Chapter 9 Linear Momentum and Collisions

Size: px
Start display at page:

Download "Chapter 9 Linear Momentum and Collisions"

Transcription

1 Chapter 9 Lnear Momentum and Collsons m = 3. kg r = ( ˆ ˆ j ) P9., r r (a) p m ( ˆ ˆj ) 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 = + = = 5. kg m s *P9.4 (a) For the system o two blocks Δ p =, or p = p Thereore, = M + ( 3M )(. m s) m Solng ges m = 6. m s (moton toward the let). kx = MM + 3 M 3M = 8.4 J (b) FIG. P9.4 (c) The orgnal energy s n the sprng. A orce had to be exerted oer a dstance to compress the sprng, transerrng energy nto t by work. The cord exerts orce, but oer no dstance. (d) System momentum s consered wth the alue zero. The orces on the two blocks are o equal magntude n opposte drectons. Ther mpulses add to zero. The nal momenta o the two blocks are o equal magntude n opposte drectons. *P9.6 From the mpulse-momentum theorem, requred to hold onto the chld s ( ) F Δ t =Δ p= m m, the aerage orce m kg 6 m h m s 3 F = = = 6.44 N ( Δt ).5 s.37 m h In tryng to hang onto the chld, he would hae to exert a orce o 6.44 kn (oer 4 lb) toward the back o the car, to slow down the chld s orward moton. He s not strong enough to exert so large a orce. I he were belted n and hs arms were rmly ted around the chld, the chld would exert ths sze orce on hm toward the ront o

2 the car. A person cannot saely exert or eel a orce o ths magntude and a saety dece should be used. P9.7 (a) I = Fdt = area under cure 3 I = (.5 s )( 8 N ) = 3.5 N s 3.5 N s (b) F = = 9. kn.5 3 s FIG. P9.7 P9.9 (c) From the graph, we see that F max = 8. kn r r Δ p = FΔt Δ p = m = m cos 6. m cos 6. = Δ p = m sn 6. sn 6. = msn 6. F ag y y y x = 3. kg. m s.866 = 5. kg m s Δpx 5. kg m s = = = 6 N Δt. s FIG. P9.9 P9. Assume the ntal drecton o the ball n the x drecton. r r r r I =Δ p = p p =.6 4. ˆ.6 5. ˆ = 5.4 î N s (a) Impulse, = = = 7. J (b) Work K K P9. A graph o the expresson or orce shows a parabola openng down, wth the alue zero at the begnnng and end o the.8 s nteral..8s.8s ( 9 N/ s 5 N/ s ) 3 t t I = Fdt = t t dt = 9 N/ s / 5 N/ s / 3 3 = 9 N/ s (.8 s) / 5 N/ s (.8 s) / 3 = 944 N s 963 N s = 98 N s The athlete mparts downward mpulse to the platorm, so the platorm mparts 98 N s o upward mpulse to her. (b) We could nd her mpact speed as a ree-all calculaton, but we choose to wrte t as a conseraton-o energy calculaton: mgy top = (/)m mpact mpact = ( g y top ) / = [(9.8 m/s ).6 m] / = 3.43 m/s down (c) Graty, as well as the platorm, mparts mpulse to her durng the nteracton wth the platorm. m + I platorm + mgt = m (65 kg)( 3.43 m/s) + 98 N s (65 kg)(9.8 m/s )(.8 s) = 65 kg.8s

3 up 3 N s + 98 N s 5 N s = 65 kg = 49 N s/65 kg = 3.83 m/s Note that the athlete s puttng a lot o eort nto jumpng and does not exert any orce "on hersel." The useulness o the orce platorm s to measure her eort by showng the orce she exerts on the loor. (d) Agan energy s consered n upward lght. (/)m takeo = mgytop y top = takeo / g = (3.83 m/s) /(9.8 m/s ) =.748 m P9.8 Energy s consered or the bob-earth system between bottom and top o swng. At the top the st rod s n compresson and the bob nearly at rest. K + U = K + U : Mb + = + Mg l = g 4l so = g l b Momentum o the bob-bullet system s consered n the collson: b FIG. P9.8 ( ) 4M m = m + M g l = gl m P9.9 Frst we nd, the speed o m at B beore collson. m = mgh = = 9.9 m s Now we use the text's analyss o one-dmensonal elastc collsons to nd, the speed o m at B just ater collson. m m = = ( 9.9 ) m s = 3.3 m s m + m 3 Now the 5-kg block bounces back up to ts hghest pont ater collson accordng to mgh = m ( 3.3) max h ( 3.3 m s) ( 9.8 m s ) = = max.556 m FIG. P9.9 *P9. (a) We assume that energy s consered n the all o the basketball and the tenns ball. Each reaches ts lowest pont wth a speed gen by ( K+ Ug) = ( K+ Ug) release + mgy = mb + b bottom = gy = 9.8 m s. m = 4.85 m s

4 (b) The two balls exert no orces on each other as they moe down. They collde wth each other ater the basketball has ts elocty reersed by the loor. We choose upward as poste. Momentum conseraton: 4.85 m/s 4.85 m/s ( 57 g )( 4.85 m s) + ( 59 g )( 4.85 m s) = ( 57 g ) + ( 59 g ) FIG. P9. To descrbe the elastc character o the collson, we use the relate elocty equaton 4.85 m s 4.85 m s = we sole by substtuton = 9.7 m s s ( ) 58 gm s = 57 g + 59 g 9.7 m s = ( 57 g ) + ( 59 g ) 5 7 gm s 83 m s = =.8 m s 647 Now the tenns ball-earth system keeps constant energy as the ball rses: g p 57 g.8 m s 57 g 9.8 m s 65 m s y = = 8.4 m 9.8 m s = P9. (a), (b) Let and be the x-components o elocty o the grl and the plank relate to the ce surace. Then we may say that g p s the elocty o the grl relate to the plank, so that g p =.5 () But also we must hae m g g + m p p =, snce total momentum o the grl-plank system s zero relate to the ce surace. Thereore 45. g +5 p =, or g = 3.33 p y Puttng ths nto the equaton () aboe ges FIG. P p p =.5 or p =.346 î m s (answer b) = =.5 ˆ m s (answer a) Then g

5 r r P9.4 (a) Usng conseraton o momentum, ( ) = ( ) p p, ges + + ( ) = ( + + ) 4. kg 5. m s kg 3. m s 3. kg 4. m s kg beore ater Thereore, =+.4 m s, or.4 m s toward the rght (b) No. For example, the -kg and 3.-kg mass were to stck together rst, they would moe wth a speed gen by solng ( 3 kg ) = ( kg )( 3. m s) + ( 3. kg )( 4. m s), or =+.38 m s Then when ths 3 kg combned mass colldes wth the 4. kg mass, we hae ( 7 kg ) = ( 3 kg )(.38 m s) + ( 4. kg )( 5. m s), and =+.4 m s just as n part (a). Couplng order makes no derence to the nal elocty. *P9.6 (a) Oer a ery short tme nteral, outsde orces hae no tme to mpart sgncant mpulse thus the nteracton s a collson. The opponent grabs the ullback and does not let go, so the two players moe together at the end o ther nteracton thus the collson s completely nelastc. (b) Frst, we consere momentum or the system o two ootball players n the x drecton (the drecton o trael o the ullback). ( 9. kg )( 5. m s) + = ( 85 kg ) V cosθ where θ s the angle between the drecton o the nal elocty V and the x axs. We nd V cosθ =.43 m s () Now consder conseraton o momentum o the system n the y drecton (the drecton o trael o the opponent). 95. kg 3. m s + = 85 kg V sn θ whch ges V snθ =.54 m s () Dde equaton () by () tanθ = =.633 From whch θ = 3.3 Then, ether () or () ges V =.88 m s 3 K = 9. kg 5. m s kg 3. m s =.55 J (c) K = ( 85 kg )(.88 m s ) = 7.67 J

6 Thus, the knetc energy lost s 786 J nto nternal energy. r r r P9.3 m + m = m + m : = ˆ ˆ r j 5. r = 3. ˆ. ˆ j m s P9.3 x-component o momentum or the system o the two objects: p x + p x = p x + p x : m + 3m = + 3m x y-component o momentum o the system: + = m y + 3m y by conseraton o energy o the system: + m + 3m = my + 3m x + y we hae also So the energy equaton becomes x = 3 y = 3 y 4 = 9 y 8 3 = y y or y = 3 (a) The object o mass m has nal speed y = 3 y = and the object o mass 3 m moes at x + y = x + y = 3 (b) θ = y tan x θ = 3 tan = P9.39 Ths object can be made by wrappng tape around a lght st unorm rod..3 m (a) M = λdx = 5. g m +.x g m dx.3 m M = 5.x g m+.x g m.3 m = 5.9 g xdm all mass (b) x CM = = M M.3 m λ xdx = M.3 m x CM = 5.9 g 5.x g m+ x 3 g m 3 5.x g m+.x g m dx.3 m =.53 m

7 P9.4 Take the orgn at the center o curature. We hae L = L πr, r = 4 π. An ncremental bt o the rod at angle θ rom the x axs has mass gen by dm rdθ = M Mr, dm = dθ where we hae used the denton o L L radan measure. Now y θ x y CM = M all mass = L π ydm= M 35 θ=45 ( L cosθ) Mr rsnθ L dθ = r L snθ dθ = 4L π + = 4 L π FIG. P9.4 The top o the bar s aboe the orgn by r = L, so the center o mass s below the π mddle o the bar by L π 4 L = π π π L =.63 5L. dm P9.5 (a) Thrust = e dt Thrust 3 4 =.6 m s.5 kg s = N = Thrust Mg= Ma 7 ( 6 6 ) = ( ) (b) F y : a a= 3. m s P9.5 (a) From the equaton or rocket propulson n the text, M M = eln = eln M M M kt k Now, M = M kt, so = eln = eln t M M M Wth the denton, ths becomes k () t = t e ln t = 5 m s ln 44 s (b) Wth e = 5 m s, and T p = 44 s,

8 ( m s) t s (m/s) t d d e ln T (c) p e at () = = = = e, or t t dt dt T T p p at ()= e T t p FIG. P9.5(b) t (s) (d) Wth e = 5 m s, and T p = 44 s, a= 5 m s 44 s t ( m s ) t s a a (m/s ) FIG. P9.5(d) 4 t (s) (e) () = + t = t = t t t dt x t dt eln dt e ln () x t t t t = e ln t x() t = e( t) ln + et t () Wth e = 5 m s=.5 km s, and T p = 44 s, t x =.5( 44 t) ln +.5t 44

9 x( km) t s x (km) FIG. P9.5() 4 t (s) P9.6 (a) Each prmate swngs down accordng to mgr = m MgR = M = gr The collson: m M m M M m = M + m + = + + cos35 M + m = M + m gr ) Swngng up: ( = gr( cos35 ) gr( cos35 )( M + m) = ( M m) gr.45m +.45m= M m.45m=.575m m M =.43 (b) No change s requred the orce s derent. The nature o the orces wthn the system o colldng objects does not aect the total momentum o the system. Wth strong magnetc attracton, the heaer object wll be mong somewhat aster and the lghter object aster stll. Ther extra knetc energy wll all be mmedately conerted nto extra nternal energy when the objects latch together. Momentum conseraton guarantees that none o the extra knetc energy remans ater the objects jon to make them swng hgher.

10 P9.67 (a) Fnd the speed when the bullet emerges rom the block by usng momentum conseraton: 4 m/s m = M V + m The block moes a dstance o 5. cm. Assume or an approxmaton that the block quckly reaches ts maxmum elocty, V, and the bullet kept gong wth a constant elocty,. The block then compresses the sprng and stops. 5. cm MV = kx ( 9 N m )( 5. m ) V = =.5 m s. kg m M V m = = = m s FIG. P ( 5. kg)( 4 m s) (. kg)(.5 m s) 3 5. kg 3 3 (b) Δ E= Δ K+Δ U = ( 5. kg)( m s) ( 5. kg)( 4 m s) + 9 N m 5. m Δ E = 374 J, or there s a mechancal energy loss o 374 J. P9.69 The orce exerted by the table s equal to the change n momentum o each o the lnks n the chan. By the calculus chan rule o derates, F dm = = = +m dp dm d dt dt dt dt We choose to account or the change n momentum o each lnk by hang t pass rom our area o nterest just beore t hts the table, so that FIG. P9.69 dm d and m = dt dt Snce the mass per unt length s unorm, we can express each lnk o length dx as hang a mass dm: M dm = dx L

11 The magntude o the orce on the allng chan s the orce that wll be necessary to stop each o the elements dm. dm M dx M F = = = dt L dt L Ater allng a dstance x, the square o the elocty o each lnk knematcs), hence = gx (rom Mgx F = L The lnks already on the table hae a total length x, and ther weght s supported by a orce : F Mgx F = L Hence, the total orce on the chan s F = F + F = total 3Mgx L That s, the total orce s three tmes the weght o the chan on the table at that nstant.

Physics 101 Lecture 9 Linear Momentum and Collisions

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

More information

Momentum. Momentum. Impulse. Momentum and Collisions

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

More information

EMU Physics Department.

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

More information

Physics for Scientists and Engineers. Chapter 9 Impulse and Momentum

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

More information

Physics 105: Mechanics Lecture 13

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

More information

Chapter 3 and Chapter 4

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

More information

Physics 207, Lecture 13, Oct. 15. Energy

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

More information

Physics 2A Chapter 9 HW Solutions

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

More information

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

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

More information

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

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

More information

Linear Momentum. Equation 1

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

More information

Chapter 8: Potential Energy and The Conservation of Total Energy

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

More information

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

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

More information

Linear Momentum and Collisions

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

More information

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

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

More information

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. 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 information

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

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

More information

Spring Force and Power

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

More information

Physics 131: Lecture 16. Today s Agenda

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

More information

Modeling motion with VPython Every program that models the motion of physical objects has two main parts:

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

More information

Physics 2A Chapter 3 HW Solutions

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

More information

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

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

More information

Momentum and Collisions. Rosendo Physics 12-B

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

More information

Lecture 09 Systems of Particles and Conservation of Linear Momentum

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

More information

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

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

More information

a) No books or notes are permitted. b) You may use a calculator.

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

More information

CHAPTER 8 Potential Energy and Conservation of Energy

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

More information

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

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

More information

Motion in One Dimension

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.

More information

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

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

More information

PHYS 1441 Section 002 Lecture #16

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

More information

Conservation of Energy

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

More information

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

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

More information

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

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

More information

Chapter 07: Kinetic Energy and Work

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

More information

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

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

More information

PHYS 1441 Section 002 Lecture #15

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

More information

Collisions! Short, Sharp Shocks

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

More information

PHYS 1443 Section 002

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

More information

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

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

More information

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

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

More information

EMU Physics Department

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

More information

Linear Momentum and Collisions

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

More information

ONE-DIMENSIONAL COLLISIONS

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

More information

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

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

More information

Prof. Dr. I. Nasser T /16/2017

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

More information

GAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME PHYSICAL SCIENCES GRADE 12 SESSION 1 (LEARNER NOTES)

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

More information

Physic 231 Lecture 14

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

More information

Conservation of Energy

Conservation 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 information

Energy and Energy Transfer

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

More information

AP Physics Enosburg Falls High School Mr. Bushey. Week 6: Work, Energy, Power

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

More information

PHYSICS 203-NYA-05 MECHANICS

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

More information

Linear Momentum. Center of Mass.

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

More information

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

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

More information

CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS

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

More information

Physics 207 Lecture 13. Lecture 13

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

More information

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

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

More information

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

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

More information

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

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

More information

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

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

More information

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

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

More information

Chapter Seven - Potential Energy and Conservation of Energy

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

More information

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

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

More information

Study Guide For Exam Two

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

More information

Chapter 7. Potential Energy and Conservation of Energy

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

More information

Conservation Laws (Collisions) Phys101 Lab - 04

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

More information

Force = F Piston area = A

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

More information

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

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

More information

Physics 2A Chapters 6 - Work & Energy Fall 2017

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

More information

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

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

More information

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

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

More information

Conservation of Energy

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

More information

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

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

More information

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

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

More information

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

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

More information

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

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

More information

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

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

More information

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

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

More information

Chapter 8. Potential Energy and Conservation of Energy

Chapter 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 information

Physics for Scientists and Engineers. Chapter 10 Energy

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

More information

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

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

More information

ENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15

ENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15 NGN 40 ynamcs and Vbratons Homework # 7 ue: Frday, Aprl 15 1. Consder a concal hostng drum used n the mnng ndustry to host a mass up/down. A cable of dameter d has the mass connected at one end and s wound/unwound

More information

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

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

More information

PHYSICS 231 Lecture 18: equilibrium & revision

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

More information

Dynamics of Rotational Motion

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 =

More information

Chapter 11 Angular Momentum

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

More information

Week 9 Chapter 10 Section 1-5

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

More information

WYSE Academic Challenge 2004 State Finals Physics Solution Set

WYSE 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 information

Physics 111: Mechanics Lecture 11

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

More information

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

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

More information

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

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

More information

PHYS 1101 Practice problem set 12, Chapter 32: 21, 22, 24, 57, 61, 83 Chapter 33: 7, 12, 32, 38, 44, 49, 76

PHYS 1101 Practice problem set 12, Chapter 32: 21, 22, 24, 57, 61, 83 Chapter 33: 7, 12, 32, 38, 44, 49, 76 PHYS 1101 Practce problem set 1, Chapter 3: 1,, 4, 57, 61, 83 Chapter 33: 7, 1, 3, 38, 44, 49, 76 3.1. Vsualze: Please reer to Fgure Ex3.1. Solve: Because B s n the same drecton as the ntegraton path s

More information

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

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

More information

Angular Momentum and Fixed Axis Rotation. 8.01t Nov 10, 2004

Angular 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 information

10/2/2003 PHY Lecture 9 1

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

More information

10/9/2003 PHY Lecture 11 1

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

More information

FOCUS ON CONCEPTS Section 7.1 The Impulse Momentum Theorem

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

More information

10/23/2003 PHY Lecture 14R 1

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

More information

Physics 181. Particle Systems

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

More information

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

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

More information