PHYSICS: MIDTERM MATHEMATICAL MODELS NAME: TYPE OF PHYSICAL QUANTITY Distance d m - How far an object is located from the origin.
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1 HYSCS: MDTERM MATHEMATCAL MODELS NAME: CHATER NTRODUCTON TO HYSCS HYSCAL QUANTTY SYMBOL UNTS MATH MODEL DEFNTON TYE OF HYSCAL QUANTTY Ditance - How fa an object i locate fo the oiin. Scala oition x o - Ditance + iection Diplaceent x o x xf - xi Chane between two poition CHATER MOTON WTH CONSTANT VELOCTY Spee / Chane between two poition oe chane in tie. Scala Velocit x o / Spee + iection Slope of poition. clock eain aph. CHATER Motion with contant acceleation xf - xi Acceleation ax o a / a t Chane between two elocitie oe chane in tie. Slope of elocit. clock eain aph. CHATER & CHATER MOTON WTH CONSTANT VELOCTY & MOTON WTH CONSTANT ACCELERATON MWCV MWCA oition xf xi x t xf xi x t ax t Velocit xf xi ax t (contant) acceleation Diplaceent (Aea une the aph) Velocit afte an iplaceent ax 0 (contant) xf - xi a t x x t x f i t (contant) xf xi ax x
2 CHATER V VECTORS B B in Vetical coponent (-coponent) B B in ( ) Hoizontal coponent (x-coponent) Bx B co ( ) : hical uantitie that euie of a anitue (nube) an a iection. Exaple: oition, iplaceent, elocit, acceleation, Foce, pule, Moentu, Electic cuent, anetic fiel, Electic Fiel. Scala: hical uantitie that euie onl of a anitue (nube) Reultant thaoean Theoe B ( Bx) + (B) Exaple: Ma, olue, enit, tepeatue, pee, itance, ene, wok, powe, Voltae, Reitance. CHATER V FORCES Foce of Eath F EonO N Foce that Eath exet on an object. Ma k Aount of atte in an object. cala Gaitational contant / Acceleation of an object ue to the foce exete b Eath Slope of F EonO. a. Foce of the Spin F SonO N Foce that a pin exet on an object. F SonO L k Elonation L Chane between two lenth of a tetche/copee pin. Spin contant k N/ Foce of kinetic Fiction F k N k Ratio between the foce exete b the pin on an object an the elonation caue on the pin. Slope of F SonO. Elonation. cala F k F N Foce exete b a uface, paallel to the uface. Noal Foce F N N Foce exete b a uface, pepenicula to the uface. Coefficient of kinetic Fiction k - Ratio between two foce F k & F N Slope of F k. F N. cala Tenion Foce F T N - Foce exete b a cable, ope, thea, tin, etc. ecto
3 CHATER V ROJECTLE MOTON FREE FALL VERTCAL LAUNCH HORZONTAL LAUNCH ANGLED LAUNCH oition HOW FAR (at an ien t) Velocit HOW FAST (at an ien t) Acceleation (at an ien t) Tie to each axiu heiht GONG U Tie in Fliht COMNG DOWN ( ½ t ) ( ½ t ) + ( i t ) + ( i) ( ½ t ) ( ½ t ) + ( i t ) + ( i) V ( t) + i V ( t) + i V ( t) + i V ( t) + i t t t - i t t t - i nitial elocit i 0 i - ( t ) i 0 i - ( t ) nitial elocit (NO t) ( i ) ( ) - ( ) ( i ) ( ) - ( ) Maxiu heiht (NO t) ( ) - ( ) i ( ) - ( ) i CHATER V CRCULAR MOTON Cicufeence c c eiete of a cicle Scala Tanential elocit T / Centipetal acceleation a C / Velocit of an object oin in cicula otion. Tanential to the T cicle an pepenicula to the Centipetal Foce. T Acceleation of an object oin in cicula otion. Towa the cente of the cicle. ac Centipetal Foce F C N Fc An tpe Foce that keep an object oin in cicula otion. Towa the cente of the cicle.
4 HYSCS: FNAL EXAM MATHEMATCAL MODELS NAME: CHATER V UNVERSAL GRAVTATON Gaitational Foce F G N G G Gaitational contant / G Unieal aitational contant G Velocit of an obitin object in / CHATER X MULSE & MOMENTUM F Foce of attaction between two object of ae an. Gaitational contant of an planet. N / k G x 0 - Contant of popotionalit G obite Vin Velocit of an object obitin anothe object. cicle Moentu p k/ p Aount of otion of an object. pule N F t ouct of Foce tie chane in clock eain. Foce exete oe a peio of tie that chane the oentu of an object. MULSE CHANGES MOMENTUM i + p F The final oentu of the te will eual the initial oentu of the te plu the The initial oentu of te can chane onl if an ipule i eliee on the te. eliee ipule on the te. CONSERVATON OF MOMENTUM The total oenta of the te ae conee afte a colliion. i f p p p The total oenta befoe the colliion eual the total oenta afte the colliion. CHATER X WORK OWER - ENERGY i i F pf Wok W J W F Foce paallel to Gaitational otential Ene U G J U G otential to o oethin otential to o oethin ue to a chane in a etical poition () Scala Scala Kinetic Ene KE J KE ½ otential to o oethin ue to a chane in a elocit () Scala Elatic otential otenti otential to o oethin ue to a chane in the Ene U S J U S ½ k L elonation (L) of an elatic object. Scala owe W W / t Rate at which wok i one cala
5 WORK CHANGES ENERGY CONSERVATON OF MECHANCAL ENERGY CHATER X TORQUE U Gi + W U GF KE i + W KE F U Si + W U SF U Gi + KE i + U Si + W U GF + KE F + U SF The initial ene of the te can chane onl if wok i one on the te. The final ene of the te will eual the initial ene of the te plu the wok one on the te. The total echanical ene of the te i neithe ceate no etoe. The total echanical ene i conee. KE Toue N ROTATONAL EQULBRUM CHATER X ELECTRCTY F Foce pepenicula to opet of a foce to ake an object otate. When the foce cauin the toue: F EonO CW CCW The u of the Toue in the counte clockwie iection ( ccw) eual the u of the Toue in the clockwie iection ( cw) Electotatic contant K N / C K 9 x 0 9 Contant of popotionalit Electic foce Coulob law F on N Fon K Attactie o epulie foce between two chae of chae an Electic fiel (at an point) Electic fiel (felt b a chae paticle) E N/ E K F E Space aoun an electic Chae. Electic fiel felt at an point aoun that electic chae. Space aoun an electic Chae. Electic fiel felt b a chae place aoun that electic chae. Electic otential Ene U J Electic potential V Chane in electic potential (Voltae) U K V ( K ) A otential to chane the elocit of chae paticle. otential to chane the ene of an electic chae place between two electic plate with a contant Electic fiel (E) an a itance (). V E Diffeence between two iffeent electic potential. cala cala cala Chane in Electic otential Ene U J U V Ene that chane when a chae oe fo one place to anothe place. cala
6 CHATER X ELECTRC CRCUTS Electic cuent A t Flow of electic chae () pe unit of tie (t). Chae in otion Oh law V R A V V R V Electic cuent () i iectl popotional to the chane in electic potential (V). Electic cuent () i ineel popotional to the eitance (R). owe (Electic) W R V R Rate at which electic wok i one. Scala HYSCAL QUANTTY CRCUTS N SERES CRCUTS N ARALLEL ELECTRC CURRENT Sta the ae T VOLTAGE V T V + V + V Sta the ae RESSTANCE R T R + R + R R R R R OWER T T T 3 CHATER XV MAGNETSM chae paticle F B N B in Manetic foce on a F B Foce (F B) felt b a chae paticle () that tael with elocit () pepenicula to a anetic fiel (B). The iection of thi foce i pepenicula to both the iection of the anetic fiel an the iection of the elocit of the paticle. Manetic foce on a cuent cain wie F B N L B in F B Foce (F B) felt b a wie of lenth (L) cain an electic cuent () place pepenicula to a anetic fiel (B). The iection of thi anetic foce i pepenicula to both the iection of the anetic fiel an the iection of the electic cuent.
7 CHATER XV WAVES eio of a iple penulu: T L T eio (econ) L Lenth of the tin (ete) G aitational contant (/ ) eio of a a-pin te: T k T eio (econ) a (kiloa) k Spin contant (N/) eio T T f Tie fo one ccle. Scala Ditance peak to peak eaue in the tie aph. Feuenc f Hz Nube of ccle in one econ. Scala Waelenth f T Lenth of one ccle. Ditance peak to peak eaue in the poition aph. Spee (wae) / Chane in poition oe the chane in tie of a itubance. Funaental Feuenc of a tanin wae on a tin o in an open pipe ( L ) f Funaental feuenc (Hetz) f wae pee (kiloa) L Lenth of pin o open pipe (ete) Feuenc of a an haonic of a tanin wae on a tin o in an open pipe f n n ( L ) (n,, 3, 4,... ) f n Feuenc of the haonic (Hetz) wae pee (kiloa) L Lenth of pin o open pipe (ete) n nube of the haonic
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