INSTITUTO POLITÉCNICO NACIONAL ESCUELA SUPERIOR DE INGENIERÍA Y ARQUITECTURA ARQUITECTURA UNIDAD PROFESIONAL ADOLFO LÓPEZ MATEOS MATEOS
ACADEMIA ACADEMI A DE HIDRÁULICA HIDRÁU LICA
DINÁMICA DINÁMI CA DE LA PARTÍCULA PARTÍCULA
Nombre: Néstor Daniel Reyes Cabañas No. De Boe!": 20!"20
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0123425306 ANTECEDENTES 'ISTÓRICOS DE LA DIN%MICA. L" $r-mer" r"m" *e " F7,-" e( *e,"rro"r,e 8#e " *-()m-"9 #e e,!#*-" e mo&-m-e(!o *e o, #er$o, ; ", 8#er+", #e o $ro&o"(. P"r" (o,o!ro, e mo&-m-e(!o e, 8#(*"me(!"me(!e e *e,$"+"m-e(!o *e #(" o," e( e e,$"-o9 e,$"-o9 ,-( emb"r( $#e*e ,er " *e ,# $o,--=( e( e e,$"-o?
$or eo e !>rm-(o "!#" m), $r=@-mo " " om$re(,-=( rm-(o cambio. E( e ,-<o I9 'er=( *e Ae"(*r7" e,r-b-= &"r-o, !r"!"*o, *e me)(-"9 e( o, #e *e,r-b7" #( ,-(8 ,-(87( 7( *e "$"r" "$"r"!o !o,, *e,! *e,!-( -("* "*o, o, " *-r*-r-<<-rr ; "$ro& "$ro&e e/"r /"r meo meorr e e,8#e e,8#er+ r+oo /#m"(o /#m"(o.. De, De ,rr-bb-=9 =9 "#(# "#(#ee *e 8orm" 8orm" "r""r"-"9 "9 " e; e; *e ""-=( =(re re" "-=( =( *e I,"" I,"" Ne Ne! !o(9 o(9 e@$er-me(!"(*o o( &"$or *e "<#". Ge(er"-+= e $r-(-$-o *e " $""(" *e Ar#7me*e,. A*em),9 A*em),9 re"-+= re"-+= #(" *e,r-$*e,r-$-=( =( *e!" *e!""*" "*" *e hýdraulis hýdraulis de Ctesibio Ctesibio #( =r<"(o #e 8#(-o("b" o( "<#". A("@-m"(*ro A("@-m"(*ro $e(,"b" #e " ("!#r"e+" ("!#r"e+" $roe*7" *e " ,e$"r"-=(9 $or me*-o *e #( e!er(o mo&-m-e(!o9 mo&-m-e(!o9 *e o, eeme(!o, o$#e,!o, $or eem$o9 eem$o9 8r-o"or9 8r-o"or9 #e e,!"b"( e(err"*o, e( ",!o,9 ,-e(*o e mo&-m-e(!o #( "mb-o *e #<"r e( e e,$"-o.
E( e ,-<o III ". C.9 Ar#7me*e, 54 ". C.505 ". C. ,-,!em"!-+= o, o(o-m-e(!o, ,obre m)#-(", ,-m$e,9 e(#(-= ", e;e, *e " $""(" ; o(,!r#;= (#mero,o, "r!-#<-o, *e -(!er>, $r)!-o. Ar-,!=!ee, *e8-(e e mo&-m-e(!o omo e paso de la potencia al acto9 ;9 *e #( mo*o m), !>(-o el acto de lo que está en potencia, en tanto que está en potencia. Co( e,!" e,!" *e8-(- *e8-(--=( -=(99 Ar-,! Ar-,!=!e =!ee, e, #-ere #-ere -(*-" -(*-"rr " me(o, me(o, ", ,-<#-e ,-<#-e(!e (!e,, -m$or! -m$or!"(! "(!e, e, #e,!-o(e,: •
El movimiento es un acto? e, #(" re"-*"* #e e $#e*e ,obre&e(-r " #(" o,". Co(
e,!o #eremo, -(*-"r #e *-/" o," $#e*e (o !e(er e mo&-m-e(!o e( "!o9 omo #"(*o e,!) e( re$o,o: ,- (o m#e&o " !-+" ; " !e(
Esa peculiar realidad o acto e( #e o(,-,!e e mo&-m-e(!o la tiene un objeto en la medida en que aún no ha actualizado totalmente aquello que puede llegar a ser;
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!"(!o e So omo o, $"(e!", <-r"b"( " ,# "re*e*or. A re"-+"r ,#, ob,er&"-o(e, ",!ro(=m-",9 Co$>r(-o *e,#br-= "(om"7", e( e ,-,!em" $!oem"-o ; ome(+= " *#*"r *e ,#, $o,!#"*o, b),-o,. E( ,# obr" $r-(-$" *-e: KC#"(*o #( b"ro ("&e<" ,-( ,"#*-*",9 o, &-"ero, &e( mo&er,e9 " -m"r(-o e<= " " o(#,-=( *e #e " T-err" ,e mo&7"9 <-r"(*o ,obre ,7 m-,m" #( <-ro om$e!o e#-&"7" " #( *7" ; "re*e*or *e ,o #( <-ro om$e!o e#-&"7" " #( "o. T"mb->( ,o,!e(7" #e e ee *e " T-err" ,e /""b" -(-("*o. A ,# &e+9 m"(!e(7" " o(e$-=( !r"*--o(" *e #(" e,8er" e@!er-or *o(*e ,e e(o(!r"b"( -(m=&-e, ", e,!re",. Se *ebe !e(er e( #e(!" #e Co$>r(-o re"-+"b" ,#, ob,er&"-o(e, ,-( o(!"r o( e "$or!e -(&"or"be *e !ee,o$-o9 #e $or e(!o(e, (o /"b7" ,-*o "( -(&e(!"*o. P"r" ob,er&"r o, #er$o, ee,!e,9 $","b" ", (o/e, e( " !orre *e ,# "," *e ", mo(!"",. Com$eme(!"b" e,!", ob,er&"-o(e, o( " e!#r" *e ", obr", "(!-<#", ; ),-", ; o( ,#, $ro$-", "(o!"-o(e, ; )#o,. S- b-e( >,!o, !-mo, (o er"( *e !o*o $re-,o,9 !o*", ,#, ob,er&"-o(e, re,$o(*7"( " (ee,-*"*e, *e or*e( !e=r-o ; ,e re"-+"b"( ,e<( #( $"( $ree,!"be-*o. Co$>r(-o ,e(!= ", b",e, *e " A,!ro(om7" Mo*er("9 #e ,er7" *e,"rro"*" #e!o*o -e(!78-oK ; !"mb->( #(o *e o, 8#(*"*ore, *e " 87,-" ),-". U!--+"(*o ob,er&"-o(e, e@$er-me(!"e,9 -*e"-+"-o(e, ; *e*#-o(e, =<-",9 o-" ; "mb-"r o(e$!o, #e e,!"b"( 8-rmeme(!e "rr"-<"*o, *e,*e /"7" ",- 5333 "o,. G"-eo "*/-r-= " " &-,-=( o$er(-"("9 ,e<#r"me(!e -(8#-*o $or o, *e,#br-m-e(!o, #e re"-+= $"r!-r *e 063. E8e!-&"me(!e9 re"-+"(*o ob,er&"-o(e, o( #( !ee,o$-o9 e,!#*-= " 8orm" ; ,#$er8--e *e " L#("9 *e,#br-= #(", e( o!ro, $"(e!", ; e(o(!r= *-8ere(-",
e(!re o, $"(e!", ; ", e,!re",9 #e mo,!r"b"( -(e#7&o"me(!e #e ", e,!re", ,e e(o(!r"b"( " *-,!"(-", m#/o m";ore,. L" T-err" ,e *e,$"+" &eo+me(!e "re*e*or *e So9 " #(o, 3 m2,e<9 ; "*em), <-r" ,obre ,# ee9 *e m"(er" #e #( $#(!o ,obre " ,#$er8--e *e e#"*or ,e m#e&e re,$e!o " ee *e ro!"-=( " #(o, 133 m2,e<. VPor #> (o (o, *"mo, #e(!" *e e,o, mo&-m-e(!o,W A#7 e, *o(*e " *e,r-$-=( *e mo&-m-e(!o <"-e"(" ,e re"-o(" o( e J,-,!em" *e m#(*oK. '",!" "(!e, *e G"-eo9 #(o *e o, "r<#me(!o, $"r" ",e<#r"r " -(mo&--*"* *e " T-err" er" #e9 ,- e,!" ,e mo&-e,e9 #( obe!o "(+"*o &er!-"me(!e /"-" "rr-b" (o *eber7" &o&er " "er e( e $#(!o *e "(+"m-e(!o9 ;" #e " T-err" ,e *e,$"+"r7" *#r"(!e e !-em$o #e !"r*" e eo *e obe!o "(+"*o. P"r" G"-eo9 e e,!"*o J("!#r"K *e mo&-m-e(!o *e #( #er$o e, e *e m"(!e(er ,# &eo-*"*. S- -(--"me(!e e,!) e( re$o,o ,e m"(!e(*r) e( re$o,o. Pero ,- -(--"me(!e ,e m#e&e o( #(" -er!" &eo-*"* (o (#"9 ; ,- (o e,!) ,ome!-*o " (-(<#(" "-=( e@!er("9 m"(!e(*r) ,# &eo-*"* o(,!"(!e. E,!e e, e $r-(-$-o *e -(er-" #e #e-" e, $rob"beme(!e #(o *e ,#, re,#!"*o, m), o(o-*o,. No e@-,!e er!e+" /-,!=r-" *e #e /";" re"-+"*o ,#, e@$er-me(!o, "(+"(*o obe!o, *e,*e " !orre *e P-,"9 ,7 e( "mb-o *e ,#, e,!#*-o, b","*o, e( e@$er-me(!o, o( $"(o, -(-("*o,. Re"-+"(*o e@$er-me(!o, ; #!--+"(*o r"+o("m-e(!o, *e e,!e !-$o o(#;= #e o, #er$o, e( "7*" -bre ,e m#e&e( o( "eer"-=( o(,!"(!e9 ; #e e," "eer"-=( *e$e(*e m#;
e&eme(!e *e $e,o *e o, #er$o,. E,!" *e$e(*e(-" ,e *ebe " ro+"m-e(!o o( e "-re ; *e,"$"ree ,- " "7*" -bre e, e( &"7o. E,!o, re,#!"*o, ,o( " b",e *e $r-(-$-o *e e#-&"e(-" #e E-(,!e-( 8orm#= e( 039 ; #e e, #(o *e o, $-"re, *e " Teor7" Ge(er" *e " Re"!-&-*"* Co( ", meor", -(!ro*#-*", $or e$er 010063 e( " !eor7" /e-o>(!r-"9 " !>rm-(o *e ,-<o XI ;" ,e o(o7" =mo er" e mo&-m-e(!o *e o, $"(e!", "re*e*or *e So. L" $r-mer" e!"$" e( " obr" *e e$er9 *e,"rro"*" *#r"(!e ,#, "o, e( Gr"+9 ,e e(!r= e( o, $robem", re"-o("*o, o( ", =rb-!", $"(e!"r-",9 ",7 omo e( ", &eo-*"*e, &"r-"be, o( #e o, $"(e!", ", reorre(9 $"r" o #e $"r!-= *e " o(e$-=( $-!"<=r-" ,e<( " #" e m#(*o ,e r-!-" *e " #e,!-=(9 re;= e(o(!r"r #(" re,$#e,!" !r-" re"-o("(*o o, -(!er&"o, e(!re ", =rb-!", *e o, ,e-, $"(e!", e(!o(e, o(o-*o, o( o, -(o ,=-*o, re<#"re,. #+<= /"ber re,#e!o ",7 #( m-,!er-o o,mo!r-o *e *-&er,o, ,-,!em", =$!-o,. Pero e !r"b"o m), -m$or!"(!e *e e$er 8#e " re&-,-=( *e o, e,#em", o,mo=<-o, o(o-*o, " $"r!-r *e "
- 'os planetas se mueven en órbitas el(pticas planas con el sol situado en uno de sus focos)
- 'os planetas en su movimiento barren áreas iguales en tiempos iguales)
C#m-(= ,# obr" *#r"(!e ,# e,!"(-" e( L-(+9 e( *o(*e e(#(-= " !erer" *e ,#, e;e, e( ,# obr" !*armonices "undi$ e( 060 #e ,e re8-ere:
- 'os cuadrados de los periodos de los planetas en su movimiento alrededor del sol son proporcionales a los cubos de sus ejes ma#ores)
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Do(*e " m"," *e #er$o "!r"-*o /" ,-*o "(#"*" ; ,# "eer"-=( (o *e$e(*e *e e"9 ,-(o #e ,o"me(!e *e #er$o "!r";e(!e9 e( e,!e ",o " T-err". Co( e,!" e;9 Ne!o( "#= e $er7o*o *e " =rb-!" *e " L#("9 #,"(*o &"ore, "(o #e *e= $er$eo, " !"(!o, *e,*e " "(!-<e*"*. Im"<-(= Ne!o( #( "(" o( "<#" ro*e"(*o " T-err"9 ; *emo,!r= #e b",!"b" " "!r"-=( *e " L#(" ,obre ,#, "<#", $"r" $ro*#-r " "r"!er7,!-" *obe o,-"-=( *-"r-" #e ,e ob,er&" e( o, $o"? $ero Ne!o( e, *-o e "r)!er ,-,!em)!-o *e #(" !eor7" (*o,e e( e m";or ",!r=(omo *e ,-<o. Sobre !o*o, e,!o, !em", m"(!#&o "
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L" ,e<#(*" om#(-"-=( $#b-"*" e( e &o#me( #e o(!e(7" " !eor7" e,$e-" *e " re"!-&-*"* e@$-" " !eor7" *e e8e!o 8o!oe>!r-o9 ,e<( " #" " #+ ,e o(&-er!e e( #(" e,$e-e *e /#b",o *e $ro;e!-e,9 " e(er<7" *e o, #"e, e, $ro$or-o(" " " 8re#e(-" *e " o(*" #m-(o,". F-("me(!e9 " !erer" om#(-"-=( o(!e(7" #(" !eor7" m"!em)!-" ,obre e mo&-m-e(!o bro(-"(o9 e, *e-r9 e *e $e#e", $"r!7#", ,#,$e(*-*", e( #( 8#-*o ; mo&->(*o,e *e #( mo*o "$"re(!eme(!e -rre<#"r $or b"o *e -(8#o *e ", $"r!7#", *e 8#-*o m), $e#e", "(. T#&-ero( #e !r"(,#rr-r !re, "o, $"r" #e " !eor7" e,$e-" 8#er" reo(o-*" e( e m#(*o *e o, 87,-o,. E( 000 $",= " ,er E-(,!e-( $ro8e,or *e " U(-&er,-*"* "em"(" *e Pr"<" e(!o(e, $er!e(e-e(!e " A#,!r-"9 ; "7 ome(+= ,# !r"b"o ,obre " Teor7" @-!o " $r#eb" e@$er-me(!". L" $r-mer" ; #-+) " m), -m$or!"(!e *e ", o(#,-o(e, $"r" ,er &er-8-"*" 8#e " *e ", *-8ere(-", $re*-!-&", e(!re ", (#e&", !eor7",
E( 00 o, -(<e,e, e(&-"ro( *o, e@$e*--o(e,9 #(" *e e", " Am>r-" *e S#r9 " o!r" " %8r-"9 $"r" 8o!o, *e #(" ,er-e *e e#"-o(e,9 /"b7" *e "b"r"r !"(!o o, 8e(=me(o, !-o,. E( 01 $oo "(!e, *e ,# m#er!e9 #e e ,or$re(*-= e( Pr-(e!o(9 ,"-= " " #+ " #"r!" e*--=( *e ,# 8"mo," obr" !1he "eaning of 2elativit#$9 "$"re-*" $or $r-mer" &e+ e( C"#!!" 053. E( e" E-(,!e-( $#b-= e( 8orm" *e!""*" ,# "(!e, -!"*" !eor7" *e "m$o #(-8-"*o " " #e /"b7" e<"*o9 /",!" -er!o $#(!o9 e( 0. E(!re o!ro, !r"b"o, -e(!78-o, ,#;o, $#e*e( -!"r,e: !2elativit#; the 3pecial and 4eneral 1heor#$ N#e&" Yor9 053? !5nvestigations on 1heor# of -ro.nian "ovement$ 056? !"ein 6eltbild$ 09 !"# hilosoph#$ 0 ; !7ut of m# 'ater 8ears$ 013 SLUG S#< e, #(" #(-*"* *e m"," e( e ,-,!em" *e #(-*"*e, FPS Foo!Po#(*Seo(* ,;,!em: S-,!em" P-eL-br"Se<#(*o E ,#< ,e *e8-(e omo " m"," #e ,e *e,$"+" " #(" "eer"-=( *e 0 8!2,_ #"(*o ,e eere #(" 8#er+" *e #(" -br" ,obre e". De " e#"-=( F[m" *e,$e"(*o m[F2" !e(*r7"mo, o ,-<#-e(!e: 0 #(-*"* *e m"," [ #(-*"* *e 8#er+" 2 #(-*"* *e "eer"-=(. lbf ∙s 1 slug = 1 ft
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N → KG ∙ F
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KG ∙ F → N
GRAEDAD E-(,!e-(9 e( " !eor7" *e " re"!-&-*"* !r-o *e " m"!er-" ,obre e e,$"-o!-em$o. C#"(*o -er!" "(!-*"* *e m"!er-" o#$" #(" re<-=( *e e,$"-o!-em$o9 $ro&o" #e >,!e ,e *e8orme. -,!o ",79 " 8#er+" ,!e9 " !r";e!or-" *e "#eo, ,er) *e,&-"*" $ro*#-e(*o ,# "eer"-=(. G [ 6.6 a 0300 N m52<5 < [ .4 m2,5 Gr"&e*"* e( *-8ere(!e, $"r!e, " !-err". C"r"",: < [ 94333 m2,5 E C"-ro: < [ 94064 m2,5 L" P"+: < [ 96 m2,5 Lo(*re,: < [ 9434 m2,5 M"*r-*: < [ 94560 m2,5 M>@-o D.F. < [ 94303 m2,5 O,o: < [ 94 m2,5 P"r7,: < [ 94 m2,5 Rom": < [ 945 m2,5 S"(!-"
"$or!"-=( " " 87,-"9 e,$e-"me(!e " " me)(-" ),-". E (e!o( e, #(" #(-*"* *er-&"*" *e SI #e ,e *e8-(e omo " 8#er+" (ee,"r-" $"r" $ro$or-o("r #(" "eer"-=( *e 0 m2,_ " #( obe!o *e 0 < *e m",". ESFUERZO A-=( *e em$e"r
ISCOSIDAD DIN%MICA L" &-,o,-*"* *-()m-" e, o(o-*" !"mb->( omo "b,o#!". -,o,-*"* e, " re,-,!e(-" -(!er(" " 8#o *e #( 8#-*o9 or-<-("*o $or e roe *e ", mo>#", #e ,e *e,-+"( #(", ,obre o!r",. A("-+" e,!o: e( #( ,=-*o9 e@-,!e #(" e,!r#!#r" r-,!"-(" *o(*e #(", mo>#", ,e e("+"( *e 8orm" r7<-*" ; ,# e,!r#!#r" (o "mb-"? e( "mb-o9 e( #( 8#-*o ", mo>#", (o $erm"(ee( e( e m-,mo #<"r *e(!ro *e " m","9 ,-(o #e ,e m#e&e(9 $ero "
" &e+ !r"!"( *e m"(!e(er,e #(-*",: e,e e,8#er+o $or $erm"(eer e( #( #<"r 8-o e, " re,-,!e(-" " 8#o ; *e!erm-(" " &-,o,-*"*. L" &-,o,-*"* *-()m-" ,e !om" *e !-em$o #e !"r*" e( 8#-r #( 7#-*o " !r"&>, *e #( !#bo "$-"r " #(" *e!erm-("*" !em$er"!#r" ; ,e m-*e e( $o-,e,
S.I:
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