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Solo eAp. 11. OINAI.lICA DE UN "UNTO :lL\TfJlIAI,
resultado del dlllSlll'rolJo de J. fisica del átomo, l. situación es aná·101Ja. Las ecuaciones da m-uinica cuántica tlmbiell oftllCen eu ellímite (para ma!;~ mayores qua las del 'tomo) lu ecuaciones de lamecániu clá~iea. Por consiguiente. lo. mecánica clúica tambi'¡n Hba incluido en la mecánic. cuántica COmo IRI easo limite.
Asl, PUM, el fomento de las ciencias no h. tborndOl la mecállie.elbic., sino que ha mOlltndo su limit.ada aplicación. Le. mecánicaclásic., basad. en las leyes de Newtoll, "la mecánica de los cuerposde grandes masu (en comparaci6n con la masa de 103 UOmOS). quese mueven a pequeli... velocidades (en complltDe/ón con 111; de l.lut).
§ 7, Primera ley de Newfon. Sistemas inercialesde referend.!l
La primera ley de Newton se enuncia del ailuiente modo: tockJcuupo ~rllUJnt(% en su Ulaoo tk rtp060 o tk movimIento rectmMO1UI1lornul mftnllllf otroJ cutrpot no actúen sob,.,. IllI le obliguen a cam·btar tk utado. Lo!l dos indieadOll estados se d.lstioruen por :rer lo. ateluación de cuerpo igu.1 • cuo. Por esta cau.sa, la enunciación de laprimera ley puede tomu la silUiente forma: la velocidad de todocuerpo queda coutante (en puticular, nula), milltltras l. acci6nde otros cuerpos sobre istel:lo pro\'oque su varladÓn.
r... primera ley de N....ton se cumple no en todo s.is.tema de refe·renei•. Mis. arriba ya iodieamos que al cadcter del movimiento depende del sisten1.1 de ref6l"encia elegido. Consideremos dos sistemasde referencia en mo\'lmiento COIl cierta acelecación, uno respecto• otro. Si con relación a uno de ell03 el cuerpo at' en repOllO. en loque ats6.e al segundo se mover.i, por lo visto, con aceleracl6n. Porlo t.nto, l. primera ley de Newton no puede cumplirse IIn los dos.sistemu a.l mismo tiempo.
Recibe el nombre de illerclo/ el sislema de referencia. en el que secumple la. primera lay de Nawton. La propio loy es a veccs llamadaI~/I de Inercia. El sistema da reforonda en el que la primera ley deNowton no se cUlnple, denominase sistema no lnereisl do refereocia,Todo ,istemll de l'9ferenela que respecto de cierto sistemll inercialesU en movimiento reclillneo uniforme (M decir, a velocid.d constanle). tllmbién ser' inerCilll. Esto se estudlarli con mú delalle enel ! 12.
De forma experimental" ha estoblecido que el sistema de referencia cuyo centro coincide con 01 Sol, mientras que los ojes est'ndirilidos hacia estrellas e1l1l1idas del modo corre.spondiante, es iner·ei.l. este recibe el nombre do fitiema IuliodnlriaJ de re/ereneio(helios en griego Sol). Cu.lquiec s.i.stema de refereneia en moYimienLotllCtiHneo uniforme respeeLo del sistema heliocéntrico, será ~nllC'C111.
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(8.8)
I l. &EGUND... !.EY DE NK\\'TOl'l ~7
titnt un. fonntl mb complie.d.:
•• 8P-Vl "'le' ( .7)
Aqul m e3 la Ibm.da tn4.Ja en reprno del cuerpo (pan u"'" O), e, la"elocldad do la luz; en el vacío. La inlerpretación de (8.7) puede serl. slguienle: la masa del euf'rpo no qued. consl.lnle (como se suponll'en meeAniea newlonianll), sino que varl:a con JI velocidad según la.l.y
m(v)-v~·
Corno resultado, la e:-:prcslón (8.7) puede ser rf'prosenlada como
p_m.(v)v, (8.9)
lo que es análogo a (8.4).Lo mua m (v) defioida con la fórmula (8.8) rooibe el nombre de
masa reÚltlvi.la. o l1\Q,SQ tn mDcimitnto. En adelante, la dcsiguat'eme»con el símbolo m•.
§ 9. Segundo ley de Newton1.1 segunda ley de N_ton dico: la. velocidad de tyu/ad4n de 4z
canlidad de mouimienlo dtl aarpo ti igual a. lA /lI.uUJ. F apUcadll Do 1/:
d, F 9?f"'" . ( .1)
La ecullción (9.t) denominase ~ua.ci6n de mDt'imitnto del cuerpo.Suslitu}'endo p en (8.4) por el producto mv }' tornando en eonsi
der.eión que en la mllCánlca ncwtoniana .!O supone que la masa esconstanle, es posible represenur la correlación (9.1) Ilsi
m.w = F, (\I.2}
donde w _ v, Do l.l&to lDodo hem08l1egndo o otr. enunciación de 'a.H,uDda. lay de Newlon: el producto de ÚI mala Ml cucrpo por '" lU:eleraci6n ti ilUAl a la /uerUJ que achJo I()bre ll.
Lo con-elaeióll (9.2) provoc.ba y cOlllillúa pro"ocando entro loslisicos Ilgudas di.scusiolle5. HIlSla la feena no hay UDIl interprolocióngene.nl de. ditno correlad6n. La dificultad radica en que no hayprocedimientos independiente5 para definir m y r, magnitudes queentran en la ecuación (9.2). P/lI'I deterrninll' IlII' de ellas (m o F>es preciso nacO' uso de l. correlación (9.2) en dOllde estu dos m.~r·tudes están ligadas entro sí y con la aceleraci6nw. Por ejemplo, en ellibro de S. E. Jaikín .Fundamentos físíCOll de mee'"ic.. en l. pá-
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ftl CAP 11 OI¡>;A)lIC" OC UN PlIN'I'O /lI.\TERI.<\L
mentar la unidad de tiempo ni vetes, la unidad de dicha magnitudaumentará nI voces.
CornD las le}'es físicas RO pueden depender de la elección de lasunidadell de lu magnitudes que en elle '¡ruran. las dimellJlione! delu dos miembru de bs ecuaciolll!$, que expreun esas leyes, debenser igua1C'.S. Esta condición puede .ser, primero, utililllda para comprobar {[ue Ins cor~lllclOlles fíllic:l.S obtenidaa SOn coneetas y. sei'Undo, "ara establecer Ins dimensiones de las magnitudes físícos.Por ejemplo, la velocidad se dotennina como v _ MAt. L. dimensi6n da Al es L, la de Al. es igual tl T. La dinlensión del segundomiembro de la correlndón O!crita es igual 11 [.4II/IMJ _ LfI'- LT-1 • LII dimensi6n dlOl primer miembro debe ser esta misma.Por lo lonto,
[vI ... LT-I. (10.2)
(11.1)
La correlación escrita denominase fórmulll de lA dimensiólI, mientrlls quo su segundo Inlembro, dimertsión de 111 eorrespondicnLe mllg·nitud (en nuestro cuo, de la velocidad).
B~ndonos en la correlllción 10 = óvf.4t podemos hallar la di·men!ión de la ac:eJcraclón:
[Aul LT-' ">'-':t(10)_ llllj =~_L. -.
La dimen.sión de la fucrnWI -= Iml IIDI =- MLT-l.
De modo análego se C!tablecen las dimensionC'.S de las demú m.gnitudes.
§ 11. Tercera ley de Newton
Todli aCción entre cuorpo! tiene cllricter de interaccióu: ~i elc¡.erpo 1 actúa ~obl'(l el cuerpo 2 con una fuerza 1',1' a su vez, elcllerpo 2 actúa sobre el cuerpo 1 con una fnl!rto Fu.
La teteero ley de Nowton afirma que las !uerzlUcon las que actúan,uno $Obre olra, lo, cuerpo. en interacci6n .o,~ 19ua/es en magnitud y desentido opuesto. Empleando lag designaciones de 1811 fuerzas dadas mbarribll, el contenido de lo ter~era ley pUl:ldo ser representado en formade una igualdad:
De la tercera ley de Newloll se deduce quo bs fuerzitS surgena pares: con coda fuuZIl aplicada a cierto cuerpo puede.ser comparadauna fuerza de igual marnilud y de dirección contruia. aplicada aotro cuerpo que interactúa con el dado.
La tercer. ley de Newton no es siempre jusla. Se cumple con ri~
rosidad en uso de interacciones de eonlaclo (es decir, aquellas que
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