Physics for Scientists and Engineers. Chapter 9 Impulse and Momentum

Size: px
Start display at page:

Download "Physics for Scientists and Engineers. Chapter 9 Impulse and Momentum"

Transcription

1 Physcs or Scentsts and Engneers Chapter 9 Impulse and Momentum Sprng, 008 Ho Jung Pak

2 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 wll be used nterchangeably Momentum s a vector quantty SI unts o momentum are kg m/s Momentum can be expressed n component orm: p x mv x, p y mv y, p z mv z 31-Mar-08 Pak p.

3 Newton s nd Law & Momentum Newton s nd law as Newton presented t: d p d F ( mv) dt dt Ths s a more general orm than the one that we used so ar Newton called m v the quantty o moton For constant mass (.e. dm/dt 0), Newton s nd law becomes d dv F ( mv) m ma dt dt 31-Mar-08 Pak p. 3

4 Conservaton o Lnear Momentum When two or more partcles n an solated system (.e. no external orces present) nteract, the total momentum o the system remans constant The momentum o the system s conserved, not the momenta o ndvdual partcles Can be expressed mathematcally n varous ways p total p 1 + p constant p 1 + p p 1 + p Conservaton o momentum can be appled to systems wth any number o partcles 31-Mar-08 Pak p. 4

5 Archer and Arrow An archer s standng on a rctonless surace Let the system be the archer wth bow (partcle 1) and the arrow (partcle ) There are no external orces n the x-drecton, so t s solated n the x-drecton Total momentum beore releasng the arrow s 0 Total momentum ater releasng the arrow s p 1 + p 0 The archer wll move n the opposte drecton o the arrow Agrees wth Newton s 3rd law Because the archer s much more massve than the arrow, hs acceleraton and velocty wll be much smaller than those o the arrow 31-Mar-08 Pak p. 5

6 Kaon Decay The kaon decays nto a postve π and a negatve π partcle Total momentum beore decay s zero Thereore, the total momentum ater the decay must equal zero: p + + p 0, or p + p 31-Mar-08 Pak p. 6

7 Impulse and Momentum From Newton s nd Law F dp/dt, dp Fdt Integratng to nd the change n momentum over some tme nterval The ntegral s called the mpulse, I, o the orce F actng on an object over Δt Ths equaton expresses the mpulsemomentum theorem 31-Mar-08 Pak p. 7

8 More About Impulse Impulse s a vector quantty The magntude o the mpulse s equal to the area under the orce-tme curve Dmensons o mpulse are ML/T, wth unts o N s kg m s -1 Impulse can also be ound by usng the tme averaged orce: I FΔt 31-Mar-08 Pak p. 8

9 Example 1: Deormed Ball A hard rubber ball, released at chest heght, alls to the pavement and bounces back to nearly the same heght. When t s n contact wth the pavement, the lower sde o the ball s temporarly lattened, wth the maxmum dent o 1 cm. Estmate the acceleraton o the ball whle t s n contact wth the pavement and the tme duraton t s deormed. To nd the contact tme, we use the mpulse equaton: I F ave Δt To nd F ave, we need to nd a. To nd a, rst nd the velocty o the ball at the nstant the bottom hts the ground, assumng the ball alls 1.50 m: v v + a( y y ) 0 + ( 9.80 m/s )( 1.50 m 0) v 5.4 m/s p 31-Mar-08 Pak p. 9 p

10 Example 1, cont We use the same equaton to nd the acceleraton, assumed constant: v Ths s approxmately the average acceleraton. The momentum o the ball goes rom p m(5.4 m/s) to p 0 as t s beng deormed. Usng the mpulse theorem: I Δt F v ave + a( y a 1470 m/s Δt p p F ave p p y ) p p ma ( 5.4 m/s) m( 5.4 m/s) 3 m( m/s ) Snce t bounces back to nearly the same heght, the tme to deorm and un-deorm s approxmately twce ths tme. + a( m) 0 s 31-Mar-08 Pak p. 10

11 Collsons Collson s an event durng whch two partcles come close to each other and nteract by means o orces The tme nterval durng whch the velocty changes rom ts ntal to nal values s assumed to be short The nteracton orce s assumed to be much greater than any external orces present Ths means the mpulse approxmaton can be used 31-Mar-08 Pak p. 11

12 Example : Car Crash In a crash test, a car o mass 1500 kg colldes wth a wall. The ntal and nal veloctes o the car are v 15.0 m/s and v.60 m/s. The collson lasts s. Fnd the mpulse and average orce on the car. Assume the orce exerted by the wall on the car s greater than any other orces that cause ts velocty to change. p (1500 kg)( 15.0 m/s).5 x 10 4 kg m/s P (1500 kg)(.60 m/s) 0.39 x 10 4 kg m/s I p -p.64 x 10 4 kg m/s F ave Δp /Δt (.64 x 10 4 kg m/s)/0.150 s 1.50 x 10 5 N 31-Mar-08 Pak p. 1

13 Collsons Examples Collsons may be the result o drect contact Impulsve orces may vary n tme n complcated ways Collson need not nclude physcal contact There are stll orces between the partcles Total momentum s always conserved 31-Mar-08 Pak p. 13

14 Types o Collsons In an elastc collson, momentum and knetc energy are conserved Perectly elastc collsons occur on a mcroscopc level Macroscopc collsons are only approxmately elastc In an nelastc collson, knetc energy s not conserved although momentum s conserved I the objects stck together ater the collson, t s a perectly nelastc collson Elastc and perectly nelastc collsons are lmtng cases; most actual collsons all n between these two types 31-Mar-08 Pak p. 14

15 Conservaton o Momentum Snce there are no external orces, F Δ t P P 0, P ext In an elastc collson, v + m v m v + m mv P In a perectly nelastc collson, they share the same velocty ater the collson m ( m m ) 1 v 1 v1 + mv + 31-Mar-08 Pak p. 15

16 Example 3: D Per Inel Collson The car and the van have masses o 1500 kg and 500 kg, respectvely. Beore the collson, the car was movng wth a speed o 5.0 m/s n the x-drecton and the van wth a speed o 0.0 m/s n the y-drecton. The car and the van make a perectly nelastc collson. What s ther velocty ater the collson? Momentum conservaton: x: m 1 v 1x (m 1 +m )v cosθ, 3.75x10 4 kg m/s 4000 v cosθ y: m v y (m 1 +m )v snθ, 5.00x10 4 kg m/s 4000 v snθ tanθ 5.00/3.75, θ 53.1, v 5.00x10 4 /(4000 sn 53.1 ) 15.6 m/s 31-Mar-08 Pak p. 16

17 Exploson Exploson s an event durng whch partcles o the system move apart rom each other ater a bre nteracton Examples: archer and arrow, recol o rle, partcle decay Exploson s the reverse o the collson problem Total momentum s conserved 31-Mar-08 Pak p. 17

18 Example 4: Radoactvty A 38 U nucleus spontaneously decays nto a small ragment that s ejected wth a speed o 1.50 x 10 7 m/s and a daughter nucleus that recols wth a speed o.56 x 10 5 m/s. What are the atomc masses o the ejected ragment and the daughter nucleus? The nucleus was ntally at rest so the total momentum remans zero. m v + m v ( m + m ) v 0, m + m Combnng these two conservaton laws, 38 u v m v + ( 38 u m ) v 0, m 38 u 34 u, m v v 31-Mar-08 Pak p u

19 Rocket Launch Ths M Here R s the For a s an exploson problem where contnues to decrease : M uel rocket gong straght upward, Ru Integratng gves M burn rate. From Newton' s nd law, r r r r ˆ dp d r dv dm r dv r F Mgj ( Mv ) M + u M Ru ext dt dt dt dt dt r r Here u s the exhaust velocty and the quantty Ru s the thrust, Mg + the dv dt or dv dt M rocket equaton 0 Rt. Ru M we have Ru g g M Rt 0 : M 0 v u ln gt M Rt 0 31-Mar-08 Pak p. 19 r F thrust.

20 Example 5: Saturn V Saturn V, the Apollo launch vehcle, has an ntal mass o M 0.85 x 10 6 kg, a payload mass o M p 0.7M 0, a uel burn rate o R x 10 3 kg/s, and a thrust o F thrust 34.0 x 10 6 N. Fnd (a) the exhaust speed u, (b) burn tme b t, (c) acceleraton at lto and burnout, and (d) nal speed o the rocket. 31-Mar-08 Pak p. 0

21 (a) Example 5, cont Exhaust speed : u F R thrust Acceleraton at burnout : kg m/s kg/s 9.80 m/s.46 km/s 6 M M 0 P (1 0.7) kg (b) Burn tme : tb 150 s 3 R kg/s dv Ru (c) Acceleraton at lto : 9.80 m/s.14 m/s dt M M 0 (d) Fnal speed at burnout : v u ln 9.80 m/s 0.7 M 0 3 v ( m/s)(1.31) 1470 m/s 1.75 km/s dv dt 34.3 m/s 150 s 31-Mar-08 Pak p. 1 0 Ru M p

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

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

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

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

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

Lecture 16. Chapter 11. Energy Dissipation Linear Momentum. Physics I. Department of Physics and Applied Physics

Lecture 16. Chapter 11. Energy Dissipation Linear Momentum. Physics I. Department of Physics and Applied Physics Lecture 16 Chapter 11 Physcs I Energy Dsspaton Lnear Momentum Course webste: http://aculty.uml.edu/andry_danylov/teachng/physcsi Department o Physcs and Appled Physcs IN IN THIS CHAPTER, you wll learn

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

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

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

ONE-DIMENSIONAL COLLISIONS

ONE-DIMENSIONAL COLLISIONS Purpose Theory ONE-DIMENSIONAL COLLISIONS a. To very the law o conservaton o lnear momentum n one-dmensonal collsons. b. To study conservaton o energy and lnear momentum n both elastc and nelastc onedmensonal

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

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

Physics 2A Chapter 9 HW Solutions

Physics 2A Chapter 9 HW Solutions Phscs A Chapter 9 HW Solutons Chapter 9 Conceptual Queston:, 4, 8, 13 Problems: 3, 8, 1, 15, 3, 40, 51, 6 Q9.. Reason: We can nd the change n momentum o the objects b computng the mpulse on them and usng

More information

Chapter 07: Kinetic Energy and Work

Chapter 07: Kinetic Energy and Work Chapter 07: Knetc Energy and Work Conservaton o Energy s one o Nature s undamental laws that s not volated. Energy can take on derent orms n a gven system. Ths chapter we wll dscuss work and knetc energy.

More information

CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS

CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS 103 Phy 1 9.1 Lnear Momentum The prncple o energy conervaton can be ued to olve problem that are harder to olve jut ung Newton law. It ued to decrbe moton

More information

First Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force.

First Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force. Secton 1. Dynamcs (Newton s Laws of Moton) Two approaches: 1) Gven all the forces actng on a body, predct the subsequent (changes n) moton. 2) Gven the (changes n) moton of a body, nfer what forces act

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

PHYS 1441 Section 002 Lecture #16

PHYS 1441 Section 002 Lecture #16 PHYS 1441 Secton 00 Lecture #16 Monday, Mar. 4, 008 Potental Energy Conservatve and Non-conservatve Forces Conservaton o Mechancal Energy Power Today s homework s homework #8, due 9pm, Monday, Mar. 31!!

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

Page 1. Physics 131: Lecture 14. Today s Agenda. Things that stay the same. Impulse and Momentum Non-constant forces

Page 1. Physics 131: Lecture 14. Today s Agenda. Things that stay the same. Impulse and Momentum Non-constant forces Physcs 131: Lecture 14 Today s Agenda Imulse and Momentum Non-constant forces Imulse-momentum momentum thm Conservaton of Lnear momentum Eternal/Internal forces Eamles Physcs 201: Lecture 1, Pg 1 Physcs

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

PHYSICS 203-NYA-05 MECHANICS

PHYSICS 203-NYA-05 MECHANICS PHYSICS 03-NYA-05 MECHANICS PROF. S.D. MANOLI PHYSICS & CHEMISTRY CHAMPLAIN - ST. LAWRENCE 790 NÉRÉE-TREMBLAY QUÉBEC, QC GV 4K TELEPHONE: 48.656.69 EXT. 449 EMAIL: smanol@slc.qc.ca WEBPAGE: http:/web.slc.qc.ca/smanol/

More information

10/9/2003 PHY Lecture 11 1

10/9/2003 PHY Lecture 11 1 Announcements 1. Physc Colloquum today --The Physcs and Analyss of Non-nvasve Optcal Imagng. Today s lecture Bref revew of momentum & collsons Example HW problems Introducton to rotatons Defnton of angular

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

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

Physics 2A Chapters 6 - Work & Energy Fall 2017

Physics 2A Chapters 6 - Work & Energy Fall 2017 Physcs A Chapters 6 - Work & Energy Fall 017 These notes are eght pages. A quck summary: The work-energy theorem s a combnaton o Chap and Chap 4 equatons. Work s dened as the product o the orce actng on

More information

EMU Physics Department

EMU Physics Department Physcs 0 Lecture 8 Potental Energy and Conservaton Assst. Pro. Dr. Al ÖVGÜN EMU Physcs Department www.aovgun.com Denton o Work W q The work, W, done by a constant orce on an object s dened as the product

More information

Spring Force and Power

Spring Force and Power Lecture 13 Chapter 9 Sprng Force and Power Yeah, energy s better than orces. What s net? Course webste: http://aculty.uml.edu/andry_danylov/teachng/physcsi IN THIS CHAPTER, you wll learn how to solve problems

More information

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle

More information

PHYS 1443 Section 004 Lecture #12 Thursday, Oct. 2, 2014

PHYS 1443 Section 004 Lecture #12 Thursday, Oct. 2, 2014 PHYS 1443 Secton 004 Lecture #1 Thursday, Oct., 014 Work-Knetc Energy Theorem Work under rcton Potental Energy and the Conservatve Force Gravtatonal Potental Energy Elastc Potental Energy Conservaton o

More information

Physics 2A Chapter 3 HW Solutions

Physics 2A Chapter 3 HW Solutions Phscs A Chapter 3 HW Solutons Chapter 3 Conceptual Queston: 4, 6, 8, Problems: 5,, 8, 7, 3, 44, 46, 69, 70, 73 Q3.4. Reason: (a) C = A+ B onl A and B are n the same drecton. Sze does not matter. (b) C

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

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

Conservation of Energy

Conservation of Energy Lecture 3 Chapter 8 Physcs I 0.3.03 Conservaton o Energy Course webste: http://aculty.uml.edu/andry_danylov/teachng/physcsi Lecture Capture: http://echo360.uml.edu/danylov03/physcsall.html 95.4, Fall 03,

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

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 11 Angular Momentum

Chapter 11 Angular Momentum Chapter 11 Angular Momentum Analyss Model: Nonsolated System (Angular Momentum) Angular Momentum of a Rotatng Rgd Object Analyss Model: Isolated System (Angular Momentum) Angular Momentum of a Partcle

More information

Week 11: Chapter 11. The Vector Product. The Vector Product Defined. The Vector Product and Torque. More About the Vector Product

Week 11: Chapter 11. The Vector Product. The Vector Product Defined. The Vector Product and Torque. More About the Vector Product The Vector Product Week 11: Chapter 11 Angular Momentum There are nstances where the product of two vectors s another vector Earler we saw where the product of two vectors was a scalar Ths was called the

More information

PHYS 1441 Section 002 Lecture #15

PHYS 1441 Section 002 Lecture #15 PHYS 1441 Secton 00 Lecture #15 Monday, March 18, 013 Work wth rcton Potental Energy Gravtatonal Potental Energy Elastc Potental Energy Mechancal Energy Conservaton Announcements Mdterm comprehensve exam

More information

10/24/2013. PHY 113 C General Physics I 11 AM 12:15 PM TR Olin 101. Plan for Lecture 17: Review of Chapters 9-13, 15-16

10/24/2013. PHY 113 C General Physics I 11 AM 12:15 PM TR Olin 101. Plan for Lecture 17: Review of Chapters 9-13, 15-16 0/4/03 PHY 3 C General Physcs I AM :5 PM T Oln 0 Plan or Lecture 7: evew o Chapters 9-3, 5-6. Comment on exam and advce or preparaton. evew 3. Example problems 0/4/03 PHY 3 C Fall 03 -- Lecture 7 0/4/03

More information

Problem While being compressed, A) What is the work done on it by gravity? B) What is the work done on it by the spring force?

Problem While being compressed, A) What is the work done on it by gravity? B) What is the work done on it by the spring force? Problem 07-50 A 0.25 kg block s dropped on a relaed sprng that has a sprng constant o k 250.0 N/m (2.5 N/cm). The block becomes attached to the sprng and compresses t 0.12 m beore momentarl stoppng. Whle

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

CHAPTER 8 Potential Energy and Conservation of Energy

CHAPTER 8 Potential Energy and Conservation of Energy CHAPTER 8 Potental Energy and Conservaton o Energy One orm o energy can be converted nto another orm o energy. Conservatve and non-conservatve orces Physcs 1 Knetc energy: Potental energy: Energy assocated

More information

Chapter 3. r r. Position, Velocity, and Acceleration Revisited

Chapter 3. r r. Position, Velocity, and Acceleration Revisited Chapter 3 Poston, Velocty, and Acceleraton Revsted The poston vector of a partcle s a vector drawn from the orgn to the locaton of the partcle. In two dmensons: r = x ˆ+ yj ˆ (1) The dsplacement vector

More information

Conservation Laws (Collisions) Phys101 Lab - 04

Conservation Laws (Collisions) Phys101 Lab - 04 Conservaton Laws (Collsons) Phys101 Lab - 04 1.Objectves The objectves o ths experment are to expermentally test the valdty o the laws o conservaton o momentum and knetc energy n elastc collsons. 2. Theory

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

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

EN40: Dynamics and Vibrations. Homework 4: Work, Energy and Linear Momentum Due Friday March 1 st

EN40: Dynamics and Vibrations. Homework 4: Work, Energy and Linear Momentum Due Friday March 1 st EN40: Dynamcs and bratons Homework 4: Work, Energy and Lnear Momentum Due Frday March 1 st School of Engneerng Brown Unversty 1. The fgure (from ths publcaton) shows the energy per unt area requred to

More information

A Tale of Friction Basic Rollercoaster Physics. Fahrenheit Rollercoaster, Hershey, PA max height = 121 ft max speed = 58 mph

A Tale of Friction Basic Rollercoaster Physics. Fahrenheit Rollercoaster, Hershey, PA max height = 121 ft max speed = 58 mph A Tale o Frcton Basc Rollercoaster Physcs Fahrenhet Rollercoaster, Hershey, PA max heght = 11 t max speed = 58 mph PLAY PLAY PLAY PLAY Rotatonal Movement Knematcs Smlar to how lnear velocty s dened, angular

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

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

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

Angular momentum. Instructor: Dr. Hoi Lam TAM ( 譚海嵐 )

Angular momentum. Instructor: Dr. Hoi Lam TAM ( 譚海嵐 ) Angular momentum Instructor: Dr. Ho Lam TAM ( 譚海嵐 ) Physcs Enhancement Programme or Gted Students The Hong Kong Academy or Gted Educaton and Department o Physcs, HKBU Department o Physcs Hong Kong Baptst

More information

Rotational and Translational Comparison. Conservation of Angular Momentum. Angular Momentum for a System of Particles

Rotational and Translational Comparison. Conservation of Angular Momentum. Angular Momentum for a System of Particles Conservaton o Angular Momentum 8.0 WD Rotatonal and Translatonal Comparson Quantty Momentum Ang Momentum Force Torque Knetc Energy Work Power Rotaton L cm = I cm ω = dl / cm cm K = (/ ) rot P rot θ W =

More information

Physics 40 HW #4 Chapter 4 Key NEATNESS COUNTS! Solve but do not turn in the following problems from Chapter 4 Knight

Physics 40 HW #4 Chapter 4 Key NEATNESS COUNTS! Solve but do not turn in the following problems from Chapter 4 Knight Physcs 40 HW #4 Chapter 4 Key NEATNESS COUNTS! Solve but do not turn n the ollowng problems rom Chapter 4 Knght Conceptual Questons: 8, 0, ; 4.8. Anta s approachng ball and movng away rom where ball was

More information

Work is the change in energy of a system (neglecting heat transfer). To examine what could

Work is the change in energy of a system (neglecting heat transfer). To examine what could Work Work s the change n energy o a system (neglectng heat transer). To eamne what could cause work, let s look at the dmensons o energy: L ML E M L F L so T T dmensonally energy s equal to a orce tmes

More information

v c motion is neither created nor destroyed, but transferred via interactions. Fri. Wed (.18,.19) Introducing Potential Energy RE 6.

v c motion is neither created nor destroyed, but transferred via interactions. Fri. Wed (.18,.19) Introducing Potential Energy RE 6. r. 6.5-.7 (.) Rest Mass,ork by Changng orces Columba Rep 3pm, here RE 6.b (last day to drop) ed. 6.8-.9(.8,.9) Introducng Potental Energy RE 6.c Tues. H6: Ch 6 Pr s 58,59, 99(a-c), 05(a-c) moton s nether

More information

Week 9 Chapter 10 Section 1-5

Week 9 Chapter 10 Section 1-5 Week 9 Chapter 10 Secton 1-5 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,

More information

Experiment 5 Elastic and Inelastic Collisions

Experiment 5 Elastic and Inelastic Collisions PHY191 Experment 5: Elastc and Inelastc Collsons 7/1/011 Page 1 Experment 5 Elastc and Inelastc Collsons Readng: Bauer&Westall: Chapter 7 (and 8, or center o mass deas) as needed Homework 5: turn n the

More information

Chapter 7. Potential Energy and Conservation of Energy

Chapter 7. Potential Energy and Conservation of Energy Chapter 7 Potental Energy and Conservaton o Energy 1 Forms o Energy There are many orms o energy, but they can all be put nto two categores Knetc Knetc energy s energy o moton Potental Potental energy

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 7: Conservation of Energy

Chapter 7: Conservation of Energy Lecture 7: Conservaton o nergy Chapter 7: Conservaton o nergy Introucton I the quantty o a subject oes not change wth tme, t means that the quantty s conserve. The quantty o that subject remans constant

More information

Physics 111: Mechanics Lecture 11

Physics 111: Mechanics Lecture 11 Physcs 111: Mechancs Lecture 11 Bn Chen NJIT Physcs Department Textbook Chapter 10: Dynamcs of Rotatonal Moton q 10.1 Torque q 10. Torque and Angular Acceleraton for a Rgd Body q 10.3 Rgd-Body Rotaton

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

Physics 106 Lecture 6 Conservation of Angular Momentum SJ 7 th Ed.: Chap 11.4

Physics 106 Lecture 6 Conservation of Angular Momentum SJ 7 th Ed.: Chap 11.4 Physcs 6 ecture 6 Conservaton o Angular Momentum SJ 7 th Ed.: Chap.4 Comparson: dentons o sngle partcle torque and angular momentum Angular momentum o a system o partcles o a rgd body rotatng about a xed

More information

You will analyze the motion of the block at different moments using the law of conservation of energy.

You will analyze the motion of the block at different moments using the law of conservation of energy. Physcs 00A Homework 7 Chapter 8 Where s the Energy? In ths problem, we wll consder the ollowng stuaton as depcted n the dagram: A block o mass m sldes at a speed v along a horzontal smooth table. It next

More information

Physics 53. Rotational Motion 3. Sir, I have found you an argument, but I am not obliged to find you an understanding.

Physics 53. Rotational Motion 3. Sir, I have found you an argument, but I am not obliged to find you an understanding. Physcs 53 Rotatonal Moton 3 Sr, I have found you an argument, but I am not oblged to fnd you an understandng. Samuel Johnson Angular momentum Wth respect to rotatonal moton of a body, moment of nerta plays

More information

TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES. PHYS 2211, Exam 2 Section 1 Version 1 October 18, 2013 Total Weight: 100 points

TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES. PHYS 2211, Exam 2 Section 1 Version 1 October 18, 2013 Total Weight: 100 points TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS, Exam Secton Verson October 8, 03 Total Weght: 00 ponts. Check your examnaton or completeness pror to startng. There are a total o nne

More information

Conservation of Energy

Conservation of Energy Conservaton o nergy The total energy o a system can change only by amounts o energy that are transerred nto or out o the system W mec th nt Ths s one o the great conservaton laws n nature! Other conservaton

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

Chapter Seven - Potential Energy and Conservation of Energy

Chapter Seven - Potential Energy and Conservation of Energy Chapter Seven - Potental Energy and Conservaton o Energy 7 1 Potental Energy Potental energy. e wll nd that the potental energy o a system can only be assocated wth specc types o orces actng between members

More information

Chapter 8 Potential Energy and Conservation of Energy Important Terms (For chapters 7 and 8)

Chapter 8 Potential Energy and Conservation of Energy Important Terms (For chapters 7 and 8) Pro. Dr. I. Nasser Chapter8_I November 3, 07 Chapter 8 Potental Energy and Conservaton o Energy Important Terms (For chapters 7 and 8) conservatve orce: a orce whch does wor on an object whch s ndependent

More information

Chapter 5. Answers to Even Numbered Problems m kj. 6. (a) 900 J (b) (a) 31.9 J (b) 0 (c) 0 (d) 31.9 J. 10.

Chapter 5. Answers to Even Numbered Problems m kj. 6. (a) 900 J (b) (a) 31.9 J (b) 0 (c) 0 (d) 31.9 J. 10. Answers to Even Numbered Problems Chapter 5. 3.6 m 4..6 J 6. (a) 9 J (b).383 8. (a) 3.9 J (b) (c) (d) 3.9 J. 6 m s. (a) 68 J (b) 84 J (c) 5 J (d) 48 J (e) 5.64 m s 4. 9. J 6. (a). J (b) 5. m s (c) 6.3

More information

Week 6, Chapter 7 Sect 1-5

Week 6, Chapter 7 Sect 1-5 Week 6, Chapter 7 Sect 1-5 Work and Knetc Energy Lecture Quz The frctonal force of the floor on a large sutcase s least when the sutcase s A.pushed by a force parallel to the floor. B.dragged by a force

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

Physics 115. Molecular motion and temperature Phase equilibrium, evaporation

Physics 115. Molecular motion and temperature Phase equilibrium, evaporation Physcs 115 General Physcs II Sesson 9 Molecular moton and temperature Phase equlbrum, evaporaton R. J. Wlkes Emal: phy115a@u.washngton.edu Home page: http://courses.washngton.edu/phy115a/ 4/14/14 Physcs

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

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

10/23/2003 PHY Lecture 14R 1

10/23/2003 PHY Lecture 14R 1 Announcements. Remember -- Tuesday, Oct. 8 th, 9:30 AM Second exam (coverng Chapters 9-4 of HRW) Brng the followng: a) equaton sheet b) Calculator c) Pencl d) Clear head e) Note: If you have kept up wth

More information

So far: simple (planar) geometries

So far: simple (planar) geometries Physcs 06 ecture 5 Torque and Angular Momentum as Vectors SJ 7thEd.: Chap. to 3 Rotatonal quanttes as vectors Cross product Torque epressed as a vector Angular momentum defned Angular momentum as a vector

More information

Energy and Energy Transfer

Energy and Energy Transfer Energy and Energy Transer Chapter 7 Scalar Product (Dot) Work Done by a Constant Force F s constant over the dsplacement r 1 Denton o the scalar (dot) product o vectors Scalar product o unt vectors = 1

More information

Slide. King Saud University College of Science Physics & Astronomy Dept. PHYS 103 (GENERAL PHYSICS) CHAPTER 5: MOTION IN 1-D (PART 2) LECTURE NO.

Slide. King Saud University College of Science Physics & Astronomy Dept. PHYS 103 (GENERAL PHYSICS) CHAPTER 5: MOTION IN 1-D (PART 2) LECTURE NO. Slde Kng Saud Unersty College of Scence Physcs & Astronomy Dept. PHYS 103 (GENERAL PHYSICS) CHAPTER 5: MOTION IN 1-D (PART ) LECTURE NO. 6 THIS PRESENTATION HAS BEEN PREPARED BY: DR. NASSR S. ALZAYED Lecture

More information

Chapters 18 & 19: Themodynamics review. All macroscopic (i.e., human scale) quantities must ultimately be explained on the microscopic scale.

Chapters 18 & 19: Themodynamics review. All macroscopic (i.e., human scale) quantities must ultimately be explained on the microscopic scale. Chapters 18 & 19: Themodynamcs revew ll macroscopc (.e., human scale) quanttes must ultmately be explaned on the mcroscopc scale. Chapter 18: Thermodynamcs Thermodynamcs s the study o the thermal energy

More information

RE 11.e Mon. Review for Final (1-11) HW11: Pr s 39, 57, 64, 74, 78 Sat. 9 a.m. Final Exam (Ch. 1-11)

RE 11.e Mon. Review for Final (1-11) HW11: Pr s 39, 57, 64, 74, 78 Sat. 9 a.m. Final Exam (Ch. 1-11) We..7 -.9, (.) Moton Wth & Wthout Torque E. ab r. otaton ab Evals.0 Quantzaton, Quz, ect Evals E.e Mon. evew or nal (-) HW: Pr s 39, 57, 64, 74, 78 Sat. 9 a.m. nal Exam (Ch. -) Usng ngular Momentum The

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

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

in state i at t i, Initial State E = E i

in state i at t i, Initial State E = E i Physcs 01, Lecture 1 Today s Topcs n More Energy and Work (chapters 7 & 8) n Conservatve Work and Potental Energy n Sprng Force and Sprng (Elastc) Potental Energy n Conservaton of Mechanc Energy n Exercse

More information

Part C Dynamics and Statics of Rigid Body. Chapter 5 Rotation of a Rigid Body About a Fixed Axis

Part C Dynamics and Statics of Rigid Body. Chapter 5 Rotation of a Rigid Body About a Fixed Axis Part C Dynamcs and Statcs of Rgd Body Chapter 5 Rotaton of a Rgd Body About a Fxed Axs 5.. Rotatonal Varables 5.. Rotaton wth Constant Angular Acceleraton 5.3. Knetc Energy of Rotaton, Rotatonal Inerta

More information

Force = F Piston area = A

Force = F Piston area = A CHAPTER III Ths chapter s an mportant transton between the propertes o pure substances and the most mportant chapter whch s: the rst law o thermodynamcs In ths chapter, we wll ntroduce the notons o heat,

More information

Spring 2002 Lecture #13

Spring 2002 Lecture #13 44-50 Sprng 00 ecture # Dr. Jaehoon Yu. Rotatonal Energy. Computaton of oments of nerta. Parallel-as Theorem 4. Torque & Angular Acceleraton 5. Work, Power, & Energy of Rotatonal otons Remember the md-term

More information

Chapter 2. Pythagorean Theorem. Right Hand Rule. Position. Distance Formula

Chapter 2. Pythagorean Theorem. Right Hand Rule. Position. Distance Formula Chapter Moton n One Dmenson Cartesan Coordnate System The most common coordnate system or representng postons n space s one based on three perpendcular spatal axes generally desgnated x, y, and z. Any

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

Physics 5153 Classical Mechanics. Principle of Virtual Work-1

Physics 5153 Classical Mechanics. Principle of Virtual Work-1 P. Guterrez 1 Introducton Physcs 5153 Classcal Mechancs Prncple of Vrtual Work The frst varatonal prncple we encounter n mechancs s the prncple of vrtual work. It establshes the equlbrum condton of a mechancal

More information

Supplemental Material: Causal Entropic Forces

Supplemental Material: Causal Entropic Forces Supplemental Materal: Causal Entropc Forces A. D. Wssner-Gross 1, 2, and C. E. Freer 3 1 Insttute for Appled Computatonal Scence, Harvard Unversty, Cambrdge, Massachusetts 02138, USA 2 The Meda Laboratory,

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

Recitation: Energy, Phys Energies. 1.2 Three stones. 1. Energy. 1. An acorn falling from an oak tree onto the sidewalk.

Recitation: Energy, Phys Energies. 1.2 Three stones. 1. Energy. 1. An acorn falling from an oak tree onto the sidewalk. Rectaton: Energy, Phys 207. Energy. Energes. An acorn fallng from an oak tree onto the sdewalk. The acorn ntal has gravtatonal potental energy. As t falls, t converts ths energy to knetc. When t hts the

More information

Supplemental Instruction sessions next week

Supplemental Instruction sessions next week Homework #4 Wrtten homework due now Onlne homework due on Tue Mar 3 by 8 am Exam 1 Answer keys and scores wll be posted by end of the week Supplemental Instructon sessons next week Wednesday 8:45 10:00

More information

2.00 kg 4.00 kg 3.00 kg m. y com. (2.00 kg)(0.500 m) 4.00 kg m 3.00 kg m m m kg 4.00 kg 3.00 kg m.

2.00 kg 4.00 kg 3.00 kg m. y com. (2.00 kg)(0.500 m) 4.00 kg m 3.00 kg m m m kg 4.00 kg 3.00 kg m. Chapter 9. We use Eq. 9-5 to sole or ( x, y ). (a) The x coordnate o the system s center o mass s: x com x m x m (.00 kg)(.0 m) 4.00 kg 0.600 m.00 kg x mx m m m.00 kg 4.00 kg.00 kg 0.500 m. Solng the equaton

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

Newton s Laws of Motion

Newton s Laws of Motion Chapter 4 Newton s Laws of Moton 4.1 Forces and Interactons Fundamental forces. There are four types of fundamental forces: electromagnetc, weak, strong and gravtatonal. The frst two had been successfully

More information