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


 Owen Henry
 6 years ago
 Views:
Transcription
1 Lecture 16 Chapter 11 Physcs I Energy Dsspaton Lnear Momentum Course webste: Department o Physcs and Appled Physcs
2 IN IN THIS CHAPTER, you wll learn to use the concepts o mpulse and momentum. Today we are gong to dscuss: Chapter 10: Energy Prncple wth Losses: Secton Chapter 11: Newton s 2 nd law (more general orm): Secton 11.1 Lnear Momentum: Secton 11.1 Impulse: Secton 11.1 Department o Physcs and Appled Physcs
3 Energy conservaton wth nonconservatve orces Consder an object experences conservatve and nonconservatve orces: F net F C F Snce the workke prncple works or ANY orces, the total work done on the object W net K Recall, rom the prevous class, a orce s conservatve, then K W C U U W C U WNC K W ( U U ) W NC K K NC K K U W NC NC y E F NC E F C ds W NC x Total Mech Energy at the nal pont As a nonconservatve orce, we are gong to have a rcton orce Total Mech Energy at the ntal pont W Department o Physcs and Appled Physcs r s k Mech. Energy converted to Thermal Energy (losses) (Work done by rcton s usually negatve)
4 Example Block sldng down Inclned Plane A block o mass m sldes down a plane o length l and angle α. Fnd the speed o the block at the bottom o the nclne plane assumng that t starts rom rest and the coecent o rcton μ s constant. k (Thermal energy s generated) α mg α Department o Physcs and Appled Physcs
5 Revew Knetc energy Gravtatonal potental energy U mgy K 1 mv 2 2 Potental energy o a sprng Total Mechancal Energy E K U U sprng 1 2 kx2 Conservaton o Mechancal Energy K U K U Wthout losses (no rcton) K U K U W NC Wth losses (wth rcton) Department o Physcs and Appled Physcs
6 Lnear Momentum Ch.11 Now we know how to use the energy approach to solve problems, so let s go back to our old good Newton s 2nd law, F=ma. F=ma worked great or pont objects, but t als to explan systems such as rockets, where mass changes wth moton (Rockets accelerate by ejectng mass backward). So, obvously, we need to mody (make t more general) our N. 2 nd law somehow. How? Department o Physcs and Appled Physcs
7 Let s rewrte N. 2 nd law n terms o lnear momentum m Let s pck an object and start descrbng t usng our old N. 2 nd law. v F ma m d v d dt (m v) dt d p dt We got a new structure mv, so let s gve t a nce name and symbol Lnear momentum s dened as the product o an object s mass and velocty: p mv Unts o momentum: kg m s Momentum s a VECTOR! So, nally, the Newton s 2 nd law wll look ths way: F Department o Physcs and Appled Physcs dp dt That s what actually Newton wrote. It s more general than our earler verson F=ma The rate o change o momentum s equal to the net orce So, a orce s requred to change momentum o an object.
8 ConcepTest The cart s change o lnear momentum Δp x s ntal nal x x Two Boxes/Momentum A) 20 kg m/s B) 10 kg m/s C) 0 kg m/s D) 30 kg m/s Δp x = 10 kg m/s ( 20 kg m/s) = 30 kg m/s Fnal momentum Intal momentum Negatve ntal momentum because moton s to the let and v x < 0.
9 Impulse Ch.11 Now we have moded Newton s 2nd law, let s apply t to get somethng,.e. mpulse How? Department o Physcs and Appled Physcs
10 Consder Ball and Wall Collson (Beore) The gure shows a partcle wth ntal velocty n the xdrecton The partcle experences an mpulsve orce o short duraton Δt. (A large orce exerted or a small nterval o tme s called an mpulsve orce) The partcle leaves wth nal velocty n the +xdrecton. Instant o maxmum compresson Now, let s descrbe the collson usng our new moded N. 2 nd law (next slde) F d p dt Department o Physcs and Appled Physcs
11 F d p dt t p Fdt dp t p Impulse Durng the collson, objects are deormed because o the large orces nvolved. How to relate those orces wth a change n momentum? From Newton s 2 nd law: Integrate t: Fdt p p dp p p Impulse= change n momentum Dene Impulse as: t t Fdt Beore collson p Ater collson Force exerted on the ball p Recall: Integral Graphcal meanng s an area So, Impulse= area under Fvst curve WorkKE Prncple Smlarty Momentum Prncple p Impulse t t Fdt Department o Physcs and Appled Physcs End o Class
12 Example Tenns Ball/Racket Collson Force (kn) The orce exerted by a tenns racket on the ball (mass 56 g) durng a serve ( v 0 ) can be approxmated by the F vs tme plot below. What s the mpulse on the ball? What s the speed o the serve? 0 2 B A C Tme (ms) 10 Momentum Prncple Department o Physcs and Appled Physcs Area under orcetme curve s an mpulse: Area p 2 Area( ABC) v t t Fdt p mv v m p p 2kN 2ms 2( ) 2 4 N s 71m/s kg 4N s
13 ConcepTest A 2.0 kg object movng to the rght wth speed 0.50 m/s experences the orce shown. What are the object s speed and drecton ater the orce ends? v =0.5m/s x Kckng Ball A) 0.5 m/s let B) At rest C) 0.5 m/s rght D) 1.0 m/s rght v ? x E) 2.0 m/s rght Δp x = x p x  p x = x p x = p x + x.. /
14 Impulse/Average orce The exact varaton o F wth tme s very oten not known (too complcated). How to get at least somethng? It s easer to nd an average orce. Let s keep the same mpulse And the same tme nterval Δt But nstead o a real orce we wll use an average orce t t Fdt F avg F avg t t p p Department o Physcs and Appled Physcs
15 Example How to avod broken legs or a cat? F avg t p Intal lnear momentum ( ) F, that s what can break cat s bones and the cat eels that and tres to reduce F as much as t can. Snce the cat alls rom a certan heght, Δp s gven and the cat cannot do anythng about that durng the all. By bendng legs and ncreasng an mpact tme, Δt. Havng a certan p, a cat by bendng ts lags tres to ncrease t (mpact tme), so that an mpact orce would be reduced. (ntutve knowledge o Physcs ) Department o Physcs and Appled Physcs Fnal lnear momentum
16 Example Average Force on a baseball The speed o a astball s about 40 m/s, and the speed o the ball comng o o player s bat or a home run s about 54 m/s. The ball (0.145kg) s n contact wth the bat or 1ms. What s the average Force exerted by the player? x F average F avg t p F average p t p p m( v t ( v )) t Pay attenton to drectons!!!!!!!! ( 0.145kg)[54 40] m / s F average s F average 136, 300N n the drecton o v or x Department o Physcs and Appled Physcs
17 Department o Physcs and Appled Physcs Thank you See you on Wednesday
18 ConcepTest Two Boxes/Momentum Two boxes, one heaver than the other, are ntally at rest on a horzontal rctonless surace. The same constant orce F acts on each one or exactly 1 second. Whch box has more lnear momentum ater the orce acts? A) the heaver one B) the lghter one C) both the same We know: p F av F p t av t p p t In ths case F and t are the same or both boxes! Both boxes wll have the same nal momentum. p 0 F lght F heavy
19 ConcepTest Two Boxes/velocty In the prevous queston, whch box has the larger velocty ater the orce acts? A) the heaver one B) the lghter one C) both the same Mv h p mv l Snce M m, then v l v h
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 informationChapter 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 informationPeriod & Frequency. Work and Energy. Methods of Energy Transfer: Energy. WorkKE 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 informationPhysics 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 informationEMU 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 informationConservation 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 informationPHYS 1441 Section 002 Lecture #16
PHYS 1441 Secton 00 Lecture #16 Monday, Mar. 4, 008 Potental Energy Conservatve and Nonconservatve Forces Conservaton o Mechancal Energy Power Today s homework s homework #8, due 9pm, Monday, Mar. 31!!
More informationChapter 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 informationPHYS 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 informationYou 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 informationPHYS 1443 Section 004 Lecture #12 Thursday, Oct. 2, 2014
PHYS 1443 Secton 004 Lecture #1 Thursday, Oct., 014 WorkKnetc Energy Theorem Work under rcton Potental Energy and the Conservatve Force Gravtatonal Potental Energy Elastc Potental Energy Conservaton o
More informationTIME 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 informationChapter 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 informationCHAPTER 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 informationPhysics 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 informationONEDIMENSIONAL COLLISIONS
Purpose Theory ONEDIMENSIONAL COLLISIONS a. To very the law o conservaton o lnear momentum n onedmensonal collsons. b. To study conservaton o energy and lnear momentum n both elastc and nelastc onedmensonal
More informationCHAPTER 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 nonconservatve orces Physcs 1 Knetc energy: Potental energy: Energy assocated
More informationLinear 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 informationPhysics 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 informationStudy Guide For Exam Two
Study Gude For Exam Two Physcs 2210 Albretsen Updated: 08/02/2018 All Other Prevous Study Gudes Modules 0106 Module 07 Work Work done by a constant force F over a dstance s : Work done by varyng force
More information10/24/2013. PHY 113 C General Physics I 11 AM 12:15 PM TR Olin 101. Plan for Lecture 17: Review of Chapters 913, 1516
0/4/03 PHY 3 C General Physcs I AM :5 PM T Oln 0 Plan or Lecture 7: evew o Chapters 93, 56. 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 informationLinear 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 ImulseMomentum Theorem
More informationA 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 informationPhysics 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 informationPage 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 informationPhysics 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. MultPartcle
More informationLecture 17. Conservation of Linear Momentum
Lecture 17 Chapter 11 Physics I Conservation of Linear Momentum Course website: http://faculty.uml.edu/ndriy_danylov/teaching/physicsi Department of Physics and pplied Physics IN THIS CHPTER, you will
More informationChapter 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 informationin 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 informationChapter 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 informationChapter 8. Potential Energy and Conservation of Energy
Chapter 8 Potental Energy and Conservaton of Energy In ths chapter we wll ntroduce the followng concepts: Potental Energy Conservatve and nonconservatve forces Mechancal Energy Conservaton of Mechancal
More informationEMU 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 informationEnergy 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 informationPage 1. Physics 131: Lecture 14. Today s Agenda. Things that stay the same. Impulse and Momentum Nonconstant forces
Physcs 131: Lecture 14 Today s Agenda Imulse and Momentum Nonconstant forces Imulsemomentum momentum thm Conservaton of Lnear momentum Eternal/Internal forces Eamles Physcs 201: Lecture 1, Pg 1 Physcs
More informationChapter 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 informationChapter 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 informationPhysics 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 informationConservation 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 informationPhysics 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 informationPhysics 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 informationWeek 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 informationPhysics 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 informationMomentum. 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 informationRE 11.e Mon. Review for Final (111) HW11: Pr s 39, 57, 64, 74, 78 Sat. 9 a.m. Final Exam (Ch. 111)
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 informationLinear Momentum. Lecture 15. Chapter 9. Physics I Department of Physics and Applied Physics
Lecture 15 Chapter 9 Physics I 10.30.2013 Linear Momentum Course website: http://faculty.uml.edu/ndriy_danylov/teaching/physicsi Lecture Capture: http://echo360.uml.edu/danylov2013/physics1fall.html Outline
More informationRecitation: 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 informationFirst 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 informationPHYS 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 informationp 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 informationv 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(ac), 05(ac) moton s nether
More informationAngular Momentum and Fixed Axis Rotation. 8.01t Nov 10, 2004
Angular Momentum and Fxed Axs Rotaton 8.01t Nov 10, 2004 Dynamcs: Translatonal and Rotatonal Moton Translatonal Dynamcs Total Force Torque Angular Momentum about Dynamcs of Rotaton F ext Momentum of a
More informationChapter 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 informationK = 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 informationAngular 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 informationPHYS 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 informationPHYSICS 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 informationGround 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 informationWeek3, 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 1s tme nterval. The velocty of the partcle
More information10/9/2003 PHY Lecture 11 1
Announcements 1. Physc Colloquum today The Physcs and Analyss of Nonnvasve Optcal Imagng. Today s lecture Bref revew of momentum & collsons Example HW problems Introducton to rotatons Defnton of angular
More informationLinear 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 informationForce = 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 informationRotational 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 informationWork 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 informationWeek 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 information9/19/2013. PHY 113 C General Physics I 11 AM12:15 PM MWF Olin 101
PHY 3 C General Physcs I AM:5 PM MF Oln 0 Plan or Lecture 8: Chapter 8  Conservaton o energy. Potental and knetc energy or conservatve orces. Energy and nonconservatve orces 3. Power PHY 3 C Fall 03
More informationConservation 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 informationChapter 11: Angular Momentum
Chapter 11: ngular Momentum Statc Equlbrum In Chap. 4 we studed the equlbrum of pontobjects (mass m) wth the applcaton of Newton s aws F 0 F x y, 0 Therefore, no lnear (translatonal) acceleraton, a0 For
More informationPhysics 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 information10/23/2003 PHY Lecture 14R 1
Announcements. Remember  Tuesday, Oct. 8 th, 9:30 AM Second exam (coverng Chapters 94 of HRW) Brng the followng: a) equaton sheet b) Calculator c) Pencl d) Clear head e) Note: If you have kept up wth
More informationPHYSICS 203NYA05 MECHANICS
PHYSICS 03NYA05 MECHANICS PROF. S.D. MANOLI PHYSICS & CHEMISTRY CHAMPLAIN  ST. LAWRENCE 790 NÉRÉETREMBLAY QUÉBEC, QC GV 4K TELEPHONE: 48.656.69 EXT. 449 EMAIL: smanol@slc.qc.ca WEBPAGE: http:/web.slc.qc.ca/smanol/
More informationτ rf = Iα I point = mr 2 L35 F 11/14/14 a*er lecture 1
A mass s attached to a long, massless rod. The mass s close to one end of the rod. Is t easer to balance the rod on end wth the mass near the top or near the bottom? Hnt: Small α means sluggsh behavor
More informationPhysics 5153 Classical Mechanics. Principle of Virtual Work1
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 informationa) No books or notes are permitted. b) You may use a calculator.
PHYS 050 Sprng 06 Name: Test 3 Aprl 7, 06 INSTRUCTIONS: a) No books or notes are permtted. b) You may use a calculator. c) You must solve all problems begnnng wth the equatons on the Inormaton Sheet provded
More informationPage 1. SPH4U: Lecture 7. New Topic: Friction. Today s Agenda. Surface Friction... Surface Friction...
SPH4U: Lecture 7 Today s Agenda rcton What s t? Systeatc catagores of forces How do we characterze t? Model of frcton Statc & Knetc frcton (knetc = dynac n soe languages) Soe probles nvolvng frcton ew
More informationPhysics 207: Lecture 27. Announcements
Physcs 07: ecture 7 Announcements akeup labs are ths week Fnal hwk assgned ths week, fnal quz next week Revew sesson on Thursday ay 9, :30 4:00pm, Here Today s Agenda Statcs recap Beam & Strngs» What
More informationPhysic 231 Lecture 14
Physc 3 Lecture 4 Man ponts o last lecture: Ipulses: orces that last only a short te Moentu p IpulseMoentu theore F t p ( ) IpulseMoentu theore ptot, p, p, p, p, ptot, Moentu and external orces F p ext
More informationPhysics 2A Chapters 6  Work & Energy Fall 2017
Physcs A Chapters 6  Work & Energy Fall 017 These notes are eght pages. A quck summary: The workenergy theorem s a combnaton o Chap and Chap 4 equatons. Work s dened as the product o the orce actng on
More informationPhysics 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 informationRETURN ONLY THE SCANTRON SHEET!
Andrzej Czajkowsk PHY/ exam Page out o Prncples o Physcs I PHY PHY Instructor: Dr. Andrzej Czajkowsk Fnal Exam December Closed book exam pages questons o equal value 5 correct answers pass the test! Duraton:
More information= 1.23 m/s 2 [W] Required: t. Solution:!t = = 17 m/s [W]! m/s [W] (two extra digits carried) = 2.1 m/s [W]
Secton 1.3: Acceleraton Tutoral 1 Practce, page 24 1. Gven: 0 m/s; 15.0 m/s [S]; t 12.5 s Requred: Analyss: a av v t v f v t a v av f v t 15.0 m/s [S] 0 m/s 12.5 s 15.0 m/s [S] 12.5 s 1.20 m/s 2 [S] Statement:
More informationPhysics 5153 Classical Mechanics. D Alembert s Principle and The Lagrangian1
P. Guterrez Physcs 5153 Classcal Mechancs D Alembert s Prncple and The Lagrangan 1 Introducton The prncple of vrtual work provdes a method of solvng problems of statc equlbrum wthout havng to consder the
More informationPhysics 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 informationEN40: 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 informationCh04 Work, Energy and Power What is work in physics?
Eunl Won Dept o Physcs, Korea Unversty 1 Ch04 Work, Energy and Power What s work n physcs? Eunl Won Dept o Physcs, Korea Unversty Eunl Won Dept o Physcs, Korea Unversty 3 Work W F d W Fd cosφ W Fd ο cos
More informationTHERMAL DISTRIBUTION IN THE HCL SPECTRUM OBJECTIVE
ame: THERMAL DISTRIBUTIO I THE HCL SPECTRUM OBJECTIVE To nvestgate a system s thermal dstrbuton n dscrete states; specfcally, determne HCl gas temperature from the relatve occupatons of ts rotatonal states.
More informationWeek 9 Chapter 10 Section 15
Week 9 Chapter 10 Secton 15 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 informationMechanics Cycle 3 Chapter 9++ Chapter 9++
Chapter 9++ More on Knetc Energy and Potental Energy BACK TO THE FUTURE I++ More Predctons wth Energy Conservaton Revst: Knetc energy for rotaton Potental energy M total g y CM for a body n constant gravty
More informationChapter 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 informationPhysics 207 Lecture 6
Physcs 207 Lecture 6 Agenda: Physcs 207, Lecture 6, Sept. 25 Chapter 4 Frames of reference Chapter 5 ewton s Law Mass Inerta s (contact and noncontact) Frcton (a external force that opposes moton) Free
More informationPhysics 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 informationChapter 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 informationLecture 16. Conservation of Linear Momentum
Lecture 16 Chapter 11 Conservation of Linear Momentum nother conservation? I like conservations! Course website: http://faculty.uml.edu/ndriy_danylov/teaching/physicsi Department of Physics and pplied
More informationLecture 22: Potential Energy
Lecture : Potental Energy We have already studed the workenergy theorem, whch relates the total work done on an object to the change n knetc energy: Wtot = KE For a conservatve orce, the work done by
More informationAP Physics Enosburg Falls High School Mr. Bushey. Week 6: Work, Energy, Power
AP Physcs Enosburg Falls Hgh School Mr. Bushey ee 6: or, Energy, Power Homewor! Read Gancol Chapter 6.1 6.10 AND/OR Read Saxon Lessons 1, 16, 9, 48! Read Topc Summary Handout! Answer Gancol p.174 Problems
More informationExperiment 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 informationPhysics 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 informationPY2101 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 informationModeling motion with VPython Every program that models the motion of physical objects has two main parts:
1 Modelng moton wth VPython Eery program that models the moton o physcal objects has two man parts: 1. Beore the loop: The rst part o the program tells the computer to: a. Create numercal alues or constants
More informationCHAPTER 10 ROTATIONAL MOTION
CHAPTER 0 ROTATONAL MOTON 0. ANGULAR VELOCTY Consder argd body rotates about a fxed axs through pont O n xy plane as shown. Any partcle at pont P n ths rgd body rotates n a crcle of radus r about O. The
More informationCenter of Mass and Linear Momentum
PH 2212A Fall 2014 Center of Mass and Lnear Momentum Lectures 1415 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