Your commnts So what do w do whn on of th r's is 0 in th quation GmM(1/r-1/r)? Do w nd to driv all of ths potntial nrgy formulas? I don't undrstand springs This was th first lctur I actually larnd somthing that I had nvr sn bfor, rgarding th nw dfinition of potntial nrgy. It's confusing, but cool Whovr got so mad about th appl problm (.g. th guy who's txt got put up during th lctur) nds to shap up and larn som humility. Whovr has th nrv to tll a profssor "you should hav known bttr" on a CHECKPOINT QUESTION nds to rconsidr thir prioritis. W'r all hr bcaus w'r smart, you don't nd to go around bing an arrogant (it got bttr but I can t put it hr) Could w go ovr mchanical nrgy and consrvativ forcs? Ovrall, vrything mad sns, I would just lik it if you quickly xplaind again how potntial nrgy is mixd in with kintic nrgy and work. I found vrything to b difficult bcaus it is th first tim I am larning ths concpts. Still waiting to find out whr to purchas "It is what it has to b to do what it dos" t- shirts/mugs/assortd mrchandis.
Gradbook & Midtrm & Offic Hours A littl commntary on th xam coming up on Oct. Around half th problms purly concptual: Undrstanding concpts is in fact th ky to solving all of th problms. Hav a look at th practic xams. Th first xam is in 2 wks (Wdnsday Oct. 3 at 7pm s plannr) If you hav a conflict you can sign up for th conflict xam in your grad-book. Don t forgt w hav xtra offic hours during xam wk. Mchanics Lctur 8, Slid 2
Physics 211 Lctur 8 Today's Concpts: a) Potntial Enrgy b) Mchanical Enrgy Mchanics Lctur 8, Slid 3
Work don by a Spring Can you spnd mor tim xplaining th spring problms. If you r worrid about th sign: Us formula to gt th magnitud Us situation and knowldg of dfinition of work to gt th sign
Clickr Qustion A box attachd at rst to a spring at its quilibrium lngth. You now push th box with your hand so that th spring is comprssd a distanc D, and you hold th box at rst in this nw location. D During this motion, th spring dos: A) Positiv Work B) Ngativ Work C) Zro work
Clickr Qustion A box attachd at rst to a spring at its quilibrium lngth. You now push th box with your hand so that th spring is comprssd a distanc D, and you hold th box at rst in this nw location. D During this motion, your hand dos: A) Positiv Work B) Ngativ Work C) Zro work
Clickr Qustion A box attachd at rst to a spring at its quilibrium lngth. You now push th box with your hand so that th spring is comprssd a distanc D, and you hold th box at rst in this nw location. During this motion, th total work don on th box is: A) Positiv B) Ngativ C) Zro D
Homwork Problm W spring = ½ k x 2 = ½ (4111) (0.456) 2 = 427 J Mchanics Lctur 8, Slid 8
Homwork Problm W tot = DK W spring = 427J = ½ mv 2 v 2 = 2 * 427 / 12 v = 8.44 m/s Mchanics Lctur 8, Slid 9
Homwork Problm W friction = -mmgd W friction = - (0.45)(12)(9.81)(2.1) W friction = - 111.2 J Mchanics Lctur 8, Slid 10
Homwork Problm W tot = DK W spring + W friction = 427 J - 111.2 J = ½ mv 2 v 2 = 2 * (427-111.2) / 12 v = 7.25 m/s Mchanics Lctur 8, Slid 11
Summary DK Wtotal Lctur 7 Work Kintic Enrgy thorm D U W Lctur 8 For springs & gravity (consrvativ forcs) E K U DE W NC Total Mchanical Enrgy E = Kintic + Potntial Work don by any forc othr than gravity and springs will chang E Mchanics Lctur 8, Slid 12
Rlax. Thr is nothing nw hr It s just r-writing th work-ke thorm: DK W tot DK DU DU W gravity springs N C Dfin Mchanical Enrgy: E K U DK DU W NC W W W gravity springs N C DU DU W gravity springs N C DE W NC In P211 vrything xcpt gravity and springs is NC DE 0 If othr forcs arn't doing work So what xactly is th point of potntial nrgy thn? Also, why is 'U' th charactr usd to rprsnt it? Mchanics Lctur 8, Slid 13
Homwork Problm DE = W NC E f - E i = W friction (U f + K f ) - (U i + K i ) = W friction ½ mv 2-427 J = - 111.2 v 2 = 2 * (427-111.2) / 12 v = 7.25 m/s Mchanics Lctur 8, Slid 14
Finding th potntial nrgy chang: Us formulas to find th magnitud Chck th sign by undrstanding th problm Mchanics Lctur 8, Slid 15
ChckPoint Thr balls of qual mass ar fird simultanously with qual spds from th sam hight h abov th ground. Ball 1 is fird straight up, ball 2 is fird straight down, and ball 3 is fird horizontally. Rank in ordr from largst to smallst thir spds v 1, v 2, and v 3 just bfor ach ball hits th ground. 2 A) v 1 > v 2 > v 3 B) v 3 > v 2 > v 1 C) v 2 > v 3 > v 1 D) v 1 = v 2 = v 3 h 1 3 Thy hav th sam U and K to start with and dlta_u is th sam
ChckPoint A box sliding on a horizontal frictionlss surfac runs into a fixd spring, comprssing it a distanc x 1 from its rlaxd position whil momntarily coming to rst. If th initial spd of th box wr doubld, how far x 2 would th spring comprss? A) x 2 x 2 1 B) x 2 x 2 1 C) x 4 x x 2 1 Mchanics Lctur 8, Slid 17
ChckPoint K 1 2 m v 2 x U 1 2 kx 2 2 x x 2 x 4 2 1 2 1 2 1 A) x B) C) x x A) Bcaus w is proportional to x^2, I thought th doubld spd would rsult in squar root of x. B) Both vlocity and th distanc comprssd ar squard so thy will changs with a 1 to 1 ratio C) bcaus th v is squard, thrfor doubling it, quadrupls th rsult Mchanics Lctur 8, Slid 18
DE DK D U 0 DK 1 2 m v 2 DU 1 2 kx 2 1 1 mv 2 2 2 2 kx x v m k Mchanics Lctur 8, Slid 19
Vrtical Springs M kx 2 x DU = ½ kd 2 - mgd = ½ ky 2 Equilibrium without mass Equilibrium with mass d Thy both look th sam!! Mchanics Lctur 8, Slid 20
From Tusday s lctur Why did you li about th appl? I didn t - w can xplain this in a diffrnt way now and still gt th sam answr: DE = W NC DK + DU 0 W hand DU = W hand Th chang in potntial nrgy of th appl is du to just th work don on it by your hand as you lift it.
From Tusday s lctur Why did you li about th appl? Last tim w usd th Work Kintic Enrgy thorm to xplain this and it says th sam thing: W tot = DK W hand + W gravity = 0 W hand = - W gravity W hand = DU gravity Sam rsult: Th chang in potntial nrgy of th appl is du to just th work don on it by your hand as you lift it.
Fun with balls rolling along tracks track A track B A) Ball on track A wins th rac B) Ball on track B wins th rac C) It s a ti balls arriv at th nd at th sam tim I will ask for voluntrs to xplain th rasoning lading to your slction.
Fun with balls rolling along tracks Explanation for why ball B wins rac Lt s now considr a slightly diffrnt scnario
It s gtting funnr and funnr A) Ball on track A wins th rac B) Ball on track B wins th rac C) It s a ti balls arriv at th nd at th sam tim I will ask for voluntrs to xplain th rasoning lading to your slction.
ChckPoint In Cas 1 w rlas an objct from a hight abov th surfac of th arth qual to 1 arth radius, and w masur its kintic nrgy just bfor it hits th arth to b K 1. In Cas 2 w rlas an objct from a hight abov th surfac of th arth qual to 2 arth radii, and w masur its kintic nrgy just bfor it hits th arth to b K 2. Compar K 1 and K 2. A) K 2 = 2K 1 B) K 2 = 4K 1 C) K 2 = 4K 1 /3 D) K 2 = 3K 1 /2 wrong Mchanics Lctur 8, Slid 26
Lts look at U For gravity: U ( r) G M m +U 0 r R E 2R E 3R E Mchanics Lctur 8, Slid 27
U ( r) What is th potntial nrgy of an objct of on th arths surfac: Clickr Qustion G M m r R E 2R E 3R E A) B) C) U surfac = U surfac = U surfac = GM m 0 GM m R E GM m 2R E R E Mchanics Lctur 8, Slid 28
U ( r) Clickr Qustion G M m What is th potntial nrgy of a objct starting at th hight of Cas 1? A) B) C) U U U 1 1 1 E r G M m R G M m 2 R 3R E G M m E R E 2R E 3R E R E Mchanics Lctur 8, Slid 29
What is th potntial nrgy of a objct starting at th hight of Cas 2? A) B) C) U ( r) U U U 2 2 2 G M m R E G M m 2 R G M m 3R E E Clickr Qustion G M m r R E 2R E 3R E R E Mchanics Lctur 8, Slid 30
GM m G M m U surfac U U 1 2 What is th chang R in potntial 2 Rin Cas 1? What is th chang in potntial in Cas 1? E E G M m 3R E A) B) 1 1 1 G M m DU G M m cas1 2R R 2 R D 1 1 1 G M m U G M m cas1 R 2 2 R R R E Mchanics Lctur 8, Slid 31
GM m G M m U surfac U U 1 2 What is th chang R in potntial 2 Rin Cas 2? What is th chang in potntial in Cas 2? E E G M m 3R E A) D 1 1 1 G M m U G M m cas 2 R 3 3 R R B) D 1 1 2 G M m U G M m cas 2 R 3 3 R R R E Mchanics Lctur 8, Slid 32
GM m D U cas1 DU cas 2 2 R 2G M m 3R What is th ratio DK DK DU 2 2 DU 1 1 2 3 4 1 3 2 A) 2 B) 4 C) 4/3 D) 3/2 Mchanics Lctur 8, Slid 33
In Cas 1 w rlas an objct from a hight abov th surfac of th arth qual to 1 arth radius, and w masur its kintic nrgy just bfor it hits th arth to b K 1. In Cas 2 w rlas an objct from a hight abov th surfac of th arth qual to 2 arth radii, and w masur its kintic nrgy just bfor it hits th arth to b K 2. Compar K 1 and K 2. Chckpoint A) K 2 = 2K 1 B) K 2 = 4K 1 C) K 2 = 4K 1 /3 D) K 2 = 3K 1 /2 Mchanics Lctur 8, Slid 34