Chapter 6 Work and Energy

Transcription

1 as p5309 L3 Chapter 6 rk and Energy Gals r Chapter 6 Study wrk as dened n physcs Relate wrk t knetc energy Cnsder wrk dne by a arable rce Study ptental energy Understand energy cnseratn Include tme and relatnshp wrk t pwer as p5309 L3 Intrductn In preus chapters we studed mtn Smetmes rce and mtn are nt enugh t sle a prblem e ntrduce wrk and energy as the next step One the mst mprtant cncepts n physcs Alternate apprach t mechancs any applcatns beynd mechancs Very useul tls Yu wll learn new (smetmes much easer) ways t sle prblems rk, Energy, Pwer Chapter 6 n a nutshell rk s Frce tmes Dstance. The change n Knetc Energy s equal t the wrk. Pwer s rk per unt tme. F d net K P / T as p5309 L3 as p5309 L3 6. rk dne by a cnstant rce Frce dstance rk s rce tmes dstance but! F s N m jule J Only the rce cmpnent n the drectn mtn cunts! as p5309 L3 as p5309 L3

2 as p5309 L3 6. rk dne by a cnstant rce Cmpnent the rce alng the dsplacement s used n denng wrk Fcss cs0 cs90 0 cs80 SI Unt wrk: Jule as p5309 L3 Actty Annual U.S. energy use t. St. Helens eruptn Burnng ne galln gas Human d ntake/day eltng an ce cube Lghtng a 00- bulb r mnute Heartbeat Turnng page a bk Hp a lea Breakng a bnd n DNA Typcal Values rk Equalent wrk (J) 8 x Example: Pullng a sutcase-n-wheels Fnd the wrk dne the rce s 45.0-N, the angle s 50.0 degrees, and the dsplacement s 75.0 m. as p5309 L3 Fcs s 45.0 Ncs m 70 J Example: Bench-Pressng as p5309 L3 An athlete s bench-pressng a barbell whse weght s 70 N. Frst, he rases the barbell a dstance 0.65 m abe hs chest, and then he lwers t the same dstance. The weght s rased and lwered at cnstant elcty. Determne the wrk dne n the barbell. Fcs0 s Fs 70N cs m 460 J Fcs80 s Fs 70N cs m 460 J Ltng phase Lwerng phase rk s negate as rce s ppste t dsplacment Example: Acceleratng a crate The truck s acceleratng at a rate +.50 m/s. The mass the crate s 0-kg and t des nt slp. The magntude the dsplacement s 65 m. hat s the ttal wrk dne n the crate by all the rces actng n t? The angle between the dsplacement and the nrmal rce s 90 degrees. The angle between the dsplacement and the weght s als 90 degrees. Fcs 90s 0 The angle between the dsplacement and the rctn rce s 0 degrees. s ma 0 kg.5m s 80N cs 065 m.0 4 J 80N ttal wrk s dne by rctnal rce here as p5309 L3 as p5309 L3

3 as p5309 L3 Example: Pushng a stalled car Stee pushes hs stalled car 9 m t clear the ntersectn. I he pushes wth a cnstant rce wth magntude 0 N (abut 47 lb), hw much wrk des he d n the car (a) he pushes n the drectn the car s headng, (b) he pushes at 30 t that drectn? 6. The rk-energy Therem and Knetc Energy Cnsder a cnstant net external rce actng n an bject. The bject s dsplaced a dstance s, n the same drectn as the net rce. F s The wrk s smply Fs mas as p5309 L3 The rk-energy Therem and Knetc Energy as p5309 L3 m as as as m DEFINITION OF KINETIC ENERGY The knetc energy KE and bject wth mass m and speed s gen by KE Knetc energy as p5309 L3 Knetc: Energy mtn. A car n the hghway has knetc energy. e hae t ree ths energy t stp t. The breaks a car get HOT! Ths s an example turnng ne rm energy nt anther (thermal energy). K m Knetc Energy The rk-energy Therem and Knetc Energy Example: Deep Space The mass the space prbe s 474-kg and ts ntal elcty s 75 m/s. I the 56.0-mN rce acts n the prbe thrugh a dsplacement m, what s ts nal speed? THE ORK-ENERGY THEORE hen a net external rce des wrk n and bject, the knetc energy the bject changes accrdng t as p5309 L3 KE KE as p5309 L3 F css

4 as p5309 L3 The preus prblem can be sled usng knematc equatns. Frst usng Newtn s secnd law, F=ma t nd acceleratn. Fcss Ncs0.40 m 474 kg 474 kg75m s 805m s S a = F/m= 0.056/474 =.8x0-4 m/s V = 75 m/s, and d =.4x0 9 m. V V V a d V 804 m / s (75) as p5309 L3 Knetc Energy rk Summary rk dne by a cnstant rce Prdes a lnk between rce and energy The wrk,, dne by a cnstant rce n an bject s dened as the prduct the cmpnent the rce alng the drectn dsplacement and the magntude the dsplacement (Fcs) x rk - (Knetc) Energy Therem ttal K K K (F cs ) s the cmpnent the rce n the drectn the dsplacement x s the dsplacement as p5309 L3 as p5309 L3 rk dne by multple rces Suppse F Tt = F + F and the dsplacement s r. TOT = (F Tt cs) r It s the ttal rce that matters!! The wrk dne by each rce s: F Tt F r = (F cs ) r = (F cs ) r Tt = + F F Tt r F F rk - Knetc Energy Therem hen wrk s dne by a net rce n an bject and the nly change n the bject s ts speed, the wrk dne s equal t the change n the bject s knetc energy ttal ttal KE KE Speed wll ncrease wrk s pste Speed wll decrease wrk s negate KE as p5309 L3 as p5309 L3

5 as p5309 L3 Example: Dwnhll Skng KE m ttal KE KE A 50-kg sker s castng dwn a 5 slpe. Near the tp the slpe, her speed s 3.6 m/s. She accelerates dwn the slpe because the gratatnal rce, een thugh a knetc rctn rce magntude 7 N ppses her mtn. Ignrng ar resstance, determne the speed at a pnt that s dsplaced 57 m dwnhll. - sle r - need F cs s as p5309 L3 In ths case the net rce s F - need F F mgsn 5 m F 50kg 9.80 sn 5 7N s cs s k 70 N puttng t all tgether 6.3 Gratatnal Ptental Energy Gratatnal Ptental Energy s the energy asscated wth the relate pstn an bject n space near the Earth s surace Objects nteract wth the earth thrugh the gratatnal rce The ptental energy the earth-bject system as p5309 L3 as p5309 L3 rk and Gratatnal Ptental Energy Cnsder blck mass m at ntal heght y rk dne by the gratatnal rce gra Fcss (mg cs) s but : s y y, cs, Thus : mg y y PE mgy Ths quantty s called ptental energy: graty gra PE PE mgy mgy PE Imprtant: wrk s related t the derence n PE s! Example: A Gymnast n a tramplne The gymnast leaes the tramplne at an ntal heght.0 m and reaches a maxmum heght 4.80 m bere allng back dwn. hat was the ntal speed the gymnast? as p5309 L3 as p5309 L3

6 as p5309 L3 mgh h graty mg h h g h h e can sle ths prblem usng knematcs V 0 V V V V a ( h ( g) ( h g ( h g ( h h h ) h h ) ) ) 9.80 m s.0 m 4.80 m 8.40 m s as p5309 L3 Ptental Energy Ptental energy s asscated wth the pstn the bject wthn sme system Ptental energy s a prperty the system, nt the bject A system s a cllectn bjects r partcles nteractng a rces r prcesses that are nternal t the system Unts Ptental Energy are the same as thse rk and Knetc Energy [J] Gratatnal Ptental Energy graty mgh mgh DEFINITION OF GRAVITATIONAL POTENTIAL ENERGY The gratatnal ptental energy PE s the energy that an bject mass m has by rtue ts pstn relate t the surace the earth. That pstn s measured by the heght h the bject relate t an arbtrary zer leel: PE mgh N m jule J as p5309 L3 as p5309 L3 6.4 Cnserate ersus Nncnserate Frces Versn A rce s cnserate when the wrk t des n a ng bject s ndependent the path between the bject s ntal and nal pstns. Cnserate Frces - Independence rm Path graty mg h h as p5309 L3 as p5309 L3

7 as p5309 L3 Cnserate ersus Nncnserate Frces Versn A rce s cnserate when t des n wrk n an bject ng arund a clsed path, startng and nshng at the same pnt. h mgh h h graty Cnserate ersus Nncnserate Frces as p5309 L3 Cnserate ersus Nncnserate Frces An example a nncnserate rce s the knetc rctnal rce k. Fcss cs80 s s The wrk dne by the knetc rctnal rce s always negate. Thus, t s mpssble r the wrk t des n an bject that es arund a clsed path t be zer. The cncept ptental energy s nt dened r a nncnserate rce. k k Frctn depends n the path - nncnserate rce The rctn rce transrms knetc energy the bject nt a type energy asscated wth temperature (heat) The blue path s shrter than the red path The wrk requred s less n the blue path than n the red path Frctn depends n the path and s s a nncnserate rce as p5309 L3 as p5309 L3 Cnserate ersus Nncnserate Frces In nrmal stuatns bth cnserate and nncnserate rces act smultaneusly n an bject, s the wrk dne by the net external rce can be wrtten as c nc Cnserate ersus Nncnserate Frces c nc KE PE nc c KE graty mgh KE mgh KE PE PE PE THE ORK-ENERGY THEORE nc KE PE as p5309 L3 as p5309 L3

8 as p5309 L3 6.5 The cnseratn mechancal energy nc KE PE nc KE PE KE PE nc KE KE PE PE E E I the net wrk n an bject by nncnserate rces s zer, then ts energy des nt change: E E The cnseratn mechancal energy THE PRINCIPLE OF CONSERVATION OF ECHANICAL ENERGY The ttal mechancal energy (E = KE + PE) an bject remans cnstant as the bject es, prded that the net wrk dne by external nncnserate rces s zer. KE PE E E KE PE as p5309 L3 The cnseratn mechancal energy Example: A daredel mtrcyclst A mtrcyclst s tryng t leap acrss the canyn by drng hrzntally a cl wth =38.0 m/s. Ignrng ar resstance, nd the speed wth whch the cycle strkes the grund n the ther sde. prjectle mtn, but use cnseratn mechancal energy as p5309 L3 as p5309 L3 mgh gh mgh gh g h h E E Example 0: The Kngda Ka rller caster The Kngda Ka s a gant rller caster. The rde ncludes a ertcal drp 7 m. Suppse the caster has a speed 6.0 m/s at the tp the drp. Neglect rctn and ar resstance and nd the speed the rders at the bttm. Cnseratn mechancal energy 9.8m s 35.0m 38.0 m s 46.m s as p5309 L3 as p5309 L3

9 as p5309 L3 KE c nc KE PE nc THE ORK-ENERGY THEORE nc KE KE KE PE Prblem Slng wth rk-energy therem Dene the system Determne whether r nt nncnserate rces are present I nly cnserate rces are present, apply cnseratn energy and sle r the unknwn Select the lcatn zer gratatnal ptental energy D nt change ths lcatn whle slng the prblem I nc = 0 KE CONSERVATION OF ECHANICAL ENERGY PE KE PE as p5309 L3 Example : Frewrks -- rk-energy therem Frewrks: m = 0.0 kg. The nncnserate rce generated by the burnng prpellant des 45 J wrk, the rcket s 9 m abe ts startng pnt. hat s the nal speed the rcket. Ignre ar resstance. ORK-ENERGY THEORE nc nc E mgh mgh E nc nc mgh mg mgh 45 J 0.0 kg 9.80 m s 9.0 m 0.0 kg 6m s h h as p5309 L3 as p5309 L3 Gratatnal Ptental Energy PE mgy graty PE PE Gratatnal ptental energy: Imprtant: wrk dne by graty s related t the derence n gratatnal PE s! A lcatn where the gratatnal ptental energy s zer must be chsen r each prblem The chce s arbtrary snce the change n the ptental energy ges the wrk dne Example: Fallng Randrps ass drpped rm heght H. hat s speed just bere httng the grund? (Neglect rctn ar) F y PE K V ( mg) ( h) F = - mg mgh V y = -h mgh gh 0 as p5309 L3 as p5309 L3

10 as p5309 L3 Independence rm Path (Cnserate Frces) Example: Slwng dwn wth rctn rce V L V 0 Intal Fnd speed at bttm the slde 0 mgh 0 gh gh Fnal Rugh spt, cecent rctn. A blck mass s ng ntally wth speed V 0. It passes er a rugh patch table length L. Gen the mass, the ntal speed V 0, and the cecent rctn, nd the nal speed the blck.. Draw the pcture.. hat s gen? 3. hat are the relatnshps? Nn-cnserate wrk: rk-energy: NC NC F L gl K as p5309 L3 Example: Slwng dwn wth rctn rce NC K NC V L V 0 Rugh spt, cecent rctn. F L gl gl V V0 gl K V V V0 V0 Pwer Oten als nterested n the rate at whch the energy transer (wrk dne) takes place Pwer s dened as ths rate energy transer (wrk dne) Aerage Pwer SI unts are atts hrse pwer P rk Tme t Jules kg m atts s s hp = 746 = k P F as p5309 L3 as p5309 L3 Pwer Example: A marathn star clmb A marathn runner wth mass 50.0 kg runs up the stars t the tp the Sears Twer (443 m) n 5.0 mnutes. hat s her aerage pwer utput n atts?... as p5309 L3 as p5309 L3

11 as p5309 L3 Example: Pwer n a Jet Engne A jet arplane engne deelps a thrust (a rward rce n the plane) 5,000 N. hen the plane s lyng at 300 m / s (rughly 600 m / h), what hrsepwer des the engne deelp? P = F... PRINCIPLE OF CONSERVATION OF ENERGY Energy can nether be created nr destryed, but can nly be cnerted rm ne rm t anther. True r any slated system..e. when we put n the brakes, the knetc energy the car s turned nt heat usng rctn n the brakes. The ttal energy the car-breaks-rad-atmsphere system s the same. The energy the car alne s nt cnsered... It s reduced by the brakng. Dng wrk n an slated system wll change ts energy... as p5309 L3 Oerew Energy Energy s cnsered Knetc energy descrbes mtn and relates t the mass an bject and ts energy squared Energy n earth rgnates rm the sun (nuclear usn) Chemcal energy s released by metablsm Energy can be stred as ptental energy n an bjects heght and mass and als thrugh elastc dermatn Energy can be dsspated as heat and nse Energy and ts transrmatn Transrmatn gratatnal ptental energy t knetc energy Elastc ptental energy stred n a stretched rubber band as p5309 L3 as p5309 L3 Energy can be dsspated as heat (mlecular mtns) Graphcal Representatn rk (arable rce) Splt ttal dsplacement (x -x ) nt many small dsplacements x Fr each small dsplacement: (Fcs) x Thus, ttal wrk s: tt F x whch s ttal area under the F(x) cure! x as p5309 L3 as p5309 L3

12 as p5309 L3 rk - Energy Therem ttal K K Summary K K U Cnseratn mech. Energy K U Cnserate Frces: c U n U n U PE Gratatnal Ptental Energy nc PE U mgy KE PE Aerage Pwer P F t