Physics 100: Lecture 1
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- Bartholomew Welch
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1 Physics : Lecure Agen for Toy Aice Scope of his course Mesuremen n Unis Funmenl unis Sysems of unis Conering beween sysems of unis Dimensionl Anlysis -D Kinemics (reiew) Aerge & insnneous elociy n ccelerion Moion wih consn ccelerion Physics : Lecure, Pg
2 Course Info & Aice See info on he Worl Wie Web (heily use in Physics ) Go o hp:// n follow courses link o he Physics homepge Course hs seerl componens: Lecure: (me lking, emos n Acie lerning) Discussion secions (group problem soling) Homework ses, Web bse Lbs: (group eplorion of physicl phenomen) If you miss lb or iscussion you shoul lwys ry o mke i up s soon s possible in noher secion!! The firs few weeks of he course shoul be reiew, hence he pce is fs. I is imporn for you o keep up! Physics : Lecure, Pg
3 Lecure Orgnizion Three min componens: Lecurer iscusses clss meril» Follows lecure noes ery closely Lecurer oes s mny emos s possible» If you see i, you go beliee i!» Look for he symbol Suens work in groups on concepul Acie Lerning problems» Usully hree per lecure Physics : Lecure, Pg 3
4 Scope of Physics Clssicl Mechnics: Mechnics: How n why hings work Clssicl:» No oo fs ( << c)» No oo smll ( >> om) Mos eeryy siuions cn be escribe in hese erms. Ph of bsebll Orbi of plnes ec... Physics : Lecure, Pg 4
5 Unis How we mesure hings! All hings in clssicl mechnics cn be epresse in erms of he funmenl unis: Lengh Mss Time L M T For emple: Spee hs unis of L / T (i.e. miles per hour). Force hs unis of ML / T ec... (s you will lern). Physics : Lecure, Pg 5
6 Lengh: Disnce Lengh (m) Rius of isible unierse 6 To Anrome Gly To neres sr 4 6 Erh o Sun.5 Rius of Erh Sers Tower 4.5 Foobll fiel. Tll person Thickness of pper -4 Welengh of blue ligh 4-7 Dimeer of hyrogen om - Dimeer of proon -5 Physics : Lecure, Pg 6
7 Time: Inerl Time (s) Age of unierse 5 7 Age of Grn Cnyon yers 9 One yer 3. 7 One hour Ligh rel from Erh o Moon.3 One cycle of guir A sring -3 One cycle of FM rio we 6-8 Lifeime of neurl pi meson -6 Lifeime of op qurk 4-5 Physics : Lecure, Pg 7
8 Mss: Objec Mss (kg) Milky Wy Gly 4 4 Sun 3 Erh 6 4 Boeing Cr 3 Suen 7 Dus pricle -9 Top qurk 3-5 Proon -7 Elecron 9-3 Neurino -38 Physics : Lecure, Pg 8
9 Unis... SI (Sysème Inernionl) Unis: mks: L = meers (m), M = kilogrms (kg), T = secons (s) cgs: L = cenimeers (cm), M = grms (gm), T = secons (s) Briish Unis: Inches, fee, miles, pouns, slugs... We will use mosly SI unis, bu you my run cross some problems using Briish unis. You shoul know how o coner bck & forh. Physics : Lecure, Pg 9
10 Conering beween ifferen sysems of unis Useful Conersion fcors: inch =.54 cm m = 3.8 f mile = 58 f mile =.6 km Emple: coner miles per hour o meers per secon: mi hr mi hr 58 f mi 3. 8 m f 36 hr s. 447 m s Physics : Lecure, Pg
11 Dimensionl Anlysis This is ery imporn ool o check your work I s lso ery esy! Emple: Doing problem you ge he nswer isnce = (elociy ime ) Unis on lef sie = L Unis on righ sie = L / T T = L T Lef unis n righ unis on mch, so nswer mus be wrong!! Physics : Lecure, Pg
12 Lecure, Ac Dimensionl Anlysis The perio P of swinging penulum epens only on he lengh of he penulum n he ccelerion of griy g. Which of he following formuls for P coul be correc? P = (g) P g () (b) (c) P g Gien: hs unis of lengh (L) n g hs unis of (L / T ). Physics : Lecure, Pg
13 Lecure, Ac Soluion Relize h he lef hn sie P hs unis of ime (T ) Try he firs equion () L 4 L L T T T 4 No Righ!! P g () (b) (c) P g P g Physics : Lecure, Pg 3
14 Lecure, Ac Soluion Try he secon equion L L T T T (b) No Righ!! P g () (b) (c) P g P g Physics : Lecure, Pg 4
15 Try he hir equion Lecure, Ac Soluion (c) L L T T T This hs he correc unis!! This mus be he nswer!! P g () (b) (c) P g P g Physics : Lecure, Pg 5
16 Moion in imension In -D, we usully wrie posiion s ( ). Since i s in -D, ll we nee o inice irecion is + or. Displcemen in ime = - is = ( ) - ( ) = - some pricle s rjecory in -D Physics : Lecure, Pg 6
17 -D kinemics Velociy is he re of chnge of posiion Aerge elociy in he ime = - is: ( ) ( ) rjecory V = slope of line connecing n. Physics : Lecure, Pg 7
18 -D kinemics... Consier limi Insnneous elociy is efine s: ( ) ( ) so ( ) = slope of line ngen o ph. Physics : Lecure, Pg 8
19 -D kinemics... Accelerion is he re of chnge of elociy Aerge ccelerion in he ime = - is: ( ) ( ) An insnneous ccelerion is efine s: ( ) ( ) ( ) using ( ) ( ) Physics : Lecure, Pg 9
20 Recp If he posiion is known s funcion of ime, hen we cn fin boh elociy n ccelerion s funcion of ime! ( ) Physics : Lecure, Pg
21 More -D kinemics We sw h = / In clculus lnguge we woul wrie =, which we cn inegre o obin: ( ) ( ) ( ) Grphiclly, his is ing up los of smll recngles: () = isplcemen Physics : Lecure, Pg
22 -D Moion wih consn ccelerion High-school clculus: Also recll h n n n cons Since is consn, we cn inegre his using he boe rule o fin: Similrly, since we cn inegre gin o ge: ( ) Physics : Lecure, Pg
23 Recp So for consn ccelerion we fin: Plne w/ lighs cons Physics : Lecure, Pg 3
24 Lecure, Ac Moion in One Dimension When hrowing bll srigh up, which of he following is rue bou is elociy n is ccelerion he highes poin in is ph? () Boh = n =. (b), bu =. y (c) =, bu. Physics : Lecure, Pg 4
25 Lecure, Ac Soluion Going up he bll hs posiie elociy, while coming own i hs negie elociy. A he op he elociy is momenrily zero. Since he elociy is coninully chnging here mus be some ccelerion. In fc he ccelerion is cuse by griy (g = 9.8 m/s ). (more on griy in few lecures) The nswer is (c) =, bu. Physics : Lecure, Pg 5
26 Physics : Lecure, Pg 6 Useful Formul Plugging in for : Soling for : ) (
27 Physics : Lecure, Pg 7 Alerne (Clculus-bse) Deriion ) ( (chin rule) ) ( ) - ( ( = consn)
28 For consn ccelerion: Recp: Wshers cons From which we know: ( ( ) ) Physics : Lecure, Pg 8
29 Problem A cr is reling wih n iniil elociy. A =, he rier pus on he brkes, which slows he cr re of b o b =, = Physics : Lecure, Pg 9
30 Problem... A cr is reling wih n iniil elociy. A =, he rier pus on he brkes, which slows he cr re of b. A wh ime f oes he cr sop, n how much frher f oes i rel? b =, = = = f, = f Physics : Lecure, Pg 3
31 Problem... Aboe, we erie: = + Relize h = - b Also relizing h = = f : fin = - b f or f = / b Physics : Lecure, Pg 3
32 Problem... To fin sopping isnce we use: ( ) In his cse = f =, = n = f ( b ) f f b Physics : Lecure, Pg 3
33 Problem... So we foun h f b, f b Suppose h o = 65 mi/hr = 9 m/s Suppose lso h b = g = 9.8 m/s Fin h f = 3 s n f = 43 m Physics : Lecure, Pg 33
34 Re! Tips: Before you sr work on problem, re he problem semen horoughly. Mke sure you unersn wh informion is gien, wh is ske for, n he mening of ll he erms use in sing he problem. Wch your unis! Alwys check he unis of your nswer, n crry he unis long wih your numbers uring he clculion. Unersn he limis! Mny equions we use re specil cses of more generl lws. Unersning how hey re erie will help you recognize heir limiions (for emple, consn ccelerion). Physics : Lecure, Pg 34
35 Scope of his course Recp of oy s lecure Mesuremen n Unis (Chper ) Sysems of unis (Te: -) Conering beween sysems of unis (Te: -) Dimensionl Anlysis (Te: -3) -D Kinemics (Chper ) Aerge & insnneous elociy n ccelerion (Te: -, -) Moion wih consn ccelerion (Te: -3) Emple cr problem (E. -7) Look Te problems Chper : # 49, 54, 7, Physics : Lecure, Pg 35
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