1: Find the mass of the Earth required to exert a force of 2.0x10 20 N on the Moon F g GMm r 2 M F g r 2 Gm M kg

64 Gravitational Definitions This is where most people mix up problems Mass, Force or Field? 25N Weight 5kg 9.8N/kg Apparent Weight Gravitational acceleration 25lb!? 1.63m/s 2

65 Did it really happen like that? Mostly true story but... 2nd law actually written in terms of "impulse":

66 Impulse defined as a change in momentum

68 We use momentum to analyze collisions

70 MOMENTUM IS THE PRODUCT OF MASS AND VELOCITY p=m v

71 What is the momentum of a 120 kg rugby player running at 11 m/s? p=mv p=120kg 11 m/s p=1320 kg m/s

More angular momentum http://www.youtube.com/watch?

72 More angular momentum ature=youtube_gdata_player M1fTD69CYtA&feature=related

73 Second Law Revisited? Rearrange by multiplying both sides by Δt: Newton originally wrote his second law in this form:

74 Impulse

75 If t is small, F can be very large

76 Can we find the average force Venus applies to this 57g tennis ball? She returns a 46m/s serve at 35m/s and the ball only contacts the racquet for 6.5ms

77 #1-7 p Start with #1,2,5,7 FIAQD Ex: #2 find Impulse 55 Ft N s

78 #1-7 p Start with #1,2,5,7 FIAQD Ex: #5 find Impulse mv 10kg 25.5m s m s

79 Principle of Momentum Conservation: Total momentum before is equal to total momentum after the collision This is true for all closed, isolated systems No one allowed in or out No net external force

80 Chabal: timing is everything

81 Can we use momentum to analyze this collision?

82 Momentum is conserved so p before must equal p after Rokocoko has a mass of 105 kg and runs at 7.5 m/s into 92 kg Betson How fast are they moving after the collision?

83 m u v 1 1 m T

84 Most common physics 11 collision: moving object collides with stationary one; they move off together Ex: a student with a mass of 105 kg runs at 7.5 m/s into a 92 kg classmate, find v

85 Same steps every time! Variables m 1 = u 1 = m 2 = u 2 = v'= p i =p f m 1 u 1 = (m 1 + m 2 )v? 0 = m 1 v 1 + m 2 v 2?

86 Explosions

87 For an explosion? Ex: bottle rocket Variables m 1 =0.320 kg v 1 =? m 2 =0.850 kg v 2 =-25 m/s p i =p f 0 = m 1 v 1 + m 2 v 2 m 1 v 1 =- m 2 v 2 v 1 =- m 2 v 2 /m 1 v 1 =-0.850kg(-25m/s)/0.320kg v 1 = 66 m/s

88 Practice Problems Finish q's 1-7p Start Ch 4 review p. 90 Force quiz tomorrow Momentum Quiz Friday Test next week Start bottle rocket design

89 Ex: question 3 Variables m 1 =0.060 kg v 1 =600 m/s m 2 =3.0 kg V 2 =? m/s p i =p f 0 = m 1 v 1 + m 2 v 2 m 2 v 2 =- m 1 v 1 v 2 =- m 1 v 1 /m 2 v 2 =-0.060kg(600m/s)/3.0kg v 2 = -12 m/s

90 Ex: question 6 Variables m 1 =1500 kg u 1 =44 m/s m 2 =1000 kg u 2 =-22 m/s m T =2500 kg v=? m/s p i =p f m 1 u 1 + m 2 u 2 = m T v (m 1 u 1 + m 2 u 2 )/m T = v v=18 m/s

91 Ex: question 13 Variables m 1 =0.250 kg u 1 =5.0 m/s m 2 =0.300 kg u 2 =2.0m/s m T =0.550 kg v=? m/s p=mv m 1 u 1 + m 2 u 2 = m T v (m 1 u 1 + m 2 u 2 )/m T = v v=3.4 m/s

92 Elastic vs. Inelastic? An elastic collision is one where mechanical energy is conserved This can be represented by a bouncing ball elastic inelastic completely inelastic

93 Elasticity when bouncing

95 Chapter Review Finish p #1-7 Finish Chapter Review p. 90 q's 1-18 Momentum Quiz Friday Chapter 4 Test next week

96 Bonus! Find the velocity of the wreckage after this horrible collision :(

97 Chapter Review Finish p. 91 #10-18 Start Test Yourself p. 92 Momentum Quiz Today

Topic 2.1: Kinematics. How do we analyze the motion of objects?

Topic 2.1: Kinematics. How do we analyze the motion of objects? Topic.1: Kinematics How do we analyze the motion of objects? Characteristic Graphs The most common kinematics problems involve uniform acceleration from rest These have a characteristic shape for each