Energy Dissipation Gravitational Potential Energy Power

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Rose Bryan
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03 negy Dissiption Gvittionl Potentil negy Powe Couse

1 Lectue 4 Chpte 8 Physics I negy Dissiption Gvittionl Potentil negy Powe Couse wesite: Lectue Cptue: , Fll 03, Lectue 4

2 xm II Info xm II Mon Nov 4, 9:00-9:50m, OH 50. xm II coves Chptes 5-8 Sme fomt s xm I Pio xmples of xm II posted Ch. 5: Using Newton s Lws, Fiction, Unifom Cicul motion Ch. 6: Univesl Lw of Gvittion, Keple s Lws Ch. 7: Wok & negy Ch. 8: Consevtion of negy xm Review Session TBA, Bll , Fll 03, Lectue 4

3 Outline Chpte 8 Consevtion of negy with Dissiptive foces Gvittionl Potentil negy scpe Velocity Powe 95.4, Fll 03, Lectue 4

4 Kinetic enegy K mv Gvittionl potentil enegy Potentil enegy of sping Review U mgy U U(x)U(0) U sping kx 0 x F x dx y y K U mgy y K U mgy Totl Mechnicl negy K U x Consevtion of Mechnicl negy K mv mgy U U K U mgy mv W net K 95.4, Fll 03, Lectue 4

wok done on the oject W W net net F net dl F F dl F C Recll, lst clss dl U W C K U F

5 Wok-K theoem with nonconsevtive foces Conside n oject expeiences consevtive nd nonconsevtive foces: F net F C F Since the wok-k pinciple woks fo ANY foces, the totl wok done on the oject W W net net F net dl F F dl F C Recll, lst clss dl U W C K U F W NC NC C dl NC W net K NC K y F NC F C d K ( U U ) W NC x K U K U W NC 95.4, Fll 03, Lectue 4

6 Geneliztion of enegy consevtion. K U K U W NC Mech. negy t points, W NC Mech. negy conveted to Theml negy If fiction cts on the oject, then consevtion of mechnicl enegy no longe holds. Mech. enegy is conveted into het, Theml negy Be ceful not to omit the wok done y the nonconsevtive foces 95.4, Fll 03, Lectue 4

7 xmple I: Block sliding down Inclined Plne A lock of mss m slides down plne of length l nd ngle α. Find the speed of the lock t the ottom of the incline plne ssuming tht it stts fom est nd the coefficient of fiction μ is constnt. F f α mg α 95.4, Fll 03, Lectue 4

8 xmple I: A lock of mss m slides down plne of length l nd ngle α. Find the speed of the lock t the ottom of the incline plne ssuming tht it stts fom est nd the coefficient of fiction μ is constnt. Theml enegy is geneted 95.4, Fll 03, Lectue 4

9 Gvittionl Potentil negy (I) We hve so f witten ne the sufce of the th : the foce of gvity: F m g the gvittionl potentil enegy: U mgh mg U mgh F g U G? F g G mm ˆ Howeve, ememe, the exct definition of the gvittionl foce is 95.4, Fll 03, Lectue 4 F g G mm Newton s lw of Univesl gvittion Let s otin the genel gvittionl potentil enegy function: U? G ˆ

d F g ˆ U Gvittionl Potentil negy (II) dl W g F g G mm W g

=0) t, whee the foce is lso zeo, nd To otin the genel P

10 d F g ˆ U Gvittionl Potentil negy (II) dl W g F g G mm W g F g d ˆ ˆ d U So, we cn use 0 U U W g d ( ) It only depends on the end points, so it s consevtive foce nd we cn intoduce potentil enegy W g K Let s tke efeence point (U =0) t, whee the foce is lso zeo, nd To otin the genel P function, we eplce with, so: Gvittionl P: U g ( ) 95.4, Fll 03, Lectue 4

11 Gvittionl Potentil negy (III) Newton s lw of Univesl gvittion Gvittionl Potentil negy F g G mm U g G mm ˆ Consevtion of negy fo gvity (exct) K U K U mv mv constnt 95.4, Fll 03, Lectue 4

scpe Velocity We e used to thinking tht n oject shot up fom the th s sufce will etun to th. Is this lwys the cse? Wht is the lowest speed we cn lunch ocket nd hve it neve come ck?

12 scpe Velocity We e used to thinking tht n oject shot up fom the th s sufce will etun to th. Is this lwys the cse? Wht is the lowest speed we cn lunch ocket nd hve it neve come ck? i Ki U i mvesc R K U 0 f f f Consevtion of negy fo gvity f i esc mv 0 R U K f R f mm G 0 K i mv esc mm Ui G R 0 v esc GM R v esc. km / s This is clled escpe velocity 95.4, Fll 03, Lectue 4

13 Powe The vege Powe is the wok done divided y the time it tkes to do the wok. P W t wok done time tken to y foce do this wok The instntneous Powe is the te t which wok is done P dw dt d ( F dl ) dt F dl dt F v Units Wtts = Joules/sec 95.4, Fll 03, Lectue 4

14 ConcepTest Time fo Wok Mike pefomed 5 J of wok in 0 secs. Joe did 3 J of wok in 5 secs. Who poduced the gete powe? A) Mike poduced moe powe B) Joe poduced moe powe C) oth poduced the sme mount of powe Becuse powe = wok / time, we see tht Mike poduced 0.5 W nd Joe poduced 0.6 W of powe. Thus, even though Mike did moe wok, he equied twice the time to do the wok, nd theefoe his powe output ws lowe.

v 0 0 v f 0 m / s The wok done y the moto in cceleting the c cn e found fom the wok-k pinciple: 0 W K K By

15 xmple: Avege powe (c) A cetin 000 kg c cn ccelete fom est to speed of 0 m/s in time of 0 s. Wht vege powe must the moto poduce in ode to cuse this cceletion? v 0 0 v f 0 m / s The wok done y the moto in cceleting the c cn e found fom the wok-k pinciple: 0 W K K By definition, the vege Powe is P W t P W t wok done time tken to 95.4, Fll 03, Lectue 4 f K t i mv f mv f 000kg(0m / 0s 0 s is the time tken fo this wok y foce do this wok s) 0000Wtt 0kW

16 xmple: Avege powe (unne) How much powe does it tke 50-kg unne to un up 5 m high hill in 0 s? h The wok done y the unne is: W mgh 0 s is the time tken fo this wok By definition, the vege Powe is P W t wok done time tken to y do foce this wok P W t mgh t 50kg(0m / s 0s )(5m) 50Wtt 95.4, Fll 03, Lectue 4

17 Thnk you See you on Wednesdy 95.4, Fll 03, Lectue 4

10 m, so the distance from the Sun to the Moon during a solar eclipse is. The mass of the Sun, Earth, and Moon are = =

10 m, so the distance from the Sun to the Moon during a solar eclipse is. The mass of the Sun, Earth, and Moon are = = Chpte 1 nivesl Gvittion 11 *P1. () The un-th distnce is 1.4 nd the th-moon 8 distnce is.84, so the distnce fom the un to the Moon duing sol eclipse is 11 8 11 1.4.84 = 1.4 The mss of the un, th, nd Moon