Physics for Scientists and Engineers. Chapter 10 Energy
|
|
- Willa Hill
- 6 years ago
- Views:
Transcription
1 Physcs or Scentsts and Engneers Chapter 0 Energy Sprng, 008 Ho Jung Pak
2 Introducton to Energy Energy s one o the ost portant concepts n scence although t s not easly dened Eery physcal process that occurs n the Unerse noles energy and energy transers The energy approach to descrbng oton s partcularly useul when the orce s not constant An approach wll nole Conseraton o Energy Ths could be extended to bologcal organss, technologcal systes and engneerng stuatons 3-Mar-08 Pak p.
3 Energy o Fallng Object Kneatc eq. Dene : knetc energy g Then, K U : Conseraton o Energy U K g a g y ( y Graty s the only orce actng Multplyng & puttng a y g, g( y y gy gy K U gy 3-Mar-08 Pak p. 3 y : gratatonal potental energy
4 Knetc Energy Knetc energy s the energy assocated wth the oton o an object Knetc energy s always gen by K ½, where s the speed o the object Knetc energy s a scalar, ndependent o drecton o Knetc energy cannot be negate Unts o energy: kg /s Joule Energy has densons o [M L T ] 3-Mar-08 Pak p. 4
5 Potental Energy Potental energy s the energy assocated wth the relate poston o objects that exert orces on each other A potental energy can only be assocated wth specc types o orces,.e. conserate orces There are any ors o potental energy: gratatonal, electroagnetc, checal, nuclear Gratatonal potental energy s assocated wth the dstance aboe Earth s surace: U g gy 3-Mar-08 Pak p. 5
6 Total Mechancal Energy The su o knetc and potental energes s the echancal energy o the syste: E K U When conserate orces act n an solated syste, knetc energy ganed (or lost by the syste as ts ebers change ther relate postons s balanced by an equal loss (or gan n potental energy Ths s the Conseraton o Mechancal Energy I there s rcton or ar drag, the total echancal energy s not consered,.e. constant 3-Mar-08 Pak p. 6
7 Gratatonal Potental Energy The syste conssts o Earth and a book Intally, the book s at rest (K 0 at y y b (U g gy b When the book alls and reaches y a, K a gy a 0 gy b K a g (y b - y a >0 The knetc energy that was conerted ro potental energy depends only on the relate dsplaceent y b - y a It doesn t atter where we take y 0 3-Mar-08 Pak p. 7
8 Exaple : Launchng a Pebble Bob uses a slngshot to shoot a 0.0 g pebble straght up wth a speed o 5.0 /s. How hgh does a pebble go? Beore: K b Ater : K 0, U a Usng energy conseraton, y a 6.5 J, Knetc energy was conerted nto gratatonal potental energy by 6.5 J. ga , gy 0.96 or K U y a a gb U 0 y ga a 39. K b U gb 3-Mar-08 Pak p. 8
9 along a Ths s Energy Conseraton n -D We wll now analyze - D oton ds Fs as, dt ds ds g sn θ ds dt Multplyng both sdes by ds, But snθds rctonless nclne. dy. ds ds g sn θds Integratng ro ntal to nal gy gy the sae equaton as n a - D oton. s postons, 3-Mar-08 Pak p. 9 s d s
10 Exaple : Downhll Sleddng Chrstne runs orward wth her sled at.0 /s. She hops onto the sled at the top o a 5.0 hgh, ery slppery slope. What s her speed at the botto? Usng the conseraton o 0 0 gy 0 g( y 0 y energy, gy 0 /s Notce that ( the ass cancelled out and ( only Δy s needed. We could hae taken the botto o the hll as y 0.0 and the top as y 5.0, and gotten the sae answer. 3-Mar-08 Pak p. 0
11 Energy Conseraton: Pendulu As the pendulu swngs, there s a contnuous exchange between potental and knetc energes At A, all the energy s potental At B, all o the potental energy at A s transored nto knetc energy Let zero potental energy be at B At C, the knetc energy has been transored back nto potental energy 3-Mar-08 Pak p.
12 Exaple 3: Ballstc Pendulu A 0 g bullet s red nto a 00 g wood block hangng ro a 50 c long strng. The bullet ebeds tsel nto the block, and the block then swngs out to an angle o 40. What was the speed o the bullet? 3-Mar-08 Pak p.
13 Exaple 3, cont Ths proble has two parts: (a the bullet and the block ake a perectly nelastc collson, n whch oentu s consered, and (b the total ass as a syste undergoes a pendulu oton, n whch energy s consered. (a Moentu conseraton : w Snce w0 0, b0 b (b Energy conseraton : Snce Thereore, 0 and we can choose b0 w b b.0 kg 0.00 kg ( b tot gl w y b tot 0, gy ( cosθ gy gl ( cosθ ( 9.80 /s (.50 ( /s 3-Mar-08 Pak p. 3 w w0 tot b b0 tot gy
14 Exaple 4: Roller Coaster A roller-coaster car s released ro rest at the top o the rst rse and then oes reely wth neglgble rcton. The roller coaster has a crcular loop o radus R n a ertcal plane. (a Suppose rst that the car barely akes t around the loop: at the top o the loop the rders are upsde down and eel weghtless,.e. n 0. Fnd the heght o the release pont aboe the botto o the loop, n ters o R so that n 0. 3-Mar-08 Pak p. 4
15 (a At the top o K gh Exaple 4, cont are n ree all. g gr R Energy s consered between the release and the top o U g 0 gh the loop, the car and rders K the loop : U gr gr Fro Newton's g g(r h.5r nd law, 3-Mar-08 Pak p. 5
16 Exaple 4, cont (b Show that the noral orce on the car at the botto o the loop exceeds the noral orce at the top o the loop by sx tes the weght o the car. (b Energy conseraton :(botto Newton's nd law :(botto Substtutng b and t, n n b b gh b gh b g R g ( h / R n g( 5 h / R The noral orce on each rder ollows the sae rule. Such a large noral orce s ery uncoortable or the rders. Roller coasters are thereore bult helcal so that soe o the gratatonal energy goes nto axal oton. 3-Mar-08 Pak p. 6 b n b (top (top n t gh n t 6g t t g R t t gh 4gR g(r
17 Hooke s Law Force exerted by a sprng s always drected opposte to the dsplaceent ro equlbru Hooke s Law: F s kδs Δs s the dsplaceent ro the equlbru poston k s the sprng constant and easures the stness o the sprng F s called the restorng orce I t s released, t wll oscllate back and orth 3-Mar-08 Pak p. 7
18 Measurng the Force Constant At equlbru, a y F y 0, F Thereore, g k Δs Measure s g kδs ( N/ and g Δs a y 0 to deterne k. 3-Mar-08 Pak p. 8
19 Energy o Object on a Sprng Use the chan rule, ds ds k( s s e ds dt or k( s s ds d Dene u Integratng, s s F s k( s s s d a s e s, e k( s s s s e ds Δs, Δs Δs e s s kudu ds dt hence du s ds ds ku ds. Δs Δs ( Δs k( Δs ( Δs k( Δs 3-Mar-08 Pak p. 9 k k
20 Elastc Potental Energy Potental energy o an object attached to a sprng s U s ½ k(δs The elastc potental energy depends on the square o the dsplaceent ro the sprng s equlbru poston The sae aount o potental energy can be conerted to knetc energy the sprng s extended or contracted by the sae dsplaceent 3-Mar-08 Pak p. 0
21 Exaple 5: Sprng Gun Proble A sprng-loaded toy gun launches a 0 g plastc ball. The sprng, wth sprng constant 0 N/, s copressed by 0 c as the ball s pushed nto the barrel. When the trgger s pulled, the sprng s released and shoots the ball out. What s the ball s speed as t leaes the barrel? Assue rcton s neglgble. k ( Δx k( Δx, 0 k( x x e 0 k( x x e (0 N/( kg 3.6 /s 3-Mar-08 Pak p.
22 Exaple 6: Pushng Apart A sprng wth sprng constant 000 N/ s sandwched between a.0 kg block and a.0 kg block on a rctonless table. The blocks are pushed together to copress the sprng by 0 c, then released. What are the eloctes o the blocks as they ly apart? 3-Mar-08 Pak p.
23 0 0 Exaple 6, cont Fro energy conseraton, k( Δx Fro oentu conseraton, Substtutng ths nto the energy equaton,,,,,,, k( Δx ( k(δx,,,,, 0, k( Δ x.8 /s,, 0,,, k(δx 3.6 /s 3-Mar-08 Pak p. 3,,,,, k( Δx,
24 Exaple 7: Sprng and Graty A 0 kg box sldes 4.0 down the rctonless rap shown n the gure, then colldes wth a sprng whose sprng constant s 50 N/. (a What s the axu copresson o the sprng? (b At what copresson o the sprng does the box hae ts axu elocty? 3-Mar-08 Pak p. 4
25 Exaple 7, cont (a Choose the orgn o the coordnate syste at the pont o axu copresson. Take the coordnate along the rap to be s. K 0 s ( Δs ( 5 N/( Δs ( 49 kg /s Δs U k U.46, g 0 K U s U g 0 0 g(4.0 Δssn (unphyscal Δs 96 kg /s o 0 3-Mar-08 Pak p. 5
26 Exaple 7, cont (b For ths part o the proble, t s easest to take the orgn at the pont where the sprng s at ts equlbru poston. K k U ( Δs o o ( Δs ( g sn 30 ( Δs g( 4.0 sn 30 To nd s U ax g gy kδs g sn 30 s wrt Δs, take the derate o o k K U d dδs U g 0 gy 0, Δs 0 ths equaton and put g sn 30 k Mar-08 Pak p. 6 o 0 d dδs 0.
27 Elastc Collsons Both oentu and knetc energy are consered (U 0 Typcally, there are two unknowns ( and, so you need both equatons: p p and K K The knetc energy equaton can be dcult to use Wth soe algebrac anpulaton, the two equatons can be used to sole or the two unknowns 3-Mar-08 Pak p. 7
28 3-Mar-08 Pak p. 8 -D Elastc Collsons p p K K, and substtutng nto the oentu equaton, or Sole or ( ( Cobne the two equatons, ( ( : ( ( ( ( :
29 -D Elastc Collsons, cont ( ( (3 :, ( Partcles exchange eloctes. (0 << ( ( 0 : (0 (00 contnues to oe at,, bounces back whle >>, 0 :, ( ( (0 whle (0 ( 0 (0 0 reans statonary oes at 3-Mar-08 Pak p. 9
30 -D Elastc Collsons Energy conseraton: ½ ½ ½ Moentu conseraton: x: cosθ cosφ y: 0 snθ snφ Note that we hae 3 equatons and 4 unknowns We cannot sole or the unknowns unless we hae one nal angle or nal elocty gen 3-Mar-08 Pak p. 30
31 Exaple 8: Bllard Ball A player wshes to snk target ball n the corner pocket. The angle to the corner pocket s 35. At what angle s the cue ball delected? Energy conseraton : Moentu conseraton : 0 cosθ snθ cos 35 sn 35 3-Mar-08 Pak p. 3
32 Exaple 8, cont Snce,, sn 35 Fro the thrd equaton,. snθ Substtutng ths nto the rst and second equatons, sn 35 sn θ cosθ sn 35 Fro these, cosθ cos35 snθ Ths leads to cotθ tan35 or θ, cos 35, sn 35 cosθ cos35 snθ sn 35 sn θ. snθ sn 35 3-Mar-08 Pak p. 3
33 Internal Energy So ar we hae consdered stuatons where there s no rcton In the absence o rcton, the echancal energy s consered: E K U constant Where rcton s present, soe energy s conerted to nternal energy, usually heat Here K E constant 3-Mar-08 Pak p. 33
34 Exaple 9: Bullet Fred nto Block A 5.00-g bullet ong wth an ntal speed o 400 /s s red nto and passes through a.00- kg block. The block, ntally at rest on a rctonless, horzontal surace, s connected to a sprng o orce constant 900 N/. The block oes 5.00 c to the rght ater pact. Fnd (a the speed at whch the bullet eerges ro the block and (b the echancal energy conerted nto nternal energy n the collson. 3-Mar-08 Pak p. 34
35 Exaple 9, cont (a Energy conseraton or the sprng: (b.50 /s MV Moentu conseraton n the collson : MV 3 MV ( kg(400 /s (.00 kg(.5 /s kg ΔE V ΔK kx M ΔU (900 N/( kg The lost energy s due to the rcton between the bullet and block. The block heats up a lttle. 3-Mar-08 Pak p. 35 kx 3 ( kg( 00 /s ( 400 /s [ ] [ ] 374 J ( 900 N/( ( 0 00 /s
36 Energy Dagras Partcle under a ree all 3-Mar-08 Pak p. 36
37 Energy Dagras, cont Partcle attached to a sprng 3-Mar-08 Pak p. 37
38 General Energy Dagra Equlbra are at ponts where du/dx 0. At equlbra, F 0. Away ro equlbra, du/dx 0 and F 0. 3-Mar-08 Pak p. 38
39 Molecular Bondng Potental energy assocated wth the orce between two neutral atos n a olecule can be odeled by the Lennard-Jones uncton: 3-Mar-08 Pak p. 39
40 Force Actng n a Molecule The orce s repulse (poste at sall separatons The orce s zero at the pont o stable equlbru Ths s the ost lkely separaton between the atos n the olecule (.9 x 0-0 at nu energy The orce s attracte (negate at large separatons At great dstances, the orce approaches zero 3-Mar-08 Pak p. 40
41 Exaple 0: Hesphercal Hll A sled starts ro rest at the top o the rctonless, hesphercal, snowcoered hll shown n the gure. (a Fnd an expresson or the sled's speed when t s at angle φ. (b Use Newton's laws to nd the axu speed the sled can hae at angle φ wthout leang the surace. (c At what angle φ ax does the sled "ly o" the hll? 3-Mar-08 Pak p. 4
42 3-Mar-08 Pak p. 4 Exaple 0, cont ( o cos 3 cos, cos cos ( two, the Equatng. and or an arbtrary angle hae We (c cos 0 hll. the leaes sled the 0, When ncreases. as decreases cos cos, (b cos cos (a ax ax ax ax ax ax ax φ φ φ φ φ φ φ φ φ gr gr gr n n n R g n R g n a F gr gr gr gy gy U K U K r r
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 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 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 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 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 informationPhysics 207, Lecture 13, Oct. 15. Energy
Physcs 07 Lecture 3 Physcs 07, Lecture 3, Oct. 5 Goals: Chapter 0 Understand the relatonshp between moton and energy Dene Potental Energy n a Hooke s Law sprng Deelop and explot conseraton o energy prncple
More 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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. Center of Mass.
Lecture 16 Chapter 9 Physcs I 11.06.2013 Lnear oentu. Center of ass. Course webste: http://faculty.ul.edu/ndry_danylov/teachng/physcsi Lecture Capture: http://echo360.ul.edu/danylov2013/physcs1fall.htl
More 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 informationYou will analyze the motion of the block at different moments using the law of conservation of energy.
Physcs 00A Homework 7 Chapter 8 Where s the Energy? In ths problem, we wll consder the ollowng stuaton as depcted n the dagram: A block o mass m sldes at a speed v along a horzontal smooth table. It next
More informationPHYS 1443 Section 004 Lecture #12 Thursday, Oct. 2, 2014
PHYS 1443 Secton 004 Lecture #1 Thursday, Oct., 014 Work-Knetc Energy Theorem Work under rcton Potental Energy and the Conservatve Force Gravtatonal Potental Energy Elastc Potental Energy Conservaton o
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 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 information1.3 Hence, calculate a formula for the force required to break the bond (i.e. the maximum value of F)
EN40: Dynacs and Vbratons Hoework 4: Work, Energy and Lnear Moentu Due Frday March 6 th School of Engneerng Brown Unversty 1. The Rydberg potental s a sple odel of atoc nteractons. It specfes the potental
More 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 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 informationPhysics 207 Lecture 13. Lecture 13
Physcs 07 Lecture 3 Goals: Lecture 3 Chapter 0 Understand the relatonshp between moton and energy Defne Potental Energy n a Hooke s Law sprng Develop and explot conservaton of energy prncple n problem
More informationCHAPTER 10 ROTATIONAL MOTION
CHAPTER 0 ROTATONAL MOTON 0. ANGULAR VELOCTY Consder argd body rotates about a fxed axs through pont O n x-y plane as shown. Any partcle at pont P n ths rgd body rotates n a crcle of radus r about O. The
More informationRemark: Positive work is done on an object when the point of application of the force moves in the direction of the force.
Unt 5 Work and Energy 5. Work and knetc energy 5. Work - energy theore 5.3 Potenta energy 5.4 Tota energy 5.5 Energy dagra o a ass-sprng syste 5.6 A genera study o the potenta energy curve 5. Work and
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 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 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 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 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 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 informationPage 1. SPH4U: Lecture 7. New Topic: Friction. Today s Agenda. Surface Friction... Surface Friction...
SPH4U: Lecture 7 Today s Agenda rcton What s t? Systeatc catagores of forces How do we characterze t? Model of frcton Statc & Knetc frcton (knetc = dynac n soe languages) Soe probles nvolvng frcton ew
More 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 informationPhysics 201 Lecture 9
Physcs 20 Lecture 9 l Goals: Lecture 8 ewton s Laws v Solve D & 2D probles ntroducng forces wth/wthout frcton v Utlze ewton s st & 2 nd Laws v Begn to use ewton s 3 rd Law n proble solvng Law : An obect
More informationClass: Life-Science Subject: Physics
Class: Lfe-Scence Subject: Physcs Frst year (6 pts): Graphc desgn of an energy exchange A partcle (B) of ass =g oves on an nclned plane of an nclned angle α = 3 relatve to the horzontal. We want to study
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 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 informationConservation of Energy
Conservaton o nergy The total energy o a system can change only by amounts o energy that are transerred nto or out o the system W mec th nt Ths s one o the great conservaton laws n nature! Other conservaton
More informationPhysics 3A: Linear Momentum. Physics 3A: Linear Momentum. Physics 3A: Linear Momentum. Physics 3A: Linear Momentum
Recall that there was ore to oton than just spee A ore coplete escrpton of oton s the concept of lnear oentu: p v (8.) Beng a prouct of a scalar () an a vector (v), oentu s a vector: p v p y v y p z v
More 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 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 informationElastic Collisions. Definition: two point masses on which no external forces act collide without losing any energy.
Elastc Collsons Defnton: to pont asses on hch no external forces act collde thout losng any energy v Prerequstes: θ θ collsons n one denson conservaton of oentu and energy occurs frequently n everyday
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 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 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 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 informationPHYS 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
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 informationLinear 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 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 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 informationRotational and Translational Comparison. Conservation of Angular Momentum. Angular Momentum for a System of Particles
Conservaton o Angular Momentum 8.0 WD Rotatonal and Translatonal Comparson Quantty Momentum Ang Momentum Force Torque Knetc Energy Work Power Rotaton L cm = I cm ω = dl / cm cm K = (/ ) rot P rot θ W =
More informationSolutions for Homework #9
Solutons for Hoewor #9 PROBEM. (P. 3 on page 379 n the note) Consder a sprng ounted rgd bar of total ass and length, to whch an addtonal ass s luped at the rghtost end. he syste has no dapng. Fnd the natural
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 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 information(T > w) F R = T - w. Going up. T - w = ma
ANSES Suspended Acceleratng-Objects A resultant orce causes a syste to accelerate. he drecton o the acceleraton s n the drecton o the resultant orce. As llustrated belo, hen suspended objects accelerate,
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 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 informationA Tale of Friction Basic Rollercoaster Physics. Fahrenheit Rollercoaster, Hershey, PA max height = 121 ft max speed = 58 mph
A Tale o Frcton Basc Rollercoaster Physcs Fahrenhet Rollercoaster, Hershey, PA max heght = 11 t max speed = 58 mph PLAY PLAY PLAY PLAY Rotatonal Movement Knematcs Smlar to how lnear velocty s dened, angular
More informationPhysics 231. Topic 8: Rotational Motion. Alex Brown October MSU Physics 231 Fall
Physcs 231 Topc 8: Rotatonal Moton Alex Brown October 21-26 2015 MSU Physcs 231 Fall 2015 1 MSU Physcs 231 Fall 2015 2 MSU Physcs 231 Fall 2015 3 Key Concepts: Rotatonal Moton Rotatonal Kneatcs Equatons
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 informationWeek 8: Chapter 9. Linear Momentum. Newton Law and Momentum. Linear Momentum, cont. Conservation of Linear Momentum. Conservation of Momentum, 2
Lnear omentum Week 8: Chapter 9 Lnear omentum and Collsons The lnear momentum of a partcle, or an object that can be modeled as a partcle, of mass m movng wth a velocty v s defned to be the product of
More informationPhysics 207: Lecture 20. Today s Agenda Homework for Monday
Physcs 207: Lecture 20 Today s Agenda Homework for Monday Recap: Systems of Partcles Center of mass Velocty and acceleraton of the center of mass Dynamcs of the center of mass Lnear Momentum Example problems
More 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 informationWeek 6, Chapter 7 Sect 1-5
Week 6, Chapter 7 Sect 1-5 Work and Knetc Energy Lecture Quz The frctonal force of the floor on a large sutcase s least when the sutcase s A.pushed by a force parallel to the floor. B.dragged by a force
More 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 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 informationa) No books or notes are permitted. b) You may use a calculator.
PHYS 050 Sprng 06 Name: Test 3 Aprl 7, 06 INSTRUCTIONS: a) No books or notes are permtted. b) You may use a calculator. c) You must solve all problems begnnng wth the equatons on the Inormaton Sheet provded
More 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 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 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 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 informationA Tale of Friction Student Notes
Nae: Date: Cla:.0 Bac Concept. Rotatonal Moeent Kneatc Anular Velocty Denton A Tale o Frcton Student Note t Aerae anular elocty: Intantaneou anular elocty: anle : radan t d Tanental Velocty T t Aerae tanental
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 informationPHYS 2211L - Principles of Physics Laboratory I
PHYS L - Prncples of Physcs Laboratory I Laboratory Adanced Sheet Ballstc Pendulu. Objecte. The objecte of ths laboratory s to use the ballstc pendulu to predct the ntal elocty of a projectle usn the prncples
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 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 informationLecture 6. Announcements. Conservation Laws: The Most Powerful Laws of Physics. Conservation Laws Why they are so powerful
Conseration Laws: The Most Powerful Laws of Physics Potential Energy gh Moentu p = + +. Energy E = PE + KE +. Kinetic Energy / Announceents Mon., Sept. : Second Law of Therodynaics Gie out Hoework 4 Wed.,
More informationPhysics 231. Topic 8: Rotational Motion. Alex Brown October MSU Physics 231 Fall
Physcs 231 Topc 8: Rotatonal Moton Alex Brown October 21-26 2015 MSU Physcs 231 Fall 2015 1 MSU Physcs 231 Fall 2015 2 MSU Physcs 231 Fall 2015 3 Key Concepts: Rotatonal Moton Rotatonal Kneatcs Equatons
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 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 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 informationChapter 9 Centre of Mass and Linear Momentum
Chater 9 Centre o Mass and Linear Moentu Centre o ass o a syste o articles / objects Linear oentu Linear oentu o a syste o articles Newton s nd law or a syste o articles Conseration o oentu Elastic and
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 informationi-clicker i-clicker A B C a r Work & Kinetic Energy
ork & c Energ eew of Preou Lecture New polc for workhop You are epected to prnt, read, and thnk about the workhop ateral pror to cong to cla. (Th part of the polc not new!) There wll be a prelab queton
More information2/24/2014. The point mass. Impulse for a single collision The impulse of a force is a vector. The Center of Mass. System of particles
/4/04 Chapte 7 Lnea oentu Lnea oentu of a Sngle Patcle Lnea oentu: p υ It s a easue of the patcle s oton It s a vecto, sla to the veloct p υ p υ p υ z z p It also depends on the ass of the object, sla
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 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 informationFrom 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 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 informationChapter 3. r r. Position, Velocity, and Acceleration Revisited
Chapter 3 Poston, Velocty, and Acceleraton Revsted The poston vector of a partcle s a vector drawn from the orgn to the locaton of the partcle. In two dmensons: r = x ˆ+ yj ˆ (1) The dsplacement vector
More informationESCI 341 Atmospheric Thermodynamics Lesson 6 Thermodynamic Processes
ESCI 341 Atmosherc Thermodynamcs Lesson 6 Thermodynamc Processes Reerences: An Introducton to Atmosherc Thermodynamcs, Tsons Introducton to Theoretcal Meteorology, Hess Physcal Chemstry (4 th edton), Lene
More information