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

Transcription

1 r (.) Rest Mass,ork by Changng orces Columba Rep 3pm, here RE 6.b (last day to drop) ed (.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 created nor destroyed, but transerred va nteractons. Energy v c E mc mc sys drsys all E mc E rest mc K E Erest mc mv ork

2 K mc K mv A ball whose mass s kg travels at a velocty o < 0, 3, 4> m/s. hat s the knetc energy o the ball? ) < 0, 6, 8 > J ) < 0, 3, 4 > J 3) J 4) 0 J 5) 5 J

3 K mc K Consder an electron (mass 9e-3 kg) movng wth speed v = 0.9c. Its rest energy s 0.8e-3 J, and ts (total) partcle energy s.86e-3 J. hat s ts knetc energy? mv ) 7.3e-3 J ) 3.8e-4 J 3) 8.e-4 J 4).05e-3 J 5).86e-3 J

4 Rest Energy and Identty Example: A statonary nucleus whose mass s kg undergoes spontaneous alpha decay. The orgnal nucleus spts out a He-4 nucleus ( neutrons & protons) o mass kg and the remanng nucleus has a mass o kg. hen the partcles are ar apart (so the electrc repulson s neglgble) what s the combned knetc energy? ntal nal parent System: these partcles Actve surroundngs: none nucleus daughter nucleus partcle E E rest or In the ntal mass s the potental or the nal moton K K K 0 0 K E rest K K E rest. E rest. K m c m m c p d kgc kgc J

5 Chemstry-Scaled Energy Unts ntal nal parent K nucleus daughter nucleus partcle kgc All chemcal nteractons are undamentally electrc nteractons, so nvolve electrc orce and scale wth electron charge. e Joul Joul 9.60 Coulombs e J C 3 J ev Volt Chemcal reactons typcally nvolve 0 mev to 0 ev o energy per molecule Joul Coulombs K J 6.50 J 8 ev ev 4.MeV A nuclear reacton nvolves mllons o tmes more energy than does Chemcal reacton!

6 Systematc Approach to Energy Problems ) Specy a system (the object or object s you re nterested n) ) Specy members o the surroundng that nteract wth the system 3) Specy the ntal state 4) Specy the nal state 5) rte out the Energy Prncple or ths system 6) Use the gven normaton to evaluate all terms you can 7) Solve or the target unknown quantty 8) Check unts and consstency o sgn.

7 You drop a metal ball rom m up. How ast s t gong just beore t hts the ground? y System= ball Actve members o envronment = Earth (neglectng ar s resstance) ntal r ball BallEarth nal v yyˆ y m? mgyˆ ork Energy Relaton Not changng E rest K E K K E E mv E mv v mgy Ball Earth BallEarth BallEarth BallEarth Constant orce, so Ball Earth Ball Earth BallEarth dr r mgyˆ yyˆ mgy Pretty sure v<<c, so Ball Earth K mgy Ball Ball mv gy 9.8 m m 4.4 m s s

8 I we throw the ball down at 5m/s, wll have greater, less, or the same speed when t lands? ) greater ) less 3) The same

9 ork Energy Relaton Slght varaton: You throw a metal ball straght down at 5 m / s rom m up. How ast s t gong just beore t hts the ground? hat changes n our soluton? E System= ball v y 5 m s yˆ ntal r ball Actve members o envronment = Earth (neglectng ar s resstance) BallEarth yyˆ y m mgyˆ Not changng E rest K K K E E Ball Earth BallEarth BallEarth BallEarth Constant orce, so Ball Earth Ball Earth BallEarth dr r mgyˆ yyˆ mgy Pretty sure v<<c, so mv m v v E E Ball Earth v mv mgy mv? v g y v nal 6.7 m s K mgy Ball Ball mv

10 I we throw the ball up at 5m/s, wll have greater, less, or the same speed when t lands compared wth what t had n when thrown 5m/s down? ) greater ) less 3) The same

11 Another Slght varaton: You throw a metal ball straght up at 5 m / s rom m up. How ast s t gong just beore t hts the ground? hat changes now? y v 5 System= ball Actve members o envronment = Earth (neglectng ar s resstance) m s r ball yˆ BallEarth yyˆ y m mgyˆ ork Energy Relaton Not changng E rest K E K K E E m v E v? Ball Earth BallEarth BallEarth BallEarth Constant orce, so Ball Earth Ball Earth BallEarth dr r mgyˆ yyˆ mgy Pretty sure v<<c, so v Ball Earth mv mgy mv v gy v 6.7 m K mgy s Ball Ball mv Nothng Changes!

12 ork Energy Relaton Example: An electron (mass 9e-3 kg) s travelng at a speed o 0.95c n an electron accelerator. Over what dstance would an electrc orce o.6e -3 N have to be appled to accelerate t to 0.99c? y v 0.95cyˆ? yˆ r e 3 e accelerator.6 0 N yˆ v System= electron Actve members o envronment = Accelerator ntal nal y 37m 0.99cyˆ E mc mc mc y mc y dr kg 30 m / s y 3 where N v c

13 Let s say the zard o Oz s balloon has a total mass o 000 kg (ncludng the zard n the basket) and has most o ts volume n the balloon whch has a radu o 0 m. I the Scarecrow, whose mass s 50 kg (he s only made o straw ater al grabs a hold, when t starts ltng o, how ast wll t be gong when t gets 3 m up at whch pont the Scarecrow lets go and drops? Recall that ar has a densty o g / cm 3.

14 Let s say the zard o Oz s balloon has a total mass o 000 kg (ncludng the zard n the basket) and has most o ts volume n the balloon whch has a radu o 0 m. I the Scarecrow, whose mass s 50 kg (he s only made o straw ater al grabs a hold, when t starts ltng o, how ast wll t be gong when t gets 3 m up at whch pont the Scarecrow lets go and drops? Recall that ar has a densty o g / cm 3. Now you try. How much work dd the balloon do on the scarecrow durng hs bre rde? System Actve Surroundngs Intal State nal State ork-energy Relaton Algebra Numbers Check unts and sgn

15 ork by Changng orce r r r r r n nt nal ntal r dr r 0 lm

16 ork by Changng orce Sprng L lm nal r 0 ntal r n nt dr L o xo = 0 x k s x =Derence between trangles areas k s k s x k s x dx x x

17 In an up-comng lab, you ll use a sprng-loaded gun to re a metal ball. I we know the ball s mass, the stness o the sprng and how much t s been stretched, then we should be able to predct where the ball wll ht the ground. Say the sprng s ntally compressed by 0.04m, and when t launches the ball t stretches to a compresson o 0.0m; the ball s 0.05kg and the gun s mounted 0.8m above the ground, then how ar over wll the ball ht the ground? v a =0 (a) v b (b) (c)

18 r (.) Rest Mass,ork by Changng orces Columba Rep 3pm, here RE 6.b (last day to drop) ed (.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 created nor destroyed, but transerred va nteractons. Energy v c E mc mc sys drsys all E mc E rest mc K E Erest mc mv ork