Energia potencial
Páginas: 5 (1067 palabras)
Publicado: 17 de diciembre de 2010
/DHQHUJtDFLQpWLFDGHFXHUSRUtJLGRSXHGHVHSDUDUVHHQGRVWpUPLQRVXQRTXH GHSHQGHGHODYHORFLGDGGHOFHQWURGHPDVD\HORWURTXHGHSHQGHGHODYHORFLGDGDQJXODU GHOFXHUSR3DUDXQPHFDQLVPRFRQYDULRV FXHUSRVODHQHUJtDFLQpWLFDWRWDOVHUiODVXPDGH ODVHQHUJtDVLQGLYLGXDOHV$VtODHQHUJtDFLQpWLFDVHSXHGHHVFULELUFRPR 9 'RQGH ^ L `UHSUHVHQWDODYHORFLGDGGHOFHQWURGHPDVDGHOFXHUSRL\ ^Z L ` UHSUHVHQWDOD YHORFLGDGDQJXODUGHOFXHUSRLDPEDVPHGLGDVHQFRRUGHQDGDVGHXQVLVWHPDLQHUFLDO 6LVHGHILQHQORVVLJXLHQWHVYHFWRUHVFROXPQDVFRPR
L
',1$0,&$'(0(&$1,6026'(81*5$'2'(/,%(57$'
9 (& ¦ PL ^9L ` ^ L ` ^Z L ` >, L @^Z L `
Q 7 7
HQWRQFHVGHILQLHQGRDSURSLDGDPHQWHXQDPDWUL]PDVD >0 @ \XQDPDWUL]GHLQHUFLD >, * @ ODHQHUJtDFLQpWLFDWRWDOGHOVLVWHPDSXHGHH[SUHVDUVHFRPR 9 9 (& ^ * ` >0 @^ * ` ^Z ` >, * @^Z ` 9 3DUDXQVLVWHPDGHXQVRORJUDGRGHOLEHUWDGORVYHFWRUHV ^ * ` \ ^Z ` SXHGHQHVFULELUVHHQ WpUPLQRVGHODYHORFLGDGJHQHUDOL]DGD T \GHXQYHFWRUGHFRHILFLHQWHVGHYHORFLGDGHV
7 7
^9* ` ^Z `
&RO Z [ Z \ Z ] Z [ Z Q]
&RO 9* [ 9* \ 9*] 9* [ 9* \ 9* ] 9*Q]
^Z ` T^. Z ` T^. * ` &RQHVWDVGHILQLFLRQHVODHQHUJtDFLQpWLFDWRWDOSXHGHHVFULELUVHHQWpUPLQRVGH T (& T ^. * ` >0 @^. * ` ^. Z ` >, * @^. Z `
7 7
^9* `
3RUDQDORJtDFRQODH[SUHVLyQSDUDODHQHUJtDFLQpWLFDGHXQDSDUWtFXODODH[SUHVLyQDQWHULRU VHSXHGHSRQHUFRPR (& T T GRQGH T
VHGHQRPLQDLQHUFLDJHQHUDOL]DGDODTXHHVXQDIXQFLyQGHT 0(&$1,60263/$126
^. * `7 >0 @^. * ` ^. Z `7 >, * @^. Z `
(QHOFDVRGHPHFDQLVPRVSODQRV
Q Q L L
(& ¦ 0 L9*L ¦ , *LZ L
GRQGHVHSXHGHSRQHUTXH 9*L 9*L[ 9*L\ SRUORTXH Z L
. ZL T Q
. *L[ . *L\ T
TXHVHSXHGHSRQHUFRPR GRQGH T
Q
(& T ¦ 0 L . *L[ .*L\ ¦ , *L . ZL Q L L
(& T T
¦0
L
L . *L[ . *L\ ¦ , *L . ZL Q L
)8(5=$6*(1(5$/,=$'$6
7RGDVODVIXHU]DV\WRUTXHVTXHWUDEDMDQVREUHHOVLVWHPDLQIOX\HQHQVXUHVSXHVWD GLQiPLFD$KRUDVHGHWHUPLQDUiXQDIXHU]DJHQHUDOL]DGDTXHFXDQGRDFW~HDWUDYpVGHXQFDPELRYLUWXDOGHFRRUGHQDGDGTUHDOLFHXQWUDEDMRYLUWXDO4GTLJXDODODVXPDGHOWUDEDMR YLUWXDOGHODVIXHU]DV\WRUTXHVUHDOHVPRYLpQGRVHDWUDYpVGHVXVGHVSOD]DPLHQWRVYLUWXDOHV DVRFLDGRV 6HDQ)L ODVIXHU]DVH[WHUQDVDSOLFDGDVHQXELFDFLRQHVGHILQLGDVSRUORVYHFWRUHV SRVLFLyQUL$QiORJDPHQWHVHDQ&M ORVWRUTXHVH[WHUQRVDFWXDQGRHQiQJXORVTM(OWUDEDMR YLUWXDOVHUi G: ¦ )L GUL ¦ & M GT MGDGRTXHWRGDVODVSRVLFLRQHVVRQIXQFLRQHVGHODFRRUGHQDGDJHQHUDOL]DGDTORV GHVSOD]DPLHQWRVYLUWXDOHVSXHGHQVHUHVFULWRVFRPR GUL G: GUL GT GT GT M GU GT M GT GT
L M
SRUORTXH
GRQGH4HVODIXHU]DJHQHUDOL]DGD 4
L
¦ )L L ¦ & M GT
L M
GT M GT
GT
4G T
\ODSRWHQFLDGHHQWUDGDVHUiLJXDOD 3RWHQFLD G: GW 4T
¦ ) GT ¦ &
L
GUL
M
M
GT M GT
(&8$&,21'((.6(5*,$1(VVDELGRTXHHOWUDEDMRUHDOL]DGRVREUHXQVLVWHPDPHFiQLFRHVLJXDODOFDPELRGH HQHUJtDFLQpWLFDGHOVLVWHPD(VWRVHSXHGHHVFULELUFRPR 3RWHQFLD HQWUDGD &RPR (QWRQFHV G (QHUJtD&LQpWLFD GW
(& T T
3RUORTXH
G TT TT 4T GT
G T 4 GT TXHHVOD(FXDFLyQGH(NVHUJLDQSDUDHOPRYLPLHQWRGHXQVLVWHPDGHXQVRORJUDGRGH OLEHUWDG G 6LVHGHILQH 9T ODHFXDFLyQDQWHULRUVHSXHGHSRQHUFRPR GT T T 9 T T 4 GRQGH 9 T VHFRQRFHFRPRHOFRHILFLHQWHFHQWUtIXJR T (1(5*,$327(1&,$/5(35(6(17$&,21'()8(5=$6&216(59$7,9$6
6XSRQJDPRVTXHODIXHU]D)L TXHDFW~DHQHOSXQWRUL HVWpFRQVWLWXLGDSRUGRVSDUWHV XQDSDUWHFRQVHUYDWLYD\ODRWUDQRFRQVHUYDWLYD/DIXHU]DFRQVHUYDWLYDSXHGHHVFULELUVH...
L
',1$0,&$'(0(&$1,6026'(81*5$'2'(/,%(57$'
9 (& ¦ PL ^9L ` ^ L ` ^Z L ` >, L @^Z L `
Q 7 7
HQWRQFHVGHILQLHQGRDSURSLDGDPHQWHXQDPDWUL]PDVD >0 @ \XQDPDWUL]GHLQHUFLD >, * @ ODHQHUJtDFLQpWLFDWRWDOGHOVLVWHPDSXHGHH[SUHVDUVHFRPR 9 9 (& ^ * ` >0 @^ * ` ^Z ` >, * @^Z ` 9 3DUDXQVLVWHPDGHXQVRORJUDGRGHOLEHUWDGORVYHFWRUHV ^ * ` \ ^Z ` SXHGHQHVFULELUVHHQ WpUPLQRVGHODYHORFLGDGJHQHUDOL]DGD T \GHXQYHFWRUGHFRHILFLHQWHVGHYHORFLGDGHV
7 7
^9* ` ^Z `
&RO Z [ Z \ Z ] Z [ Z Q]
&RO 9* [ 9* \ 9*] 9* [ 9* \ 9* ] 9*Q]
^Z ` T^. Z ` T^. * ` &RQHVWDVGHILQLFLRQHVODHQHUJtDFLQpWLFDWRWDOSXHGHHVFULELUVHHQWpUPLQRVGH T (& T ^. * ` >0 @^. * ` ^. Z ` >, * @^. Z `
7 7
^9* `
3RUDQDORJtDFRQODH[SUHVLyQSDUDODHQHUJtDFLQpWLFDGHXQDSDUWtFXODODH[SUHVLyQDQWHULRU VHSXHGHSRQHUFRPR (& T T GRQGH T
VHGHQRPLQDLQHUFLDJHQHUDOL]DGDODTXHHVXQDIXQFLyQGHT 0(&$1,60263/$126
^. * `7 >0 @^. * ` ^. Z `7 >, * @^. Z `
(QHOFDVRGHPHFDQLVPRVSODQRV
Q Q L L
(& ¦ 0 L9*L ¦ , *LZ L
GRQGHVHSXHGHSRQHUTXH 9*L 9*L[ 9*L\ SRUORTXH Z L
. ZL T Q
. *L[ . *L\ T
TXHVHSXHGHSRQHUFRPR GRQGH T
Q
(& T ¦ 0 L . *L[ .*L\ ¦ , *L . ZL Q L L
(& T T
¦0
L
L . *L[ . *L\ ¦ , *L . ZL Q L
)8(5=$6*(1(5$/,=$'$6
7RGDVODVIXHU]DV\WRUTXHVTXHWUDEDMDQVREUHHOVLVWHPDLQIOX\HQHQVXUHVSXHVWD GLQiPLFD$KRUDVHGHWHUPLQDUiXQDIXHU]DJHQHUDOL]DGDTXHFXDQGRDFW~HDWUDYpVGHXQFDPELRYLUWXDOGHFRRUGHQDGDGTUHDOLFHXQWUDEDMRYLUWXDO4GTLJXDODODVXPDGHOWUDEDMR YLUWXDOGHODVIXHU]DV\WRUTXHVUHDOHVPRYLpQGRVHDWUDYpVGHVXVGHVSOD]DPLHQWRVYLUWXDOHV DVRFLDGRV 6HDQ)L ODVIXHU]DVH[WHUQDVDSOLFDGDVHQXELFDFLRQHVGHILQLGDVSRUORVYHFWRUHV SRVLFLyQUL$QiORJDPHQWHVHDQ&M ORVWRUTXHVH[WHUQRVDFWXDQGRHQiQJXORVTM(OWUDEDMR YLUWXDOVHUi G: ¦ )L GUL ¦ & M GT MGDGRTXHWRGDVODVSRVLFLRQHVVRQIXQFLRQHVGHODFRRUGHQDGDJHQHUDOL]DGDTORV GHVSOD]DPLHQWRVYLUWXDOHVSXHGHQVHUHVFULWRVFRPR GUL G: GUL GT GT GT M GU GT M GT GT
L M
SRUORTXH
GRQGH4HVODIXHU]DJHQHUDOL]DGD 4
L
¦ )L L ¦ & M GT
L M
GT M GT
GT
4G T
\ODSRWHQFLDGHHQWUDGDVHUiLJXDOD 3RWHQFLD G: GW 4T
¦ ) GT ¦ &
L
GUL
M
M
GT M GT
(&8$&,21'((.6(5*,$1(VVDELGRTXHHOWUDEDMRUHDOL]DGRVREUHXQVLVWHPDPHFiQLFRHVLJXDODOFDPELRGH HQHUJtDFLQpWLFDGHOVLVWHPD(VWRVHSXHGHHVFULELUFRPR 3RWHQFLD HQWUDGD &RPR (QWRQFHV G (QHUJtD&LQpWLFD GW
(& T T
3RUORTXH
G TT TT 4T GT
G T 4 GT TXHHVOD(FXDFLyQGH(NVHUJLDQSDUDHOPRYLPLHQWRGHXQVLVWHPDGHXQVRORJUDGRGH OLEHUWDG G 6LVHGHILQH 9T ODHFXDFLyQDQWHULRUVHSXHGHSRQHUFRPR GT T T 9 T T 4 GRQGH 9 T VHFRQRFHFRPRHOFRHILFLHQWHFHQWUtIXJR T (1(5*,$327(1&,$/5(35(6(17$&,21'()8(5=$6&216(59$7,9$6
6XSRQJDPRVTXHODIXHU]D)L TXHDFW~DHQHOSXQWRUL HVWpFRQVWLWXLGDSRUGRVSDUWHV XQDSDUWHFRQVHUYDWLYD\ODRWUDQRFRQVHUYDWLYD/DIXHU]DFRQVHUYDWLYDSXHGHHVFULELUVH...
Leer documento completo
Regístrate para leer el documento completo.