# EMU Physics Department.

Size: px
Start display at page:

Transcription

1 Physcs 0 Lecture 9 Lnear Momentum and Collsons Assst. Pro. Dr. Al ÖVGÜN EMU Physcs Department

2 Lnear Momentum q Conseraton o Energy q Momentum q Impulse q Conseraton o Momentum q -D Collsons q -D Collsons q The Center o Mass and Collsons

3 Conseraton o Energy q D E = D K + D U = 0 conserate orces are the only orces that do work on the system. q The total amount o energy n the system s constant. m + mgy + kx = m + mgy + kx q D E = D K + D U = - k d rcton orces are dong work on the system. q The total amount o energy n the system s stll constant, but the change n mechancal energy goes nto nternal energy or heat. - k d = æ ç è m + mgy + kx ö - ø æ ç è m + mgy + kx ö ø

4 Lnear Momentum q Ths s a new undamental quantty, lke orce, energy. It s a ector quantty (ponts n same drecton as elocty). q The lnear momentum p o an object o mass m mong wth a elocty s dened to be the product o the mass and elocty: p = m q The terms momentum and lnear momentum wll be used nterchangeably n the text q Momentum depend on an object s mass and elocty

5 Lnear Momentum q Lnear momentum s a ector quantty p= m n Its drecton s the same as the drecton o the elocty q The dmensons o momentum are ML/T q The SI unts o momentum are kg m / s q Momentum can be expressed n component orm: p x = m x p y = m y p z = m z

6 Newton s Law and Momentum q Newton s Second Law can be used to relate the momentum o an object to the resultant orce actng on t D D( m) F net = ma = m = Dt Dt q The change n an object s momentum dded by the elapsed tme equals the constant net orce actng on the object p D change n momentum = = Dt tme nteral F net

7 Impulse q When a sngle, constant orce acts on the object, there s an mpulse delered to the object n n I = FDt s dened as the mpulse I n The equalty s true een the orce s not constant n Vector quantty, the drecton s the same as the drecton o the orce p D change n momentum = = F net Dt tme nteral

8 Impulse-Momentum q The theorem states that the mpulse actng on a system s equal to the change n momentum o the system Dp = FnetDt = I I = Dp = m - m Theorem

9 Calculatng the Change o D p= p - p ater Momentum beore = m - ater m beore = m ( - ) ater For the teddy bear [ 0 ( )] beore D p= m -- = m For the bouncng ball [ ] D p= -- ( ) = m

10 Ex: How Good Are the Bumpers? q In a crash test, a car o mass kg colldes wth a wall and rebounds as n gure. The ntal and nal eloctes o the car are =-5 m/s and =.6 m/s, respectely. I the collson lasts or 0.5 s, nd (a) the mpulse delered to the car due to the collson (b) the sze and drecton o the aerage orce exerted on the car

11 How Good Are the Bumpers? q In a crash test, a car o mass kg colldes wth a wall and rebounds as n gure. The ntal and nal eloctes o the car are =-5 m/s and =.6 m/s, respectely. I the collson lasts or 0.5 s, nd (a) the mpulse delered to the car due to the collson (b) the sze and drecton o the aerage orce exerted on the car p p = m = m = ( = (.5 0 kg)( -5m / s) = kg)( +.6m / s) = kg m / s 4 kg m/ s I = Dp Dt p - I = Dt p = ( = = m 4 kg m / s) - (-.5 0 kg m / s - m kg m / s 0.5s.76 kg m / s) 0 5 F a = = = 4 N

12 Ex: Impulse-Momentum q Theorem A chld bounces a 00 g superball on the sdewalk. The elocty o the superball changes rom 0 m/s downward to 0 m/s upward. I the contact tme wth the sdewalk s 0.s, what s the magntude o the mpulse mparted to the superball? (A) 0 (B) kg-m/s (C) 0 kg-m/s (D) 00 kg-m/s (E) 000 kg-m/s I = Dp = m - m

13 Ex3: Impulse-Momentum q Theorem A chld bounces a 00 g superball on the sdewalk. The elocty o the superball changes rom 0 m/s downward to 0 m/s upward. I the contact tme wth the sdewalk s 0.s, what s the magntude o the orce between the sdewalk and the superball? (A) 0 (B) N I Dp m - F = = = (C) 0 N Dt Dt Dt (D) 00 N (E) 000 N m

14 Conseraton o Momentum q In an solated and closed system, the total momentum o the system remans constant n tme. n Isolated system: no external orces n Closed system: no mass enters or leaes n The lnear momentum o each colldng body may change n The total momentum P o the system cannot change.

15 Conseraton o Momentum q Start rom mpulse-momentum theorem Dt = - m F FDt = m - m q Snce q Then q So F t = -F D Dt - m = -( m - m + = m m m m + )

16 Conseraton o Momentum q When no external orces act on a system consstng o two objects that collde wth each other, the total momentum o the system remans constant n tme F Dt = Dp = p - p net q When F net = 0 then q For an solated system p = p Dp = 0 q Speccally, the total momentum beore the collson wll equal the total momentum ater the collson + = m m m m +

17 Ex4: The Archer q An archer stands at rest on rctonless ce and res a 0.5-kg arrow horzontally at 50.0 m/s. The combned mass o the archer and bow s 60.0 kg. Wth what elocty does the archer moe across the ce ater rng the arrow? p = p + m = m + m m = 60.0kg, m = 0.5kg, = = 0, = 50m / s, = 0 = + m m? m 0.5kg = - = - (50.0m / s) = -0.47m / m 60.0kg s

18 Ex5: Conseraton o Momentum q A 00 kg man and 50 kg woman on ce skates stand acng each other. I the woman pushes the man backwards so that hs nal speed s m/s, at what speed does she recol? (A) 0 (B) 0.5 m/s (C) m/s (D).44 m/s (E) m/s

19 Types o Collsons q Momentum s consered n any collson q Inelastc collsons: rubber ball and hard ball n Knetc energy s not consered n Perectly nelastc collsons occur when the objects stck together q Elastc collsons: bllard ball n both momentum and knetc energy are consered

20 Collsons Summary q In an elastc collson, both momentum and knetc energy are consered q In a non-perect nelastc collson, momentum s consered but knetc energy s not. Moreoer, the objects do not stck together q In a perectly nelastc collson, momentum s consered, knetc energy s not, and the two objects stck together ater the collson, so ther nal eloctes are the same q Elastc and perectly nelastc collsons are lmtng cases, most actual collsons all n between these two types q Momentum s consered n all collsons

21 More about Perectly Inelastc Collsons q When two objects stck together ater the collson, they hae undergone a perectly nelastc collson q Conseraton o momentum m ) + m = ( m + m = m m + + m m q Knetc energy s NOT consered

22 Ex6: An SUV Versus a Compact q An SUV wth mass kg s traellng eastbound at +5.0 m/s, whle a compact car wth mass kg s traellng westbound at -5.0 m/s. The cars collde head-on, becomng entangled. (a) Fnd the speed o the entangled cars ater the collson. (b) Fnd the change n the elocty o each car. (c) Fnd the change n the knetc energy o the system consstng o both cars.

23 An SUV Versus a Compact (a) Fnd the speed o the entangled cars ater the collson. p = p m ) + m = ( m + m m m = = kg, kg, = + 5m / s = -5m / s = m m + + m m = +5.00m / s

24 An SUV Versus a Compact (b) Fnd the change n the elocty o each car. D D = +5.00m / = - s - = 0.0m / = + - = 0.0m / s s m m = = kg, kg, = + 5m / s = -5m / s 4 m D = m ( - ) = kg m/ s 4 m D = m ( - ) = kg m s / m D + md = 0

25 An SUV Versus a Compact (c) Fnd the change n the knetc energy o the system consstng o both cars. = +5.00m / s m m = = kg, kg, = + 5m / s = -5m / s KE KE 5 = m + m = J 4 = m + m = J DKE = KE - KE = J

26 More About Elastc Collsons q Both momentum and knetc energy are consered q Typcally hae two unknowns q Momentum s a ector quantty n n + + = = Drecton s mportant Be sure to hae the correct sgns q Sole the equatons smultaneously + +

27 Elastc Collsons q A smpler equaton can be used n place o the KE equaton + = + ) ( - = - - m m + = + ) )( ( ) )( ( m m + - = + - ) ( ) ( m m - = - ) ( ) ( m m - = - m m + = + m m + = +

28 Summary o Types o Collsons q In an elastc collson, both momentum and knetc energy are consered + = + + m = m + m q In an nelastc collson, momentum s consered but knetc energy s not + = m + q In a perectly nelastc collson, momentum s consered, knetc energy s not, and the two objects stck together ater the collson, so ther nal eloctes are the same m ) + m = ( m + m

29 Ex7: Conseraton o q Momentum An object o mass m moes to the rght wth a speed. It colldes head-on wth an object o mass 3m mong wth speed /3 n the opposte drecton. I the two objects stck together, what s the speed o the combned object, o mass 4m, ater the collson? (A) 0 (B) / (C) (D) (E) 4

30 Problem Solng or D Collsons, q Coordnates: Set up a coordnate axs and dene the eloctes wth respect to ths axs n It s conenent to make your axs concde wth one o the ntal eloctes q Dagram: In your sketch, draw all the elocty ectors and label the eloctes and the masses

31 Problem Solng or D Collsons, q Conseraton o Momentum: Wrte a general expresson or the total momentum o the system beore and ater the collson n Equate the two total momentum expressons n Fll n the known alues + m = m + m

32 Problem Solng or D Collsons, 3 q Conseraton o Energy: I the collson s elastc, wrte a second equaton or conseraton o KE, or the alternate equaton n Ths only apples to perectly elastc collsons + = + q Sole: the resultng equatons smultaneously

33 One-Dmenson s Two- Dmenson

34 Two-Dmensonal Collsons q For a general collson o two objects n twodmensonal space, the conseraton o momentum prncple mples that the total momentum o the system n each drecton s consered x + x = x + x y + y = y + y

35 Two-Dmensonal Collsons q The momentum s consered n all drectons q Use subscrpts or n Identyng the object m n Indcatng ntal or nal alues n The elocty components q I the collson s elastc, use conseraton o knetc energy as a second equaton n Remember, the smpler equaton can only be used or one-dmensonal stuatons x y + + x y = = x y = + x y

36 Glancng Collsons q The ater eloctes hae x and y components q Momentum s consered n the x drecton and n the y drecton q Apply conseraton o momentum separately to each drecton x y + + x y = = x y + + x y

37 -D Collson, example q Partcle s mong at elocty and partcle s at rest q In the x-drecton, the ntal momentum s m q In the y-drecton, the ntal momentum s 0

38 -D Collson, example cont q Ater the collson, the momentum n the x-drecton s m cos q + m cos q Ater the collson, the momentum n the y-drecton s m sn q + m sn = + 0 = cosq + sn q - sn cos q I the collson s elastc, apply the knetc energy equaton m = m + m

39 Ex8: Collson at an Intersecton q A car wth mass kg traelng east at a speed o 5 m/s colldes at an ntersecton wth a kg an traelng north at a speed o 0 m/s. Fnd the magntude and drecton o the elocty o the wreckage ater the collson, assumng that the ehcles undergo a perectly nelastc collson and assumng that rcton between the ehcles and the road can be neglected. m c cx = = 5m / s, kg, m y =.5 0 = 0m / s, 3 kg =? q =?

40 m c cx Collson at an Intersecton = = 5 m/s, kg, m y =.5 0 = 0 m/s, 3 kg =? q =? 4 å px = mccx + mx = mccx = kg m/s å px = mccx + mx = ( mc + m ) cosq kg m/s = ( kg) cosq 4 å py = mccy + my = my = kg m/s å py = mccy + my = ( mc + m ) snq kg m/s = ( kg) snq

41 m c cx Collson at an Intersecton = = 5m / s, 4 4 kg, m y =.5 0 = 0m / s, kg m/s = ( kg m/s = ( kg) kg) 3 kg =? q =? snq cosq kg m/ s tanq = kg m/ s =.33 - q = tan (.33) = kg m/s 3 ( kg)sn53. = = 5.6 m/s

42 P: P:

43 P3: P4:

44 P5: P6:

45 P7: P8:

46 P9: P0:

47

48

49

50

51

52

53

54

55

56

57

58

59

60

### 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

### 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

### 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 =

### 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

### Physics for Scientists and Engineers. Chapter 9 Impulse and Momentum

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

### 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

### 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

### 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

### 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)

### 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

### 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

### 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

### 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 = +

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

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

Lesson 0: Collsons, Rotatonal netc Energy, Torque, Center o Graty (Sectons 7.8 Last te we used ewton s second law to deelop the pulse-oentu theore. In words, the theore states that the change n lnear oentu

### Chapter 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

### 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

### 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

### Physics 111: Mechanics Lecture 8

Physics 111: Mechanics Lecture 8 Bin Chen NJIT Physics Department Chapter 8 Momentum, Impulse, and Collisions q q q q q q 8.1 Momentum and Impulse 8.2 Conservation of Momentum 8.3 Momentum Conservation

### 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

### 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

### 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

### 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

### 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

### 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*,,

### AP 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

### 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

### 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

### 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

### Dynamics 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 =

### a) 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

### 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

### 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

### 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

### 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

### 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

### 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

### GAUTENG 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

### 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

### 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

### 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

### Modeling 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

### 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

### Prof. 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

### 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!!

### 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

### 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

### 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.

### 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,

### 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

### 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

### 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

### Macroscopic Momentum Balances

Lecture 13 F. Morrson CM3110 2013 10/22/2013 CM3110 Transport I Part I: Flud Mechancs Macroscopc Momentum Balances Professor Fath Morrson Department of Chemcal Engneerng Mchgan Technologcal Unersty 1 Macroscopc

### 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

### Name: 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

### 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

### 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

### 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

### Physics for Scientists and Engineers. Chapter 10 Energy

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

### 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

### Use these variables to select a formula. x = t Average speed = 100 m/s = distance / time t = x/v = ~2 m / 100 m/s = 0.02 s or 20 milliseconds

The speed o a nere mpulse n the human body s about 100 m/s. I you accdentally stub your toe n the dark, estmatethe tme t takes the nere mpulse to trael to your bran. Tps: pcture, poste drecton, and lst

### 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

### 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

### 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

### Motion 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.

### Chapter 11 Torque and Angular Momentum

Chapter Torque and Angular Momentum I. Torque II. Angular momentum - Defnton III. Newton s second law n angular form IV. Angular momentum - System of partcles - Rgd body - Conservaton I. Torque - Vector

### 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 =

### 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/

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

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

SPH4U Agenda Fro Newton Two New Concepts Ipulse & oentu Ipulse Collisions: you gotta consere oentu! elastic or inelastic (energy consering or not) Inelastic collisions in one diension and in two diensions

### 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

### FOCUS ON CONCEPTS Section 7.1 The Impulse Momentum Theorem

WEEK-6 Recitation PHYS 3 FOCUS ON CONCEPTS Section 7. The Impulse Momentum Theorem Mar, 08. Two identical cars are traeling at the same speed. One is heading due east and the other due north, as the drawing

### Physics 240: Worksheet 30 Name:

(1) One mole of an deal monatomc gas doubles ts temperature and doubles ts volume. What s the change n entropy of the gas? () 1 kg of ce at 0 0 C melts to become water at 0 0 C. What s the change n entropy

### 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

### 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

### 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

### Linearity. If kx is applied to the element, the output must be ky. kx ky. 2. additivity property. x 1 y 1, x 2 y 2

Lnearty An element s sad to be lnear f t satsfes homogenety (scalng) property and addte (superposton) property. 1. homogenety property Let x be the nput and y be the output of an element. x y If kx s appled

### 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

### PHYS 1443 Section 002 Lecture #20

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

### CJ57.P.003 REASONING AND SOLUTION According to the impulse-momentum theorem (see Equation 7.4), F t = mv

Solution to HW#7 CJ57.CQ.003. RASONNG AND SOLUTON a. Yes. Momentum is a ector, and the two objects hae the same momentum. This means that the direction o each object s momentum is the same. Momentum is