Chapter 8. Momentum, Impulse and Collisions (continued) 10/22/2014 Physics 218

Size: px
Start display at page:

Download "Chapter 8. Momentum, Impulse and Collisions (continued) 10/22/2014 Physics 218"

Transcription

1 Chater 8 Moentu, Iulse and Collsons (contnued 0//04 Physcs 8

2 Learnng Goals The eanng of the oentu of a artcle(syste and how the ulse of the net force actng on a artcle causes the oentu to change. The condtons under whch the total oentu of the syste of artcles s constant (consered. How to sole two-body collson robles. The dstncton between elastc, nelastc and coletely nelastc collsons. The defnton of the center of ass of a syste and what deternes how the center of ass oes. Lastly, a ery bref ntroducton to rocket roulson. 0//04 Physcs 8

3 Stats fro re-lectures 0//04 Physcs 8 3

4 Defnton of Moentu d d F Net ( dt dt wedefned thequantty as the oentu of as d F Net dt an alternate for of (rested the artcle Newton's nd Law 0//04 Physcs 8 4

5 The Defnton of Iulse 0//04 Physcs 8 5 assung a constant net force ( t F t t F J net ( ths becoes ng for the ulse, substtut J t t F t t F Net net

6 Conseraton of Moentu If the ector su of the external forces on a syste s zero, the total oentu of the syste s consered. d F Net 0 dt and the oentu of the systes constant 0//04 Physcs 8 6

7 Exale of a -body collson (Note:usng dfferent nuber fro Y&F Moentu before 0.4 kg /s to Rt Moentu after 0.4 kg /s to Rt.0 /s 0//04 Physcs 8 7

8 Now n -densons. 0//04 Physcs 8 8 constant constant after total before total y y x x x 0 we hae searatng out thecoonents

9 Now on to a dscusson of Elastc and Inelastc Collsons For an solated syste wth no external forces actng on t and wth nternal forces that are only conserate, we fnd that no echancal energy s lost or ganed n the collson. We call these collsons, Elastc Collsons. collson n whch the knetc energy after the collson s less than before the collson we call, an Inelastc Collson. n nelastc collson where the bodes stck together and go off as a sngle object after the collson we call a Coletely Inelastc Collson. 0//04 Physcs 8 9

10 Note In any collson n whch external forces can be neglected, oentu s consered and the total oentu before equals the total oentu after; ONLY n elastc collsons wll the total knetc energy before and after the collson be the sae! 0//04 Physcs 8 0

11 Elastc collsons n -D 0//04 Physcs 8 before and for the eloctes after the collson We can sole these equatons after after total before total KE KE

12 Fgure 8.8 Is ths collson elastc (a or nelastc (b? What s consered n ths collson? a Moentu b Mechancal energy c Moentu and echancal energy d None of the aboe

13 0//04 Physcs 8 3 cos ( ( ( ( energy as t swngs. Now we can consere echancal bedded? the block swng after the bullet s How hgh wll ( so ( gl gh after total before total

14 Elastc Collsons Only conserate forces actng on the artcles noled n these collsons. 0//04 Physcs 8 4

15 Fgure 8.4

16 Center of Mass of a syste r centerof ass r r 3r3 3 r Where s ths ont located n a syste of dscrete asses? In a contnuous ass dstrbuton? 0//04 Physcs 8 6

17 reakng down by coonents x y z centerof ass centerof ass centerof ass x x z z y y 3 y3 3x z3 x z y 0//04 Physcs 8 7

18 Takng the derate wth resect to te ges nterestng results ( center of ass d dt center of ass r r 3r3 ( 3 total dr dt a ( center of ass a d dt center of ass 33 ( 3 a F nternal d dt F External F a NetExternal 0//04 Physcs 8 8

19 ( then for two artcles ( the oentu as Fndng the total oentu of the syste n the center-of-ass ( ( ( centerof ass c c ( ( easured n the c becoes c ( ( 0//04 Physcs 8 9 so total c 0!!

20 Fgure 8.9

21 Fgure 8.3a

22 Fgure 8.30

How does the momentum before an elastic and an inelastic collision compare to the momentum after the collision?

How does the momentum before an elastic and an inelastic collision compare to the momentum after the collision? Experent 9 Conseraton o Lnear Moentu - Collsons In ths experent you wll be ntroduced to the denton o lnear oentu. You wll learn the derence between an elastc and an nelastc collson. You wll explore how

More information

p p +... = p j + p Conservation Laws in Physics q Physical states, process, and state quantities: Physics 201, Lecture 14 Today s Topics

p p +... = p j + p Conservation Laws in Physics q Physical states, process, and state quantities: Physics 201, Lecture 14 Today s Topics Physcs 0, Lecture 4 Conseraton Laws n Physcs q Physcal states, process, and state quanttes: Today s Topcs Partcle Syste n state Process Partcle Syste n state q Lnear Moentu And Collsons (Chapter 9.-9.4)

More information

Momentum and Collisions. Rosendo Physics 12-B

Momentum and Collisions. Rosendo Physics 12-B Moentu and Collsons Rosendo Physcs -B Conseraton o Energy Moentu Ipulse Conseraton o Moentu -D Collsons -D Collsons The Center o Mass Lnear Moentu and Collsons February 7, 08 Conseraton o Energy D E =

More information

Physic 231 Lecture 14

Physic 231 Lecture 14 Physc 3 Lecture 4 Man ponts o last lecture: Ipulses: orces that last only a short te Moentu p Ipulse-Moentu theore F t p ( ) Ipulse-Moentu theore ptot, p, p, p, p, ptot, Moentu and external orces F p ext

More information

Lecture 09 Systems of Particles and Conservation of Linear Momentum

Lecture 09 Systems of Particles and Conservation of Linear Momentum Lecture 09 Systes o Partcles and Conseraton o Lnear oentu 9. Lnear oentu and Its Conseraton 9. Isolated Syste lnear oentu: P F dp dt d( dt d dt a solated syste F ext 0 dp dp F, F dt dt dp dp d F F 0, 0

More information

Chapter 8. Momentum Impulse and Collisions. Analysis of motion: 2 key ideas. Newton s laws of motion. Conservation of Energy

Chapter 8. Momentum Impulse and Collisions. Analysis of motion: 2 key ideas. Newton s laws of motion. Conservation of Energy Chapter 8 Moentu Ipulse and Collsons Analyss o oton: key deas Newton s laws o oton Conseraton o Energy Newton s Laws st Law: An object at rest or traelng n unor oton wll rean at rest or traelng n unor

More information

Linear Momentum. Center of Mass.

Linear Momentum. Center of Mass. Lecture 16 Chapter 9 Physcs I 11.06.2013 Lnear oentu. Center of ass. Course webste: http://faculty.ul.edu/ndry_danylov/teachng/physcsi Lecture Capture: http://echo360.ul.edu/danylov2013/physcs1fall.htl

More information

total If no external forces act, the total linear momentum of the system is conserved. This occurs in collisions and explosions.

total If no external forces act, the total linear momentum of the system is conserved. This occurs in collisions and explosions. Lesson 0: Collsons, Rotatonal netc Energy, Torque, Center o Graty (Sectons 7.8 Last te we used ewton s second law to deelop the pulse-oentu theore. In words, the theore states that the change n lnear oentu

More information

10/2/2003 PHY Lecture 9 1

10/2/2003 PHY Lecture 9 1 Announceents. Exa wll be returned at the end of class. Please rework the exa, to help soldfy your knowledge of ths ateral. (Up to 0 extra cre ponts granted for reworked exa turn n old exa, correctons on

More information

Physics 105: Mechanics Lecture 13

Physics 105: Mechanics Lecture 13 Physcs 05: Mechancs Lecture 3 Wenda Cao NJIT Physcs Department Momentum and Momentum Conseraton Momentum Impulse Conseraton o Momentum Collsons Lnear Momentum A new undamental quantty, lke orce, energy

More information

Collisions! Short, Sharp Shocks

Collisions! Short, Sharp Shocks d b n, b d,, -4 Introducng Collsons Quz 9 L9 Mult-artcle Systes 6-8 Scatterng 9- Collson Colcatons L Collsons 5, Derent Reerence Fraes ranslatonal ngular Moentu Quz RE a RE b RE c EP9 RE a; HW: Pr s 3*,,

More information

Physics 3A: Linear Momentum. Physics 3A: Linear Momentum. Physics 3A: Linear Momentum. Physics 3A: Linear Momentum

Physics 3A: Linear Momentum. Physics 3A: Linear Momentum. Physics 3A: Linear Momentum. Physics 3A: Linear Momentum Recall that there was ore to oton than just spee A ore coplete escrpton of oton s the concept of lnear oentu: p v (8.) Beng a prouct of a scalar () an a vector (v), oentu s a vector: p v p y v y p z v

More information

Momentum. Momentum. Impulse. Momentum and Collisions

Momentum. Momentum. Impulse. Momentum and Collisions Momentum Momentum and Collsons From Newton s laws: orce must be present to change an object s elocty (speed and/or drecton) Wsh to consder eects o collsons and correspondng change n elocty Gol ball ntally

More information

EMU Physics Department.

EMU Physics Department. Physcs 0 Lecture 9 Lnear Momentum and Collsons Assst. Pro. Dr. Al ÖVGÜN EMU Physcs Department www.aogun.com Lnear Momentum q Conseraton o Energy q Momentum q Impulse q Conseraton o Momentum q -D Collsons

More information

Physics for Scientists and Engineers. Chapter 10 Energy

Physics for Scientists and Engineers. Chapter 10 Energy Physcs or Scentsts and Engneers Chapter 0 Energy Sprng, 008 Ho Jung Pak Introducton to Energy Energy s one o the ost portant concepts n scence although t s not easly dened Eery physcal process that occurs

More information

Physics 101 Lecture 9 Linear Momentum and Collisions

Physics 101 Lecture 9 Linear Momentum and Collisions Physcs 0 Lecture 9 Lnear Momentum and Collsons Dr. Al ÖVGÜN EMU Physcs Department www.aogun.com Lnear Momentum and Collsons q q q q q q q Conseraton o Energy Momentum Impulse Conseraton o Momentum -D Collsons

More information

5/24/2007 Collisions ( F.Robilliard) 1

5/24/2007 Collisions ( F.Robilliard) 1 5/4/007 Collsons ( F.Robllard) 1 Interactons: In our earler studes o orce and work, we saw, that both these quanttes arse n the context o an nteracton between two bodes. We wll now look ore closely at

More information

Linear Momentum. Center of Mass.

Linear Momentum. Center of Mass. Lecture 6 Chapter 9 Physcs I 03.3.04 Lnear omentum. Center of ass. Course webste: http://faculty.uml.edu/ndry_danylov/teachng/physcsi Lecture Capture: http://echo360.uml.edu/danylov03/physcssprng.html

More information

2/24/2014. The point mass. Impulse for a single collision The impulse of a force is a vector. The Center of Mass. System of particles

2/24/2014. The point mass. Impulse for a single collision The impulse of a force is a vector. The Center of Mass. System of particles /4/04 Chapte 7 Lnea oentu Lnea oentu of a Sngle Patcle Lnea oentu: p υ It s a easue of the patcle s oton It s a vecto, sla to the veloct p υ p υ p υ z z p It also depends on the ass of the object, sla

More information

Physics 207: Lecture 20. Today s Agenda Homework for Monday

Physics 207: Lecture 20. Today s Agenda Homework for Monday Physcs 207: Lecture 20 Today s Agenda Homework for Monday Recap: Systems of Partcles Center of mass Velocty and acceleraton of the center of mass Dynamcs of the center of mass Lnear Momentum Example problems

More information

Physics 207, Lecture 13, Oct. 15. Energy

Physics 207, Lecture 13, Oct. 15. Energy Physcs 07 Lecture 3 Physcs 07, Lecture 3, Oct. 5 Goals: Chapter 0 Understand the relatonshp between moton and energy Dene Potental Energy n a Hooke s Law sprng Deelop and explot conseraton o energy prncple

More information

Chapter 9 Centre of Mass and Linear Momentum

Chapter 9 Centre of Mass and Linear Momentum Chater 9 Centre o Mass and Linear Moentu Centre o ass o a syste o articles / objects Linear oentu Linear oentu o a syste o articles Newton s nd law or a syste o articles Conseration o oentu Elastic and

More information

Physics 11 HW #7 Solutions

Physics 11 HW #7 Solutions hysics HW #7 Solutions Chapter 7: Focus On Concepts: 2, 6, 0, 3 robles: 8, 7, 2, 22, 32, 53, 56, 57 Focus On Concepts 7-2 (d) Moentu is a ector quantity that has a agnitude and a direction. The agnitudes

More information

Chapter 8. Linear Momentum, Impulse, and Collisions

Chapter 8. Linear Momentum, Impulse, and Collisions Chapte 8 Lnea oentu, Ipulse, and Collsons 8. Lnea oentu and Ipulse The lnea oentu p of a patcle of ass ovng wth velocty v s defned as: p " v ote that p s a vecto that ponts n the sae decton as the velocty

More information

Chapter 7. Impulse and Momentum

Chapter 7. Impulse and Momentum Chapter 7 Ipulse and Moentu 7. The Ipulse-Moentu Theore There are any situations when the force on an object is not constant. 7. The Ipulse-Moentu Theore DEFINITION OF IMPULSE The ipulse of a force is

More information

Chapter 8. Momentum, Impulse and Collisions. 10/22/14 Physics 218

Chapter 8. Momentum, Impulse and Collisions. 10/22/14 Physics 218 Chapter 8 Moentu, Ipulse and Collisions 0//4 Physics 8 Learning Goals n n n n n n The eaning of the oentu of a particle(syste) and how the ipulse of the net force acting on a particle causes the oentu

More information

From Newton s 2 nd Law: v v. The time rate of change of the linear momentum of a particle is equal to the net force acting on the particle.

From Newton s 2 nd Law: v v. The time rate of change of the linear momentum of a particle is equal to the net force acting on the particle. From Newton s 2 nd Law: F ma d dm ( ) m dt dt F d dt The tme rate of change of the lnear momentum of a artcle s equal to the net force actng on the artcle. Conseraton of Momentum +x The toy rocket n dee

More information

1.3 Hence, calculate a formula for the force required to break the bond (i.e. the maximum value of F)

1.3 Hence, calculate a formula for the force required to break the bond (i.e. the maximum value of F) EN40: Dynacs and Vbratons Hoework 4: Work, Energy and Lnear Moentu Due Frday March 6 th School of Engneerng Brown Unversty 1. The Rydberg potental s a sple odel of atoc nteractons. It specfes the potental

More information

Elastic Collisions. Definition: two point masses on which no external forces act collide without losing any energy.

Elastic Collisions. Definition: two point masses on which no external forces act collide without losing any energy. Elastc Collsons Defnton: to pont asses on hch no external forces act collde thout losng any energy v Prerequstes: θ θ collsons n one denson conservaton of oentu and energy occurs frequently n everyday

More information

Physics 231. Topic 8: Rotational Motion. Alex Brown October MSU Physics 231 Fall

Physics 231. Topic 8: Rotational Motion. Alex Brown October MSU Physics 231 Fall Physcs 231 Topc 8: Rotatonal Moton Alex Brown October 21-26 2015 MSU Physcs 231 Fall 2015 1 MSU Physcs 231 Fall 2015 2 MSU Physcs 231 Fall 2015 3 Key Concepts: Rotatonal Moton Rotatonal Kneatcs Equatons

More information

Chapter 4: Linear Momentum and Collisions

Chapter 4: Linear Momentum and Collisions Chater 4: Lear oetu ad Collsos 4.. The Ceter o ass, Newto s Secod Law or a Syste o artcles 4.. Lear oetu ad Its Coserato 4.3. Collso ad Iulse 4.4. oetu ad Ketc Eergy Collsos 4.. The Ceter o ass. Newto

More information

Center of Mass and Linear Momentum

Center of Mass and Linear Momentum PH 221-2A Fall 2014 Center of Mass and Lnear Momentum Lectures 14-15 Chapter 9 (Hallday/Resnck/Walker, Fundamentals of Physcs 9 th edton) 1 Chapter 9 Center of Mass and Lnear Momentum In ths chapter we

More information

Week 8: Chapter 9. Linear Momentum. Newton Law and Momentum. Linear Momentum, cont. Conservation of Linear Momentum. Conservation of Momentum, 2

Week 8: Chapter 9. Linear Momentum. Newton Law and Momentum. Linear Momentum, cont. Conservation of Linear Momentum. Conservation of Momentum, 2 Lnear omentum Week 8: Chapter 9 Lnear omentum and Collsons The lnear momentum of a partcle, or an object that can be modeled as a partcle, of mass m movng wth a velocty v s defned to be the product of

More information

Study Guide For Exam Two

Study Guide For Exam Two Study Gude For Exam Two Physcs 2210 Albretsen Updated: 08/02/2018 All Other Prevous Study Gudes Modules 01-06 Module 07 Work Work done by a constant force F over a dstance s : Work done by varyng force

More information

Linear Momentum and Collisions

Linear Momentum and Collisions Lnear Momentum and Collsons Chater 9 Lnear Momentum [kg m/s] x y mv x mv y Newton s nd Law n terms o momentum: Imulse I - [kg m/s] I t t Fdt I = area under curve bounded by t axs Imulse-Momentum Theorem

More information

PHYS 2211L - Principles of Physics Laboratory I

PHYS 2211L - Principles of Physics Laboratory I PHYS L - Prncples of Physcs Laboratory I Laboratory Adanced Sheet Ballstc Pendulu. Objecte. The objecte of ths laboratory s to use the ballstc pendulu to predct the ntal elocty of a projectle usn the prncples

More information

Linear Momentum. Equation 1

Linear Momentum. Equation 1 Lnear Momentum OBJECTIVE Obsere collsons between two carts, testng or the conseraton o momentum. Measure energy changes durng derent types o collsons. Classy collsons as elastc, nelastc, or completely

More information

Physics 207 Lecture 13. Lecture 13

Physics 207 Lecture 13. Lecture 13 Physcs 07 Lecture 3 Goals: Lecture 3 Chapter 0 Understand the relatonshp between moton and energy Defne Potental Energy n a Hooke s Law sprng Develop and explot conservaton of energy prncple n problem

More information

Conservation of Momentum

Conservation of Momentum Conseration of Moentu We left off last with the idea that when one object () exerts an ipulse onto another (), exerts an equal and opposite ipulse onto. This happens in the case of a classic collision,

More information

CHAPTER 10 ROTATIONAL MOTION

CHAPTER 10 ROTATIONAL MOTION CHAPTER 0 ROTATONAL MOTON 0. ANGULAR VELOCTY Consder argd body rotates about a fxed axs through pont O n x-y plane as shown. Any partcle at pont P n ths rgd body rotates n a crcle of radus r about O. The

More information

Physics 231. Topic 8: Rotational Motion. Alex Brown October MSU Physics 231 Fall

Physics 231. Topic 8: Rotational Motion. Alex Brown October MSU Physics 231 Fall Physcs 231 Topc 8: Rotatonal Moton Alex Brown October 21-26 2015 MSU Physcs 231 Fall 2015 1 MSU Physcs 231 Fall 2015 2 MSU Physcs 231 Fall 2015 3 Key Concepts: Rotatonal Moton Rotatonal Kneatcs Equatons

More information

System in Weibull Distribution

System in Weibull Distribution Internatonal Matheatcal Foru 4 9 no. 9 94-95 Relablty Equvalence Factors of a Seres-Parallel Syste n Webull Dstrbuton M. A. El-Dacese Matheatcs Departent Faculty of Scence Tanta Unversty Tanta Egypt eldacese@yahoo.co

More information

Class: Life-Science Subject: Physics

Class: Life-Science Subject: Physics Class: Lfe-Scence Subject: Physcs Frst year (6 pts): Graphc desgn of an energy exchange A partcle (B) of ass =g oves on an nclned plane of an nclned angle α = 3 relatve to the horzontal. We want to study

More information

Revision: December 13, E Main Suite D Pullman, WA (509) Voice and Fax

Revision: December 13, E Main Suite D Pullman, WA (509) Voice and Fax .9.1: AC power analyss Reson: Deceber 13, 010 15 E Man Sute D Pullan, WA 99163 (509 334 6306 Voce and Fax Oerew n chapter.9.0, we ntroduced soe basc quanttes relate to delery of power usng snusodal sgnals.

More information

Chapter 3 and Chapter 4

Chapter 3 and Chapter 4 Chapter 3 and Chapter 4 Chapter 3 Energy 3. Introducton:Work Work W s energy transerred to or rom an object by means o a orce actng on the object. Energy transerred to the object s postve work, and energy

More information

CHAPTER 7: Linear Momentum

CHAPTER 7: Linear Momentum CHAPTER 7: Linear Moentu Solution Guide to WebAssign Probles 7.1 [1] p v ( 0.08 kg) ( 8.4 s) 0.4 kg s 7. [] Fro Newton s second law, p Ft. For a constant ass object, p v. Equate the two expression for

More information

2. REASONING According to the impulse-momentum theorem, the rocket s final momentum mv f

2. REASONING According to the impulse-momentum theorem, the rocket s final momentum mv f CHAPTER 7 IMPULSE AND MOMENTUM PROLEMS. REASONING According to the ipulse-oentu theore, the rocket s inal oentu diers ro its initial oentu by an aount equal to the ipulse ( ΣF ) o the net orce eerted on

More information

Chapter 9 Linear Momentum and Collisions

Chapter 9 Linear Momentum and Collisions Chapter 9 Lnear Momentum and Collsons m = 3. kg r = ( ˆ ˆ j ) P9., r r (a) p m ( ˆ ˆj ) 3. 4. m s = = 9.. kg m s Thus, p x = 9. kg m s and p y =. kg m s (b) p px p y p y θ = tan = tan (.33) = 37 px = +

More information

EXAM 3 REVIEW: hardest problems

EXAM 3 REVIEW: hardest problems PHYS 17: oern echanics Spring 011 xa 3 results: ultiple choice: 4.5/70 = 60.7% Hanwritten: XXX FINAL XA: 1. Coprehensie. About 0-5 ultiple choice questions only. If you hae Final xa conflict: 1. Notify

More information

The Dirac Equation. Elementary Particle Physics Strong Interaction Fenomenology. Diego Bettoni Academic year

The Dirac Equation. Elementary Particle Physics Strong Interaction Fenomenology. Diego Bettoni Academic year The Drac Equaton Eleentary artcle hyscs Strong Interacton Fenoenology Dego Betton Acadec year - D Betton Fenoenologa Interazon Fort elatvstc equaton to descrbe the electron (ncludng ts sn) Conservaton

More information

Chapter 7. Impulse and Momentum

Chapter 7. Impulse and Momentum Chapter 7 Ipulse and Moentu 7. The Ipulse-Moentu Theore 7. The Ipulse-Moentu Theore There are any situations when the force on an object is not constant. 7. The Ipulse-Moentu Theore DEFINITION OF IMPULSE

More information

7. Momentum balances Partly based on Chapter 7 of the De Nevers textbook (sections ).

7. Momentum balances Partly based on Chapter 7 of the De Nevers textbook (sections ). Lecture Notes CHE 31 Fluid Mechanics (Fall 010) 7 Moentu balances Partly based on Chater 7 of the De Neers tetbook (sections 71-73) Introduction Net to ass and energy oentu is an iortant quantity fluid

More information

Physics for Scientists and Engineers. Chapter 9 Impulse and Momentum

Physics for Scientists and Engineers. Chapter 9 Impulse and Momentum Physcs or Scentsts and Engneers Chapter 9 Impulse and Momentum Sprng, 008 Ho Jung Pak Lnear Momentum Lnear momentum o an object o mass m movng wth a velocty v s dened to be p mv Momentum and lnear momentum

More information

Introduction To Robotics (Kinematics, Dynamics, and Design)

Introduction To Robotics (Kinematics, Dynamics, and Design) ntroducton To obotcs Kneatcs, Dynacs, and Desgn SESSON # 6: l Meghdar, Professor School of Mechancal Engneerng Sharf Unersty of Technology Tehran, N 365-9567 Hoepage: http://eghdar.sharf.edu So far we

More information

Momentum, p = m v. Collisions and Work(L8) Crash! Momentum and Collisions. Conservation of Momentum. elastic collisions

Momentum, p = m v. Collisions and Work(L8) Crash! Momentum and Collisions. Conservation of Momentum. elastic collisions Collisions and Work(L8) Crash! collisions can be ery coplicated two objects bang into each other and exert strong forces oer short tie interals fortunately, een though we usually do not know the details

More information

Description of the Force Method Procedure. Indeterminate Analysis Force Method 1. Force Method con t. Force Method con t

Description of the Force Method Procedure. Indeterminate Analysis Force Method 1. Force Method con t. Force Method con t Indeternate Analyss Force Method The force (flexblty) ethod expresses the relatonshps between dsplaceents and forces that exst n a structure. Prary objectve of the force ethod s to deterne the chosen set

More information

Rotational Dynamics. Physics 1425 Lecture 19. Michael Fowler, UVa

Rotational Dynamics. Physics 1425 Lecture 19. Michael Fowler, UVa Rotatonal Dynamcs Physcs 1425 Lecture 19 Mchael Fowler, UVa Rotatonal Dynamcs Newton s Frst Law: a rotatng body wll contnue to rotate at constant angular velocty as long as there s no torque actng on t.

More information

Period & Frequency. Work and Energy. Methods of Energy Transfer: Energy. Work-KE Theorem 3/4/16. Ranking: Which has the greatest kinetic energy?

Period & Frequency. Work and Energy. Methods of Energy Transfer: Energy. Work-KE Theorem 3/4/16. Ranking: Which has the greatest kinetic energy? Perod & Frequency Perod (T): Tme to complete one ull rotaton Frequency (): Number o rotatons completed per second. = 1/T, T = 1/ v = πr/t Work and Energy Work: W = F!d (pcks out parallel components) F

More information

Lecture 6. Announcements. Conservation Laws: The Most Powerful Laws of Physics. Conservation Laws Why they are so powerful

Lecture 6. Announcements. Conservation Laws: The Most Powerful Laws of Physics. Conservation Laws Why they are so powerful Conseration Laws: The Most Powerful Laws of Physics Potential Energy gh Moentu p = + +. Energy E = PE + KE +. Kinetic Energy / Announceents Mon., Sept. : Second Law of Therodynaics Gie out Hoework 4 Wed.,

More information

> To construct a potential representation of E and B, you need a vector potential A r, t scalar potential ϕ ( F,t).

> To construct a potential representation of E and B, you need a vector potential A r, t scalar potential ϕ ( F,t). MIT Departent of Chestry p. 54 5.74, Sprng 4: Introductory Quantu Mechancs II Instructor: Prof. Andre Tokakoff Interacton of Lght wth Matter We want to derve a Haltonan that we can use to descrbe the nteracton

More information

Applied Physics I (Phys 182)

Applied Physics I (Phys 182) Applied Physics I (Phys 182) Dr. Joseph J. Trout E-ail: joseph.trout@drexel.edu Cell: (610)348-6495 Office: Disque 902 1 Moentu Ipulse Conservation of Moentu Explosions Inelastic Collisions Elastic Collisions

More information

PHYS 1443 Section 002

PHYS 1443 Section 002 PHYS 443 Secton 00 Lecture #6 Wednesday, Nov. 5, 008 Dr. Jae Yu Collsons Elastc and Inelastc Collsons Two Dmensonal Collsons Center o ass Fundamentals o Rotatonal otons Wednesday, Nov. 5, 008 PHYS PHYS

More information

Ground Rules. PC1221 Fundamentals of Physics I. Linear Momentum, cont. Linear Momentum. Lectures 17 and 18. Linear Momentum and Collisions

Ground Rules. PC1221 Fundamentals of Physics I. Linear Momentum, cont. Linear Momentum. Lectures 17 and 18. Linear Momentum and Collisions PC Fundamentals of Physcs I Lectures 7 and 8 Lnear omentum and Collsons Dr Tay Seng Chuan Ground Rules Swtch off your handphone and pager Swtch off your laptop computer and keep t No talkng whle lecture

More information

Lecture-24. Enzyme kinetics and Enzyme inhibition-ii

Lecture-24. Enzyme kinetics and Enzyme inhibition-ii Lecture-24 Enzye knetcs and Enzye nhbton-ii Noncopette Inhbton A noncopette nhbtor can bnd wth enzye or wth enzye-substrate coplex to produce end coplex. Hence the nhbtor ust bnd at a dfferent ste fro

More information

Page 1. Clicker Question 9: Physics 131: Lecture 15. Today s Agenda. Clicker Question 9: Energy. Energy is Conserved.

Page 1. Clicker Question 9: Physics 131: Lecture 15. Today s Agenda. Clicker Question 9: Energy. Energy is Conserved. Physcs 3: Lecture 5 Today s Agenda Intro to Conseraton o Energy Intro to some derent knds o energy Knetc Potental Denton o Mechancal Energy Conseraton o Mechancal Energy Conserate orces Examples Pendulum

More information

Page 1. t F t m v. N s kg s. J F t SPH4U. From Newton Two New Concepts Impulse & Momentum. Agenda

Page 1. t F t m v. N s kg s. J F t SPH4U. From Newton Two New Concepts Impulse & Momentum. Agenda SPH4U Agenda Fro Newton Two New Concepts Ipulse & oentu Ipulse Collisions: you gotta consere oentu! elastic or inelastic (energy consering or not) Inelastic collisions in one diension and in two diensions

More information

Page 1. Physics 131: Lecture 16. Today s Agenda. Collisions. Elastic Collision

Page 1. Physics 131: Lecture 16. Today s Agenda. Collisions. Elastic Collision Physics 131: Lecture 16 Today s Agenda Elastic Collisions Definition Exaples Work and Energy Definition of work Exaples Physics 01: Lecture 10, Pg 1 Collisions Moentu is alost always consered during as

More information

Chapter 8: Potential Energy and The Conservation of Total Energy

Chapter 8: Potential Energy and The Conservation of Total Energy Chapter 8: Potental Energy and The Conservaton o Total Energy Work and knetc energy are energes o moton. K K K mv r v v F dr Potental energy s an energy that depends on locaton. -Dmenson F x d U( x) dx

More information

Physics 201, Lecture 15

Physics 201, Lecture 15 Physics 0, Lecture 5 Today s Topics q More on Linear Moentu And Collisions Elastic and Perfect Inelastic Collision (D) Two Diensional Elastic Collisions Exercise: Billiards Board Explosion q Multi-Particle

More information

Physics Momentum: Collisions

Physics Momentum: Collisions F A C U L T Y O F E D U C A T I O N Departent o Curriculu and Pedagogy Physics Moentu: Collisions Science and Matheatics Education Research Group Supported by UBC Teaching and Learning Enhanceent Fund

More information

Physics 181. Particle Systems

Physics 181. Particle Systems Physcs 181 Partcle Systems Overvew In these notes we dscuss the varables approprate to the descrpton of systems of partcles, ther defntons, ther relatons, and ther conservatons laws. We consder a system

More information

General Results of Local Metric Dimensions of. Edge-Corona of Graphs

General Results of Local Metric Dimensions of. Edge-Corona of Graphs Internatonal Matheatcal Foru, Vol 11, 016, no 16, 793-799 HIKARI Ltd, www-hkarco htt://dxdoorg/101988/f0166710 General Results of Local Metrc Densons of Edge-Corona of Grahs Rnurwat Deartent of Matheatcs,

More information

THERMODYNAMICS of COMBUSTION

THERMODYNAMICS of COMBUSTION Internal Cobuston Engnes MAK 493E THERMODYNAMICS of COMBUSTION Prof.Dr. Ce Soruşbay Istanbul Techncal Unversty Internal Cobuston Engnes MAK 493E Therodynacs of Cobuston Introducton Proertes of xtures Cobuston

More information

Momentum. Momentum. Impulse. Impulse Momentum Theorem. Deriving Impulse. v a t. Momentum and Impulse. Impulse. v t

Momentum. Momentum. Impulse. Impulse Momentum Theorem. Deriving Impulse. v a t. Momentum and Impulse. Impulse. v t Moentu and Iule Moentu Moentu i what Newton called the quantity of otion of an object. lo called Ma in otion The unit for oentu are: = oentu = a = elocity kg Moentu Moentu i affected by a and elocity eeding

More information

PHYS 1443 Section 002 Lecture #20

PHYS 1443 Section 002 Lecture #20 PHYS 1443 Secton 002 Lecture #20 Dr. Jae Condtons for Equlbru & Mechancal Equlbru How to Solve Equlbru Probles? A ew Exaples of Mechancal Equlbru Elastc Propertes of Solds Densty and Specfc Gravty lud

More information

K = 100 J. [kg (m/s) ] K = mv = (0.15)(36.5) !!! Lethal energies. m [kg ] J s (Joule) Kinetic Energy (energy of motion) E or KE.

K = 100 J. [kg (m/s) ] K = mv = (0.15)(36.5) !!! Lethal energies. m [kg ] J s (Joule) Kinetic Energy (energy of motion) E or KE. Knetc Energy (energy of moton) E or KE K = m v = m(v + v y + v z ) eample baseball m=0.5 kg ptche at v = 69 mph = 36.5 m/s K = mv = (0.5)(36.5) [kg (m/s) ] Unts m [kg ] J s (Joule) v = 69 mph K = 00 J

More information

Phys101 Lectures 13, 14 Momentum and Collisions

Phys101 Lectures 13, 14 Momentum and Collisions Phs0 Lectures 3, 4 Moentu and ollisions Ke points: Moentu and ipulse ondition for conservation of oentu and wh How to solve collision probles entre of ass Ref: 7-,,3,4,5,6,7,8,9,0. Page Moentu is a vector:

More information

Chapter 7 Impulse and Momentum. So far we considered only constant force/s BUT There are many situations when the force on an object is not constant

Chapter 7 Impulse and Momentum. So far we considered only constant force/s BUT There are many situations when the force on an object is not constant Chapter 7 Ipulse and Moentu So far we considered only constant force/s BUT There are any situations when the force on an object is not constant Force varies with tie 7. The Ipulse-Moentu Theore DEFINITION

More information

Physics 141. Lecture 14. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 14, Page 1

Physics 141. Lecture 14. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 14, Page 1 Physcs 141. Lecture 14. Frank L. H. Wolfs Department of Physcs and Astronomy, Unversty of Rochester, Lecture 14, Page 1 Physcs 141. Lecture 14. Course Informaton: Lab report # 3. Exam # 2. Mult-Partcle

More information

One Dimensional Collisions

One Dimensional Collisions One Diensional Collisions These notes will discuss a few different cases of collisions in one diension, arying the relatie ass of the objects and considering particular cases of who s oing. Along the way,

More information

Chapter 13. Gas Mixtures. Study Guide in PowerPoint. Thermodynamics: An Engineering Approach, 5th edition by Yunus A. Çengel and Michael A.

Chapter 13. Gas Mixtures. Study Guide in PowerPoint. Thermodynamics: An Engineering Approach, 5th edition by Yunus A. Çengel and Michael A. Chapter 3 Gas Mxtures Study Gude n PowerPont to accopany Therodynacs: An Engneerng Approach, 5th edton by Yunus A. Çengel and Mchael A. Boles The dscussons n ths chapter are restrcted to nonreactve deal-gas

More information

PHYSICS 231 Review problems for midterm 2

PHYSICS 231 Review problems for midterm 2 PHYSICS 31 Revew problems for mdterm Topc 5: Energy and Work and Power Topc 6: Momentum and Collsons Topc 7: Oscllatons (sprng and pendulum) Topc 8: Rotatonal Moton The nd exam wll be Wednesday October

More information

Quantum Particle Motion in Physical Space

Quantum Particle Motion in Physical Space Adv. Studes Theor. Phys., Vol. 8, 014, no. 1, 7-34 HIKARI Ltd, www.-hkar.co http://dx.do.org/10.1988/astp.014.311136 Quantu Partcle Moton n Physcal Space A. Yu. Saarn Dept. of Physcs, Saara State Techncal

More information

PHYSICS 231 Lecture 18: equilibrium & revision

PHYSICS 231 Lecture 18: equilibrium & revision PHYSICS 231 Lecture 18: equlbrum & revson Remco Zegers Walk-n hour: Thursday 11:30-13:30 am Helproom 1 gravtaton Only f an object s near the surface of earth one can use: F gravty =mg wth g=9.81 m/s 2

More information

Chapter 7 Impulse and Momentum. So far we considered only constant force/s BUT There are many situations when the force on an object is not constant

Chapter 7 Impulse and Momentum. So far we considered only constant force/s BUT There are many situations when the force on an object is not constant Chapter 7 Ipulse and Moentu So far we considered only constant force/s BUT There are any situations when the force on an object is not constant JUST IN TIME TEACHING E-ail or bring e your questions prior

More information

LECTURE :FACTOR ANALYSIS

LECTURE :FACTOR ANALYSIS LCUR :FACOR ANALYSIS Rta Osadchy Based on Lecture Notes by A. Ng Motvaton Dstrbuton coes fro MoG Have suffcent aount of data: >>n denson Use M to ft Mture of Gaussans nu. of tranng ponts If

More information

Momentum, p. Crash! Collisions (L8) Momentum is conserved. Football provides many collision examples to think about!

Momentum, p. Crash! Collisions (L8) Momentum is conserved. Football provides many collision examples to think about! Collisions (L8) Crash! collisions can be ery coplicated two objects bang into each other and exert strong forces oer short tie interals fortunately, een though we usually do not know the details of the

More information

increases. In part (b) the impulse and initial momentum are in opposite directions and the velocity decreases.

increases. In part (b) the impulse and initial momentum are in opposite directions and the velocity decreases. 8IDENTIFY and SET U: p = K = EXECUTE: (a) 5 p = (, kg)( /s) = kg /s 5 p kg /s (b) (i) = = = 6 /s (ii) kg =, so T T SUV SUV, kg ( /s) 68 /s T SUV = T = = SUV kg EVALUATE:The SUV ust hae less speed to hae

More information

Quasi-Static transient Thermal Stresses in a Robin's thin Rectangular plate with internal moving heat source

Quasi-Static transient Thermal Stresses in a Robin's thin Rectangular plate with internal moving heat source 31-7871 Weely Scence Research Journal Orgnal Artcle Vol-1, Issue-44, May 014 Quas-Statc transent Theral Stresses n a Robn's n Rectangular late w nternal ovng heat source D. T. Solane and M.. Durge ABSTRACT

More information

CHAPTER 7 IMPULSE AND MOMENTUM

CHAPTER 7 IMPULSE AND MOMENTUM CHAPTER 7 IMPULSE AND MOMENTUM PROBLEMS 1. SSM REASONING The ipulse that the olleyball player applies to the ball can be ound ro the ipulse-oentu theore, Equation 7.4. Two orces act on the olleyball while

More information

Outline. Unit Eight Calculations with Entropy. The Second Law. Second Law Notes. Uses of Entropy. Entropy is a Property.

Outline. Unit Eight Calculations with Entropy. The Second Law. Second Law Notes. Uses of Entropy. Entropy is a Property. Unt Eght Calculatons wth Entropy Mechancal Engneerng 370 Thermodynamcs Larry Caretto October 6, 010 Outlne Quz Seven Solutons Second law revew Goals for unt eght Usng entropy to calculate the maxmum work

More information

Applied Mathematics Letters

Applied Mathematics Letters Appled Matheatcs Letters 2 (2) 46 5 Contents lsts avalable at ScenceDrect Appled Matheatcs Letters journal hoepage: wwwelseverco/locate/al Calculaton of coeffcents of a cardnal B-splne Gradr V Mlovanovć

More information

Linear Momentum and Collisions

Linear Momentum and Collisions 9 Lnear Moentu and Collsons CHAPTER OUTLINE 9. Lnear Moentu and Its Conseraton 9. Ipulse and Moentu 9.3 Collsons n One Denson 9.4 Two-Densonal Collsons 9.5 The Center o Mass 9.6 Moton o a Syste o Partcles

More information

Solutions for Homework #9

Solutions for Homework #9 Solutons for Hoewor #9 PROBEM. (P. 3 on page 379 n the note) Consder a sprng ounted rgd bar of total ass and length, to whch an addtonal ass s luped at the rghtost end. he syste has no dapng. Fnd the natural

More information

PHYS 705: Classical Mechanics. Newtonian Mechanics

PHYS 705: Classical Mechanics. Newtonian Mechanics 1 PHYS 705: Classcal Mechancs Newtonan Mechancs Quck Revew of Newtonan Mechancs Basc Descrpton: -An dealzed pont partcle or a system of pont partcles n an nertal reference frame [Rgd bodes (ch. 5 later)]

More information

We last left off by talking about how the area under a force vs. time curve is impulse.

We last left off by talking about how the area under a force vs. time curve is impulse. Lecture 11 Ipulse and Moentu We last left off by talking about how the area under a force vs. tie curve is ipulse. Recall that for our golf ball we had a strongly peaked force curve: F F avg t You have

More information

XII.3 The EM (Expectation-Maximization) Algorithm

XII.3 The EM (Expectation-Maximization) Algorithm XII.3 The EM (Expectaton-Maxzaton) Algorth Toshnor Munaata 3/7/06 The EM algorth s a technque to deal wth varous types of ncoplete data or hdden varables. It can be appled to a wde range of learnng probles

More information

26 Impulse and Momentum

26 Impulse and Momentum 6 Ipulse and Moentu First, a Few More Words on Work and Energy, for Coparison Purposes Iagine a gigantic air hockey table with a whole bunch of pucks of various asses, none of which experiences any friction

More information

PY2101 Classical Mechanics Dr. Síle Nic Chormaic, Room 215 D Kane Bldg

PY2101 Classical Mechanics Dr. Síle Nic Chormaic, Room 215 D Kane Bldg PY2101 Classcal Mechancs Dr. Síle Nc Chormac, Room 215 D Kane Bldg s.ncchormac@ucc.e Lectures stll some ssues to resolve. Slots shared between PY2101 and PY2104. Hope to have t fnalsed by tomorrow. Mondays

More information

Physics 131: Lecture 16. Today s Agenda

Physics 131: Lecture 16. Today s Agenda Physcs 131: Lecture 16 Today s Agenda Intro to Conseraton o Energy Intro to some derent knds o energy Knetc Potental Denton t o Mechancal Energy Conseraton o Mechancal Energy Conserate orces Examples Pendulum

More information