Physics 207, Lecture 13, Oct. 15. Energy
|
|
- Anissa Lindsey
- 5 years ago
- Views:
Transcription
1 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 n problem solng Chapter Understand the relatonshp between orce, dsplacement and work Assgnment: HW6 due Wednesday, Oct. For Monday: Read all o Chapter Physcs 07: Lecture 3, Pg Energy I only conserate orces are present, the total energy (sum o potental, U, and knetc energes, K) ) o a system s consered For an object n a gratatonal eld ½ m y + mgy = ½ m y + mgy K ½ m U mgy E mech = K + U E mech = K + U = constant K and U may change, but E mech = K + U remans a xed alue. E mech s called mechancal energy Physcs 07: Lecture 3, Pg Page
2 Physcs 07 Lecture 3 Example o a conserate system: The smple pendulum. Suppose we release a mass m rom rest a dstance h aboe ts lowest possble pont. What s the maxmum speed o the mass and where does ths happen? To what heght h does t rse on the other sde? m h h Physcs 07: Lecture 3, Pg 3 Example: The smple pendulum. What s the maxmum speed o the mass and where does ths happen? E = K + U = constant and so K s maxmum when U s a mnmum. y y=h y=0 Physcs 07: Lecture 3, Pg 4 Page
3 Physcs 07 Lecture 3 Example: The smple pendulum. What s the maxmum speed o the mass and where does ths happen? E = K + U = constant and so K s maxmum when U s a mnmum E = mgh at top E = mgh = ½ m at bottom o the swng y y=h y=0 h Physcs 07: Lecture 3, Pg 5 Example: The smple pendulum. To what heght h does t rse on the other sde? E = K + U = constant and so when U s maxmum agan (when K = 0) t wll be at ts hghest pont. E = mgh = mgh or h = h y y=h =h y=0 Physcs 07: Lecture 3, Pg 6 Page 3
4 Physcs 07 Lecture 3 Example The Loop-the-Loop agan To complete the loop the loop, how hgh do we hae to let the release the car? Condton or completng the loop the loop: Crcular moton at the top o the loop (a c = / R) Use act that E = U + K = constant! y=0 U b =mgh U=mgR h? Car has mass m R Recall that g s the source o the centrpetal acceleraton and N just goes to zero s the lmtng case. Also recall the mnmum speed at the top s = Physcs 07: Lecture 3, Pg 7 gr Example The Loop-the-Loop agan Use E = K + U = constant mgh + 0 = mg R + ½ m mgh = mg R + ½ mgr = 5/ mgr = gr h = 5/ R h? R Physcs 07: Lecture 3, Pg 8 Page 4
5 Physcs 07 Lecture 3 What speed wll the skateboarder reach halway down the hll there s no rcton and the skateboarder starts at rest? Assume we can treat the skateboarder as a pont Assume zero o gratatonal U s at bottom o the hll R=0 m m = 5 kg R=0 m Example Skateboard y=0 Physcs 07: Lecture 3, Pg 9 What speed wll the skateboarder reach halway down the hll there s no rcton and the skateboarder starts at rest? Assume we can treat the skateboarder as pont Assume zero o gratatonal U s at bottom o the hll R=0 m m = 5 kg R=0 m Example Skateboard Use E = K + U = constant E beore = E ater 0 + m g R = ½ m + mgr (-sn 30 ) mgr/ = ½ m gr = = (gr) ½ = (0 x 0) ½ = 0 m/s Physcs 07: Lecture 3, Pg 0 Page 5
6 Physcs 07 Lecture 3 Potental Energy, Energy Transer and Path A ball o mass m, ntally at rest, s released and ollows three derence paths. All suraces are rctonless. Ball s dropped. Ball sldes down a straght nclne 3. Ball sldes down a cured nclne Ater traelng a ertcal dstance h, how do the three speeds compare? 3 h (A) > > 3 (B) 3 > > (C) 3 = = (D) Can t tell Physcs 07: Lecture 3, Pg Potental Energy, Energy Transer and Path A ball o mass m, ntally at rest, s released and ollows three derence paths. All suraces are rctonless. The ball s dropped. The ball sldes down a straght nclne 3. The ball sldes down a cured nclne Ater traelng a ertcal dstance h, how do the three speeds compare? 3 h (A) > > 3 (B) 3 > > (C) 3 = = (D) Can t tell Physcs 07: Lecture 3, Pg Page 6
7 Physcs 07 Lecture 3 Example Skateboard Now what s the normal orce on the skate boarder? N.. R=0 m m = 5 kg R=0 m 60 mg Σ F r = ma r = m / R = N mg cos 60 N = m /R + mg cos 60 N = 5 00 / (0.87) N = =470 Newtons Physcs 07: Lecture 3, Pg 3 Elastc s. Inelastc Collsons A collson s sad to be elastc when energy as well as momentum s consered beore and ater the collson. K beore = K ater Carts colldng wth a perect sprng, bllard balls, etc. Physcs 07: Lecture 3, Pg 4 Page 7
8 Physcs 07 Lecture 3 Elastc s. Inelastc Collsons A collson s sad to be nelastc when energy s not consered beore and ater the collson, but momentum s consered. K beore K ater Car crashes, collsons where objects stck together, etc. Physcs 07: Lecture 3, Pg 5 Inelastc collson n -D: Example A block o mass M s ntally at rest on a rctonless horzontal surace. A bullet o mass m s red at the block wth a muzzle elocty (speed). The bullet lodges n the block, and the block ends up wth a speed V. What s the ntal energy o the system? What s the nal energy o the system? Is energy consered? V x beore ater Physcs 07: Lecture 3, Pg 6 Page 8
9 Physcs 07 Lecture 3 Inelastc collson n -D: Example What s the momentum o the bullet wth speed? What s the ntal energy o the system? m r m r r = m What s the nal energy o the system? ( m + M )V Is momentum consered (yes)? m + M 0 = ( m + M )V Is energy consered? Examne E beore -E ater m [( m + M )V]V = m m ( m) m + M m = m ( m + M ) No! V beore ater x Physcs 07: Lecture 3, Pg 7 Example Fully Elastc Collson Suppose I hae dentcal bumper cars. One s motonless and the other s approachng t wth elocty. I they collde elastcally, what s the nal elocty o each car? Identcal means m = m = m Intally Green = and Red = 0 COM m + 0 = m + m = + COE ½ m = ½ m + ½ m = + = ( + ) = + + = 0 Soln : = 0 and = Soln : = 0 and = Physcs 07: Lecture 3, Pg 8 Page 9
10 Physcs 07 Lecture 3 Varable orce deces: Hooke s Law Sprngs Sprngs are eerywhere, (probe mcroscopes, DNA, an eecte nteracton between atoms) F Rest or equlbrum poston In ths sprng, the magntude o the orce ncreases as the sprng s urther compressed (a dsplacement). Hooke s Law, F s = - k s s s s the amount the sprng s stretched or compressed rom t restng poston. Physcs 07: Lecture 3, Pg 9 Hooke s Law Sprng For a sprng we know that F x = -k s. F(x) s s s relaxed poston -k s F = - k s F = - k s Physcs 07: Lecture 3, Pg 0 Page 0
11 Physcs 07 Lecture 3 Home Exercse Hooke s Law 8 m 9 m What s the sprng constant k? 50 kg F sprng ΣF = 0 = F s mg = k s - mg Use k = mg/ s = 5 N / 0.0 m (A) 50 N/m (B) 00 N/m (C) 400 N/m (D) 500 N/m mg Physcs 07: Lecture 3, Pg F-s relaton or a sngle DNA molecule Physcs 07: Lecture 3, Pg Page
12 Physcs 07 Lecture 3 Measurement technque: optcal tweezers Physcs 07: Lecture 3, Pg 3 Force s. Energy or a Hooke s Law sprng F = - k (x x equlbrum ) F = ma = m d/dt = m (d/dx dx/dt) = m d/dx = m d/dx So - k (x x equlbrum ) dx = m d Let u = x x eq. & du = dx x m ku du= m d x kx + kx = x ku x = m m m kx + m = kx + m Physcs 07: Lecture 3, Pg 4 Page
13 Physcs 07 Lecture 3 Energy or a Hooke s Law sprng kx + m = kx + m Assocate ½ kx wth the potental energy o the sprng m U s + K = U + s K Hooke s Law sprngs are conserate so the mechancal energy s constant Physcs 07: Lecture 3, Pg 5 In general: Energy dagrams Energy Ball allng E mech K U Energy Sprng/Mass system E mech K U y s Physcs 07: Lecture 3, Pg 6 Page 3
14 Physcs 07 Lecture 3 Energy dagrams Sprng/Mass/Graty system Force sprng alone y -mg sprng & graty m Energy E mech K K U g U sprng U Total y Physcs 07: Lecture 3, Pg 7 Equlbrum Example Sprng: F x = 0 => du / dx = 0 or x=0 The sprng s n equlbrum poston In general: du / dx = 0 equlbrum or ANY uncton establshes U U stable equlbrum unstable equlbrum Physcs 07: Lecture 3, Pg 8 Page 4
15 Physcs 07 Lecture 3 Comment on Energy Conseraton We hae seen that the total knetc energy o a system undergong an nelastc collson s not consered. Mechancal energy s lost: Heat (rcton) Bendng o metal and deormaton Knetc energy s not consered by these non-conserate orces occurrng durng the collson! Momentum along a specc drecton s consered when there are no external orces actng n ths drecton. In general, easer to satsy conseraton o momentum than energy conseraton. Physcs 07: Lecture 3, Pg 9 Physcs 07, Lecture 3, Oct. 5 Assgnment: HW6 due Wednesday For Monday: Read all o chapter Physcs 07: Lecture 3, Pg 30 Page 5
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 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 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 informationHow 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 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 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 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 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 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 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 Non-conservatve Forces Conservaton o Mechancal Energy Power Today s homework s homework #8, due 9pm, Monday, Mar. 31!!
More informationPHYS 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 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 informationLecture 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 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 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 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 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 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 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 non-conservatve orces Physcs 1 Knetc energy: Potental energy: Energy assocated
More informationMomentum 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 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 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 informationPhysic 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 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 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 informationSpring 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 informationLinear 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 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 informationPeriod & 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 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 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 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 informationPhysics 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 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 informationStudy 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 informationCollisions! 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 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 Imulse-Momentum Theorem
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 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 informationLecture 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 informationName: PHYS 110 Dr. McGovern Spring 2018 Exam 1. Multiple Choice: Circle the answer that best evaluates the statement or completes the statement.
Name: PHYS 110 Dr. McGoern Sprng 018 Exam 1 Multple Choce: Crcle the answer that best ealuates the statement or completes the statement. #1 - I the acceleraton o an object s negate, the object must be
More informationProblem 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 informationtotal 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 informationChapter 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 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 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 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 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 informationONE-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 informationPHYSICS 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 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 work-energy theorem s a combnaton o Chap and Chap 4 equatons. Work s dened as the product o the orce actng on
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 information9/19/2013. PHY 113 C General Physics I 11 AM-12:15 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 non-conservatve orces 3. Power PHY 3 C Fall 03--
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 informationLecture 22: Potential Energy
Lecture : Potental Energy We have already studed the work-energy 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 information2.00 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 informationProf. Dr. I. Nasser T /16/2017
Pro. Dr. I. Nasser T-171 10/16/017 Chapter Part 1 Moton n one dmenson Sectons -,, 3, 4, 5 - Moton n 1 dmenson We le n a 3-dmensonal world, so why bother analyzng 1-dmensonal stuatons? Bascally, because
More informationSlide. 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 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 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 information10/2/2003 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 information5/24/2007 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 informationGAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME PHYSICAL SCIENCES GRADE 12 SESSION 1 (LEARNER NOTES)
PHYSICAL SCIENCES GRADE 1 SESSION 1 (LEARNER NOTES) TOPIC 1: MECHANICS PROJECTILE MOTION Learner Note: Always draw a dagram of the stuaton and enter all the numercal alues onto your dagram. Remember to
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 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 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 informationPHYSICS 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 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 informationPage 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 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 informationChapter 8. Momentum, Impulse and Collisions (continued) 10/22/2014 Physics 218
Chater 8 Moentu, Iulse and Collsons (contnued 0//04 Physcs 8 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
More informationConservation of Energy
Chapter 8 Conseraton o Ener 8.3 U + K = U + K mh + = m ( ) + m ( 3.5 ) = ( ) + F= m = 3. n+ m= m 3. n = m = m =.m 3 n =. 5. 9.8 m s =.98 N downward FIG. 8.3 (5. 3.) Δ A B 8.4 (a) K = W = W = m Δ h = m
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(a-c), 05(a-c) moton s nether
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 non-conservatve forces Mechancal Energy Conservaton of Mechancal
More informationRE 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 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 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 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. Mult-Partcle
More informationChapter 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 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 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 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 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 informationWYSE Academic Challenge 2004 State Finals Physics Solution Set
WYSE Acaemc Challenge 00 State nals Physcs Soluton Set. Answer: c. Ths s the enton o the quantty acceleraton.. Answer: b. Pressure s orce per area. J/m N m/m N/m, unts o orce per area.. Answer: e. Aerage
More informationDynamics of Rotational Motion
Dynamcs of Rotatonal Moton Torque: the rotatonal analogue of force Torque = force x moment arm = Fl moment arm = perpendcular dstance through whch the force acts a.k.a. leer arm l F l F l F l F = Fl =
More informationPhysics 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 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 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 1-s tme nterval. The velocty of the partcle
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 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 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 non-contact) Frcton (a external force that opposes moton) Free
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 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 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 information10/9/2003 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 information1. The number of significant figures in the number is a. 4 b. 5 c. 6 d. 7
Name: ID: Anwer Key There a heet o ueul ormulae and ome converon actor at the end. Crcle your anwer clearly. All problem are pont ecept a ew marked wth ther own core. Mamum core 100. There are a total
More informationPhysics 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 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 informationMotion in One Dimension
Moton n One Dmenson Speed ds tan ce traeled Aerage Speed tme of trael Mr. Wolf dres hs car on a long trp to a physcs store. Gen the dstance and tme data for hs trp, plot a graph of hs dstance ersus tme.
More information86 Chapter 7 Energy 7-11 POWER. Answers to the Conceptual Questions
86 Chater 7 Energy nented to make eerythng alrght. We eel t s mortant to show that the nenton o other orms o energy s not whmscal or a arce. A newly nented orm o energy would be alse the new orm was not
More information