Content-Type: multipart/related; start=; boundary=----------KEJspQrabKyR93bKgddRbs Content-Location: http://es.wikipedia.org/wiki/Trabajo_(f%C3%ADsica) Subject: =?utf-8?Q?Trabajo=20(f=C3=ADsica)=20-=20Wikipedia,=20la=20enciclopedia=20libre?= MIME-Version: 1.0 ------------KEJspQrabKyR93bKgddRbs Content-Disposition: inline; filename*=utf-8''Trabajo_%28f%C3%ADsica%29.htm Content-Type: text/html; charset=UTF-8; name*=utf-8''Trabajo_%28f%C3%ADsica%29.htm Content-ID: Content-Location: http://es.wikipedia.org/wiki/Trabajo_(f%C3%ADsica) Content-Transfer-Encoding: Quoted-Printable Trabajo (f=C3=ADsica) - Wikipedia, la enciclopedia libre

Trabajo (f=C3=ADsica)

De Wikipedia, la enciclopedia libre
=
Trabajo (W)
3D"Trabajo.png"
Trabajo realizado por una fuerza constante.
Magnitud Trabajo (W)
Definici=C3=B3n<= /th> Producto de la fuerza ejercida sobre un cuerpo= por su desplazamiento
Tipo Magnitud escalar
Unidad SI Julio (J)
Otras unidades Kilojulio (kJ)
Kilogr=C3=A1metro (kgm)

En mec=C3=A1nica cl=C3=A1sica, se dice que una fuerza realiza trabajo cuando= altera el estado de movimiento de un cuerpo. El trabajo de la fuerza so= bre ese cuerpo ser=C3=A1 equivalente a la energ=C3=ADa necesaria para desplazarlo<= /a><= span class=3D"corchete-llamada">[1] de manera acelerada. El trabajo es una magnitud f=C3=AD= sica escalar que se representa con la letra 3D"\ (del ingl=C3=A9s Wo= rk) y se expresa en unidades de energ=C3=ADa, esto es en julios o joules (J) en el Sistema Internacional de Unidades.

Ya que por definici=C3=B3n el trabajo es un tr=C3=A1nsito de energ=C3= =ADa,[2] nunca se refiere a =C3=A9l como in= cremento de trabajo, ni se simboliza como =CE=94W.

El tr= abajo en mec=C3=A1nica[editar]

3D""
Trabajo de una fuerza.

Consideremos una part=C3=ADcula 3D"P" sobre la que act=C3=BAa una fuerza , funci= =C3=B3n de la posici=C3=B3n de la part=C3=ADcula en el espacio, esto es = 3D"F=3DF(\mathbf y sea =3D"\mathrm un desplazamiento elemental (infinitesimal) experim= entado por la part=C3=ADcula durante un intervalo de tiempo 3D"\mathrm. Llam= amos trabajo elemental, , de la fuerza 3D"\mathbf durante el desplazam= iento elemental 3D= al producto escalar 3D"\; esto es,

3D"\mathrm

Si representamos por la longitud de arco (medido sobre la tra= yectoria de la part=C3=ADcula) en el desplazamiento elemental, esto es <= img class=3D"mwe-math-fallback-image-inline tex" alt=3D"\mathrm d s =3D = |\mathrm d \mathbf r|" src=3D"//upload.wikimedia.org/math/3/f/0/3f009b9d= 9e275ebfa5d05d3ccbecf322.png" /> , entonces el vector tangente a la tray= ectoria viene dado por y podemos escribir la expresi=C3=B3n anterior en la forma

3D"\mathrm

donde 3D"\theta= representa el =C3=A1ngulo determinado por los vectores 3D"\mathrm y 3D"\m= y 3D"F_{\text{s}}" es la componente de la fuerza <= b>F en la direcci=C3=B3n del desplazamiento elemental 3D"\mathrm.


El trabajo realizado por la fuerza 3D"\mathbf durante un desplazamiento eleme= ntal de la part=C3=ADcula sobre la que est=C3=A1 aplicada es una magnitu= d escalar, que podr=C3=A1 ser positiva, nula o negativa, seg=C3=BAn que = el =C3=A1ngulo 3D"= sea agudo, recto u obtuso.

Si la part=C3=ADcula P recorre una cierta trayectoria en el espacio, = su desplazamiento total entre dos posiciones A y B puede considerarse co= mo el resultado de sumar infinitos desplazamientos elementales 3D"\mathrm y el trabajo total realizado por la fuerza 3D"\mathbf en ese desplazam= iento ser=C3=A1 la suma de todos esos trabajos elementales; o sea

3D"W_{\text{AB}=

Esto es, el trabajo viene dado por la integral curvil=C3=ADnea de a lo largo de la curva 3D"C" que une los dos puntos; en otras palabras, por l= a circulaci=C3=B3n de 3D"\mathbf sobre la curva 3D"C" entre los puntos A y B. A= s=C3=AD pues, el trabajo es una magnitud f=C3=ADsica escalar que depende= r=C3=A1 en general de la trayectoria que una los puntos A y B, a no ser = que la fuerza 3D"\= sea conservativa, en cuyo caso el trabajo resultar=C3= =A1 ser independiente del camino seguido para ir del punto A al punto B,= siendo nulo en una trayectoria cerrada. As=C3=AD, podemos afirmar que e= l trabajo no es una variable de estado.

Casos particul= ares[editar]

Fuerza constante sobre una part=C3=ADcula

En el caso particular de que la fuerza aplicada a la part=C3=ADcula s= ea constante (en m=C3=B3dulo, direcci=C3=B3n[3] y sentido<= sup id=3D"cite_ref-4" class=3D"reference">[4]<= /span> ), se tiene que

3D"W_{\text{AB}=

es decir, el trabajo realizado por una fuerza constante viene expresa= do por el producto escalar de la fuerza por el vector desplazamiento tot= al entre la posici=C3=B3n inicial y la final. Cuando el vector fuerza es= perpendicular al vector desplazamiento del cuerpo sobre el qu= e se aplica, dicha fuerza no realiza trabajo alguno. Asimismo, si no hay= desplazamiento, el trabajo tambi=C3=A9n ser=C3=A1 nulo.

Si sobre una part=C3=ADcula act=C3=BAan varias fuerzas y queremos cal= cular el trabajo total realizado sobre esta ella, entonces 3D" repre= sentar=C3=A1 al vector resultante de todas las fuerzas aplicadas.

Trabajo sobre un s=C3=B3lido r=C3=ADgido

Para el caso de un s=C3=B3lido el trabajo total sobre el mismo se cal= cula sumando las contribuciones sobre todas las part=C3=ADculas. Matem=C3= =A1ticamente ese trabajo puede expresarse como integral:

3D"W

Si se trata de un s=C3=B3lido r=C3=ADgido las fuerzas de volumen 3D"\scriptstyle puede escribirse en t=C3=A9rminos de la fu= erza resultante , el momento resultante 3D"\scriptstyle, la velocidad del centro de masas 3D"\scriptstyle y la velocidad angular 3D"\scriptstyle:

3D"W

Trabajo y energ=C3=ADa cin=C3=A9tica[editar= ]

Para el caso de una part=C3=ADcula tanto en mec=C3=A1nica c= l=C3=A1sica como en mec=C3=A1nica relativista es= v=C3=A1lida la siguiente expresi=C3=B3n:

3D"\mathbf{F}

Multiplicando esta expresi=C3=B3n escalarmente por la velocidad e int= egrando respecto al tiempo se obtiene que el trabajo realizado sobre una= part=C3=ADcula (cl=C3=A1sica o relativista) iguala a la variaci=C3=B3n = de energ=C3=ADa cin=C3=A9tica:

3D"W=

= El trabajo en termodin=C3=A1mica[editar]

En el caso de un sistema termodin=C3=A1mico, el trabajo = no es necesariamente de naturaleza puramente mec=C3=A1nica, ya que la en= erg=C3=ADa intercambiada en las interacciones puede ser tambi=C3=A9n calor=C3=ADfica, el=C3=A9ctrica, magn=C3=A9tica o qu=C3=ADmica,= por lo que no siempre podr=C3=A1 expresarse en la forma de trabajo mec=C3= =A1nico.

No obstante, existe una situaci=C3=B3n particularmente simple e impor= tante en la que el trabajo est=C3=A1 asociado a los cambios de volumen que experimenta un sistema= (v.g., un fluido contenido en un recinto de forma variable).

As=C3=AD, si consideramos un fluido que se encuentra sometido a una <= a href=3D"/wiki/Presi%C3%B3n" title=3D"Presi=C3=B3n">presi=C3=B3n ex= terna 3D"p_{\text{= y que evoluciona desde un estado caracterizado por un= volumen 3D"V_1" a otro con un volumen 3D"V_2", el trabajo realizado ser=C3=A1:

3D"W_{12}

resultando un trabajo positivo (3D"W) si se trata de una expansi=C3=B3= n del sistema 3D"\= y negativo en caso contrario, de acuerdo co= n el convenio de signos aceptado en = la Termodin=C3=A1mica. En un proceso cuasiest=C3=A1tico y sin fricci=C3=B3= n la presi=C3=B3n exterior (3D"p_{\text{ext}}") ser=C3=A1 igual en cada instante= a la presi=C3=B3n () del fluido, de modo que el trabajo intercambiado por = el sistema en estos procesos se expresa como

3D"W_{12}

De estas expresiones se infiere que la presi=C3=B3n se comporta como = una fuerza generalizada, en tanto que el volumen act=C3=BA= a como un desplazamiento generalizado; la= presi=C3=B3n y el volumen constituyen una pareja de variables conjugada= s.

En el caso que la presi=C3=B3n del sistema permanezca constante durante el proceso,= el trabajo viene dado por:

3D"W

Unidades de t= rabajo[editar]=

Sistema Internacional de Unidades= [editar]

Art=C3=AD= culo principal: Sistema Internacional = de Unidades
  • Julio = o joule, unidad de trabajo en el SI
  • Kilojulio: 1 kJ =3D 103 J

= Sistema T=C3=A9cnico de Unidades[editar]

Art=C3=AD= culo principal: Sistema T=C3=A9cnico de = Unidades

Sis= tema Cegesimal de Unidades[editar]

Art=C3=AD= culo principal: Sistema Cegesimal de Unidades<= /a>

Sistema anglosaj=C3=B3n de unidades[editar]

= Sistema t=C3=A9cnico ingl=C3=A9s[editar]

Otras unidades[editar]

V=C3=A9as= e tambi=C3=A9n[editar]

Referencias[editar]

  1. =E2=86=91 Serway, Raymond A.; Jewett = Jr., John W., =C2=AB7=C2=BB, escrito en Polanco, Ciudad de M=C3=A9xico (en espa=C3=B1o= l), Physics for Scientists and Engineers, 6th. Volume I [F=C3=AD= sica para ciencias e ingenier=C3=ADas, 6a], 1 (6=C2=AA edici=C3=B3n)= , International Thomson Editores, S.A. de C.V., p. 185, =C2=AB. Un= a consideraci=C3=B3n importante para una aproximaci=C3=B3n de sistema a = problemas, es observar que el trabajo es una transferencia de energ=C3= =ADa. [...] Esto resultar=C3=A1 en un cambio en la energ=C3=ADa alma= cenada en el sistema.=C2=BB =
  2. =E2=86=91 =C2=ABC=C3=A1tedra de Termodin=C3=A1mica I y = II de Ingenier=C3=ADa Qu=C3=ADmica=C2=BB. Uni= versidad Nacional de La Plata. =C2=ABNOTA: basado en el libro d= e la C=C3=A1tedra, Cap P1, y con la colaboraci=C3=B3n de personal de la = misma=C2=BB.
  3. =E2=86=91 Direcci=C3=B3n: L=C3=ADnea sobre la que se mueve= un punto, que puede ser recorrida en dos sentidos opuestos. Diccionario= de la lengua espa=C3=B1ola, consultado el 23 de enero de 2012
  4. =E2=86=91 Sentido: Cada una de las dos orientaciones opuestas de una mis= ma direcci=C3=B3n. Diccionario de la lengua espa=C3=B1ola, consultado el= 23 de enero de 2012

Bibliograf=C3=AD= a[editar]

  • Feynman, Leighton and Sands. Lectures on physics (en ingl=C3=A9s). Addison-Wesley. ISBN 0-8053-9045-6. 
  • = Marion, Jerry B. (1996). Din=C3=A1mica cl=C3=A1sica de las part=C3=AD= culas y sistemas. Barcelona: Ed. Revert=C3=A9. ISBN 84-291-4094-8. <= /li>
  • Ortega, Manuel R. (1989-2006). Lecciones de F=C3=ADsica (4 vol=C3= =BAmenes). Monytex. ISBN 84-404-4290-4= , ISBN 84-398-9218-7, ISBN 84-= 398-9219-5, ISBN 84-604-4445-7. 
  • Ortega, Manuel R. & Iba=C3=B1e= z, Jos=C3=A9 A. (1989-2003). Lecciones de F=C3=ADsica (Termof=C3=ADsi= ca). Monytex. ISBN 84-404-4291-2. 
  • Resnick,Robert & Krane, Kenneth S. (2001). = Physics (en ingl=C3=A9s). New Yor= k: John Wiley & Sons. I= SBN 0-471-32057-9= . 
  • (en ingl=C3=A9s) (6= =C2=AA edici=C3=B3n). Brooks/Cole. ISBN 0-534-40842-7= .  La = referencia utiliza par=C3=A1metros obsoletos (ayuda)
  • T= ipler, Paul A. (2000). F=C3=ADsica para la ciencia y la tecnolog=C3=AD= a (2 vol=C3=BAmenes). Barcelona: Ed. Revert=C3=A9. ISBN 84-291-4382-3. 

Enlaces externos= [editar]<= /h2>

Men=C3=BA de navegaci=C3=B3n

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