Physics for Scientists and Engineers I

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1 Physics for Scieniss nd Engineers I PHY 48, Secion 4 Dr. Beriz Roldán Cueny Uniersiy of Cenrl Florid, Physics Deprmen, Orlndo, FL

2 Chper - Inroducion I. Generl II. Inernionl Sysem of Unis III. Conersion of unis IV. Dimensionl Anlysis V. Problem Soling Sregies

3 I. Objecies of Physics - Find he limied number of fundmenl lws h goern nurl phenomen. - Use hese lws o deelop heories h cn predic he resuls of fuure eperimens. -Epress he lws in he lnguge of mhemics. - Physics is diided ino si mjor res:. Clssicl Mechnics (PHY48). Reliiy 3. Thermodynmics 4. Elecromgneism (PHY49) 5. Opics (PHY49) 6. Qunum Mechnics

4 II. Inernionl Sysem of Unis POWER PREFIX ABBREVIATION QUANTITY Lengh UNIT NAME meer UNIT SYMBOL m 5 9 pe er gig P T G Time second s 6 meg M Mss kilogrm kg 3 kilo k Speed m/s heco h Accelerion m/s dek d Force Newon N - deci D Pressure Pscl P N/m - ceni c Energy Power Joule W J Nm W J/s milli micro nno m µ n Temperure Kelin K - pico p -5 femo f

5 III. Conersion of unis Chin-link conersion mehod: The originl d re muliplied successiely by conersion fcors wrien s uniy. Unis cn be reed like lgebric quniies h cn cncel ech oher ou. Emple: 36 fee/h m/s fee h m 36.7 m/ s h 36s 3.8 fee IV. Dimensionl Anlysis Dimension of quniy: indices he ype of quniy i is; lengh [L], mss [M], ime [T] Dimensionl consisency: boh sides of he equion mus he he sme dimensions. Emple: / [ ] [ L] Noe: There re no dimensions for he consn (/) [ L] [ ] [ ] [ L] T T T [ ] [ T ] [ L] [ L] [ L] L

Significn figure one h is relibly known. Zeros my or my no be significn: E: - Those used o posiion he deciml poin re no significn. - To remoe mbiguiy, use scienific noion.

6 Significn figure one h is relibly known. Zeros my or my no be significn: E: - Those used o posiion he deciml poin re no significn. - To remoe mbiguiy, use scienific noion..56 m/s hs 3 significn figures, deciml plces..56 m/s hs 3 significn figures nd 6 deciml plces.. m hs 3 significn figures. 5 m is mbiguous.5 3 ( figures),.5 3 (3 fig.) Order of mgniude he power of h pplies.

7 V. Problem soling cics Eplin he problem wih your own words. Mke good picure describing he problem. Wrie down he gien d wih heir unis. Coner ll d ino S.I. sysem. Idenify he unknowns. Find he connecions beween he unknowns nd he d. Wrie he physicl equions h cn be pplied o he problem. Sole hose equions. Alwys include unis for eery quniy. Crry he unis hrough he enire clculion. Check if he lues obined re resonble order of mgniude nd unis.

8 MECHANICS Kinemics Chper - Moion long srigh line I. Posiion nd displcemen II. Velociy III. Accelerion IV. Moion in one dimension wih consn ccelerion V. Free fll Pricle: poin-like objec h hs mss bu infiniesiml size.

9 I. Posiion nd displcemen Posiion: Defined in erms of frme of reference: or y is in D. - The objec s posiion is is locion wih respec o he frme of reference. Posiion-Time grph: shows he moion of he pricle (cr). The smooh cure is guess s o wh hppened beween he d poins.

10 I. Posiion nd displcemen Displcemen: Chnge from posiion o - (.) during ime inerl. - Vecor quniy: Mgniude (bsolue lue) nd direcion (sign). - Coordine (posiion) Displcemen Coordine sysem > Only he iniil nd finl coordines influence he displcemen mny differen moions beween nd gie he sme displcemen.

11 Disnce: lengh of ph followed by pricle. - Sclr quniy Displcemen Disnce Emple: round rip house-work-house disnce reled km displcemen Reiew: - Vecor quniies need boh mgniude (size or numericl lue) nd direcion o compleely describe hem. - We will use nd signs o indice ecor direcions. - Sclr quniies re compleely described by mgniude only.

12 II. Velociy Aerge elociy: Rio of he displcemen h occurs during priculr ime inerl o h inerl. g (.) Moion long -is -Vecor quniy indices no jus how fs n objec is moing bu lso in which direcion i is moing. -SI Unis: m/s - Dimensions: Lengh/Time [L]/[T] - The slope of srigh line connecing poins on n -ersus- plo is equl o he erge elociy during h ime inerl.

13 Aerge speed: Tol disnce coered in ime inerl. S g Tol disnce (.3) S g mgniude V g S g lwys > Sclr quniy Sme unis s elociy Emple: A person dries 4 mi 3mi/h nd 4 mi nd 5 mi/h Is he erge speed >,<, 4 mi/h? <4 mi/h 4 mi/(3 mi/h).3 h ; 4 mi/(5 mi/h).8 h o.3 h S g 8 mi/.3h 37.5mi/h

14 Insnneous elociy: How fs pricle is moing gien insn. lim d d (.4) - Vecor quniy - The limi of he erge elociy s he ime inerl becomes infiniesimlly shor, or s he ime inerl pproches zero. - The insnneous elociy indices wh is hppening eery poin of ime. - Cn be posiie, negie, or zero. () - The insnneous elociy is he slope of he line ngen o he s. cure (green line).

15 Insnneous elociy: Posiion Slope of he pricle s posiion-ime cure gien insn of ime. V is ngen o () when Time When he elociy is consn, he erge elociy oer ny ime inerl is equl o he insnneous elociy ny ime. Insnneous speed: Mgniude of he insnneous elociy. Emple: cr speedomeer. - Sclr quniy Aerge elociy (or erge ccelerion) lwys refers o n specific ime inerl. Insnneous elociy (ccelerion) refers o n specific insn of ime.

16 III. Accelerion Aerge ccelerion: Rio of chnge in elociy o he ime inerl in which he chnge occurs. g (.5) - Vecor quniy - Dimensions [L]/[T], Unis: m/s - The erge ccelerion in - plo is he slope of srigh line connecing poins corresponding o wo differen imes. V

17 Insnneous ccelerion: Limi of he erge ccelerion s pproches zero. - Vecor quniy d d lim d d (.6) - The insnneous ccelerion is he slope of he ngen line (- plo) priculr ime. (green line in B) - Aerge ccelerion: blue line. - When n objec s elociy nd ccelerion re in he sme direcion (sme sign), he objec is speeding up. - When n objec s elociy nd ccelerion re in he opposie direcion, he objec is slowing down.

18 - Posiie ccelerion does no necessrily imply speeding up, nd negie ccelerion slowing down. Emple (): -5m/s ; m/s in 5s pricle slows down, g 5m/s - An objec cn he simulneously nd Emple (): ()A ()A ()A ; A s, () bu ()A Emple (3): - The cr is moing wih consn posiie elociy (red rrows minining sme size) Accelerion equls zero. Emple (4): ccelerion elociy - Velociy nd ccelerion re in he sme direcion, is uniform (blue rrows of sme lengh) Velociy is incresing (red rrows re geing longer).

19 Emple (5): - ccelerion elociy - Accelerion nd elociy re in opposie direcions. - Accelerion is uniform (blue rrows sme lengh). - Velociy is decresing (red rrows re geing shorer).

20 g - Equions for moion wih consn ccelerion: (.3) ) ( (. ) (.7) (. ) ) ( (. ) (.7) (.) ) ( ) ( ) ( (. ) (.7) (. ) (.9) (.8) (.9) (.7) (.8) (.7) g g g g missing IV. Moion in one dimension wih consn ccelerion - Aerge ccelerion nd insnneous ccelerion re equl. g

21 PROBLEMS - Chper P. A red cr nd green cr moe owrd ech oher in djcen lnes nd prllel o The -is. A ime, he red cr is nd he green cr m. If he red cr hs consn elociy of km/h, he crs pss ech oher 44.5 m, nd if i hs consn elociy of 4 km/h, hey pss ech oher 76.6m. Wh re () he iniil elociy, nd (b) he ccelerion of he green cr? r 4km/h r km/h O X r 76.6m 3 km h m 4.m / s h 36s km X r 44.5 m d m X g m r g r g r g () () r r 44.5m 8s r 5.55m / s 76.6m 6.9s r.m / s r r g g.5 g.5 g g g g g (6.9s).5 (6.9s) (8s).5 (8s) g g The cr moes o he lef (-) in my reference sysem <, < g. m/s g 3.55 m/sc

22 P: A he insn he rffic ligh urns green, n uomobile srs wih consn ccelerion of. m/s. A he sme insn, ruck, reling wih consn speed of 9.5 m/s, oerkes nd psses he uomobile. () How fr beyond he rffic signl will he uomobile oerke he ruck? (b) How fs will he uomobile be reling h insn? c. m/s, c m/s s Cr (m) Truck s 9.5 m/s d? (m) T d 9.5 () Truck d c T C c d.5 (.m / s). () Cr ( ) s d (9.5m / s)(8.63s) 8m ( b) d (.m / s) (8m) 9m / s f c f P3: A proon moes long he -is ccording o he equion: 5, where is in meers nd is in seconds. Clcule () he erge elociy of he proon during he firs 3s of is moion. () 3 () ( 5)() 3 ( )() 3 g 8 m/s. 3 (b) Insnneous elociy of he proon 3s. d ( ) 5 (3s) 5 3 m / s d (c) Insnneous ccelerion of he proon 3s. ( ) m / s (3s) d d

23 (d) Grph ersus nd indice how he nswer o () (erge elociy) cn be obined from he plo. (e) Indice he nswer o (b) (insnneous elociy) on he grph. (f) Plo ersus nd indice on i he nswer o (c). 5 5 P4. An elecron moing long he -is hs posiion gien by: 6 ep(-) m, where is in seconds. How fr is he elecron from he origin when i momenrily sops? () when ()?? d d 6e 6e 6e ( ) ( ) ; ( e > ) s ( ) 6/ e 5. 9m

24 P5. When high speed pssenger rin reling 6 km/h rounds bend, he engineer is shocked o see h locomoie hs improperly enered ino he rck from siding nd is disnce D 676 m hed. The locomoie is moing 9 km/h. The engineer of he high speed rin immediely pplies he brkes. () Wh mus be he mgniude of he resuln decelerion if collision is o be oided? (b) Assume h he engineer is when he firs spos he locomoie. Skech () cures represening he locomoie nd high speed rin for he siuion in which collision is jus oided nd is no quie oided. s Trin Locomoie d L (m) > s D Dd L (m) T 6km/h 44.7 m/s T D moemen wih <ce L 9 km/h 8.5 m/s is consn d d L L d 8.5 L () Locomoie L 8.5 D d () T T L T Trin

25 P5. Tf Tf T T (3) (4) d T L T T ( D d 38.3m 44.7m/ s ( 44.7m / s)(8.5m / s) 36m ( eq. ) d d L ) T (44.7m / s) (676m d ) L (4) L L / s (3) from () 47.4s 8.5 () (3) T d L 36m / s 38.3m.947m / s Locomoie Collision cn be oided L T T - Collision cn be oided: Trin Slope of () s. locomoie 47.4 s (he poin were boh Lines mee) insnneous locom > Slope of () s. rin Collision cn no be oided - Collision cnno be oided: Slope of () s. locomoie 47.4 s < Slope of () s. rin

26 - The moion equions cn lso be obined by indefinie inegrion: d d d d C; ( )() C C d d d d d ( ) d () () C' d C' d d C'; V. Free fll Moion direcion long y-is ( y > upwrds) Free fll ccelerion: (ner Erh s surfce) -g -9.8 m/s (in ce ccelerion mo. eqs.) Due o griy downwrd on y, direced owrd Erh s cener

27 Approimions: - Loclly, Erh s surfce essenilly fl free fll hs sme direcion slighly differen poins. - All objecs he sme plce he sme free fll (neglecing ir influence). VI. Grphicl inegrion in moion nlysis From () ersus grph inegrion re beween ccelerion cure nd ime is, from o () d Similrly, from () ersus grph inegrion re under cure from o () d

28 P6: A rocke is lunched ericlly from he ground wih n iniil elociy of 8m/s. I scends wih consn ccelerion of 4 m/s o n liude of km. Is moors hen fil, nd he rocke coninues upwrd s free fll pricle nd hen flls bck down. () Wh is he ol ime elpsed from keoff unil he rocke srikes he ground? (b) Wh is he mimum liude reched? (c) Wh is he elociy jus before hiing ground? ) Ascen 4m/s y y y m y km -g 4m/s, 3, 4 -g y y.5 (4m / s s ) (53.48s) 8m / s 94m / s ) Ascen -9.8 m/s m s g 94 / 9. 96s 9.8m / s Tol ime scen s9.96 s s 8m/s 3 3) Descen -9.8 m/s s y ol s 9.96 s 4. s37.6 s h m y y - 4 m -4.9 (94 m/s)(9.96s)-(4.9m/s )(9.96s) 44 m h m 4.4 km 3( ) g g 53.35m / s 3 4 4

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