UNAM FACULTAD DE INGENERIA División de Ciencias Básicas DEPARTA DEPARTAMENTO MENTO DE MATEMÁTICAS MATEMÁTICAS APLICADAS
LABORATORIO LABORATORIO DE MECÁNICA CINEMATICA Y DINAMICA PRACTICA: 1 “MOVIMIENTO RECTILÍNEO
UNIFORMEMENTE ACELERADO” GRUPO: 8 BRIGADA: ! INTEGRANTES DE LA BRIGADA: 1. 2. 3. 4.
5. SEMESTRE: 2014-2 FEC"A: 3/03/14
INTRODUCCIÓN: Mo!"!#$%o '%!()$#o*"o!"!#$%o '+, %&,#'%o&! # +$ ()$# '%. ! #( "!( $o '"! # #$%!o* ( $!' &!'!$ +# +## #6#&!"#$%& ( #(o'! # ( # + "+(o. E%o #&"!%# '(!7!'& #( "o!"!#$%o '%!()$#o #$ "o!"!#$%o '%!()$#o , +$!7o&"#* ! #( "+(o # ( #(o'! $o &)* , "o!"!#$%o '%!()$#o +$!7o&"#"#$%# &!o ! #( "+(o # ( #(o'! &) # "$#& 'o$%$%# #$ #( %&$'+&o #( %!#"o. ! # 'o$!#& +# #( "o!"!#$%o '%!()$#o %!#$# (+& #$ +$ o( !"#$!$* ( o!'!$ #( "!( #$ '+(+!#& !$%$%# +# #%#&"!$ o& #( "+(o #( #'%o& # o!'!$. Mo!"!#$%o '%!()$#o , +$!7o&"#* #%# "o!"!#$%o # '&'%#&!9 o&+# + %&,#'%o&! # +$ ()$# '% , #( "+(o* ( !''!$ , #( #$%!o # ( #(o'! #&"$#'#$ 'o$%$%# #$ #( %!#"o. E$ 'o$#'+#$'!* $o #6!%# '#(#&'!$* , +# ( '#(#&'!$ %$#$'!( # $+(* +#%o +# #( "+(o # ( #(o'! # 'o$%$%#* , ( '#(#&'!$ $o&"( # $+( o&+# ( !''!$ # ( #(o'! # 'o$%$%#. L #'+'!$ # ( o!'!$ & +$ "!( +# # #(9 'o$ +$ "o!"!#$%o '%!()$#o , +$!7o&"# 'o$ +$ #(o'! #: 6 60;<% Do$# 60 # ( o!'!$ #( "!( #$ #( !$%$%# !$!'!(. =o& %$%o* #( "!( 'o& #'!o !+(# #$ %!#"o !+(#. E( "o!"!#$%o '%!()$#o +$!7o&"#"#$%# &!o # '&'%#&!9 o&+# + %&,#'%o&! # +$ ()$# '% , #( "+(o # ( #(o'! &) &oo&'!o$("#$%# ( %!#"o. =o& 'o$!+!#$%#* ( '#(#&'!$ $o&"( # $+( o&+# ( #(o'! $o '"! # !''!$ , ( '#(#&'!$ %$#$'!( # 'o$%$%#* , +# #( "+(o # ( #(o'! &) +$!7o&"#"#$%# 'o$ #( %!#"o. E%# "o!"!#$%o +## #& '#(#&o ! #( "+(o # ( #(o'! +"#$% "#! +# %&$'+& #( %!#"o , %&o ! #( "+(o # ( #(o'! !"!$+,# #$ #( %&$'+&o #( %!#"o. L #'+'!$ # ( #(o'! # +$ "!( +# # #(9 'o$ +$ "o!"!#$%o '%!()$#o +$!7o&"#"#$%# &!o 'o$ +$ '#(#&'!$ #: 0;<%
Do$# 0 # ( #(o'! #( "!( #$ #( !$%$%# !$!'!(. =o& %$%o* ( #(o'! +"#$% '$%!# !+(# #$ %!#"o !+(#.
O>?ETIVO: 1.-D#%#&"!$& ( "$!%+ # ( '#(#&'!$ # +$ '+#&o* #$ %&,#'%o&! '%!()$# o +$ ($o !$'(!$o* +%!(!9$o #+!o # '"+%o , o7%@ !$%(o & ( (!9'!$ # ( &'%!'. 2.-R#(!9& ( &7!': %* % , %* +# #$%$ #( 'o"o&%"!#$%o #( "o!"!#$%o # !'Bo '+#&o. EUI=O A UTILIAR: 1. 2. 3. 4. 5. G.
R!#( 'o$ oo&%#. C&&o !$"!'o. I$%#&7# “'!#$'# o&Bo”. #$o& # "o!"!#$%o. I$!'o& # $+(o. Co"+%o&.
DEARROLLLO: =ARTE I: 1.-Co$ ,+ # + &o7#o&* #&!7!+# +# %oo #( #+!o #%H 'o$#'%o #'+"#$%#. I$%(# #( &(o "o%&o #$ ( 7!+& No. 1 'o$!#&$o #( $+(o # !$'(!$'!$ # 10J . 2.-E$'!#$ ( 'o"+%o& , ( !$%#&79* ## +# '&+# %o%("#$%# #( !%#". 3.-DH o(# '(!' #$ #( )'o$o D% %+!o* # "+#%& +$ #$%$ 'o"o ( # ( 7!+& No. 2. A 'o$%!$+'!$ B +$ '(!' #$ C%# E6#&!"#$% "o%&$o ) ( #$%$ # ( 7!+& No. 3. 4.-ABo&* $o +$ '(!' o #( '$( 1 # ( 7!+& # ( !$%#&79 K7!+& No. 3 # #(!# +$ (!% # #$o K7!+& No. 4 # ( '+( # ## #(#''!o$& Mo%!o$
#$o& B'!#$o o(# '(!'. E( &o&" "+#%& +# #( #$o& #% 'o$#'%o ( !$%#&79 , (!%o & !$!'!& 'o$ #( #6#&!"#$%o K7!+& No. 5. 5.-Co$ #( 7!$ # &7!'& #( 'o"o&%"!#$%o # ( o!'!$ #( '&&o !$"!'o +&$%# + "o!"!#$%o* &&% # ( &%# +#&!o& !9+!#& ( o'!$ o!%!o$ 'B 1 2 K" ( &%# !$7#&!o& !9+!#& o ( o'!$ RA= K7!+& No. 8. E% ''!$ "o%&& ( #$%$ # &7!''!$ K7!+& No. P. G.-Co(o+# #( '&&o !$"!'o o #( ($o !$'(!$o #$ ( o!'!$ !$!'!(* H +$ '(!' o #( o%$ %&% , +#(%# #( '&&o # "$#& +# H%# !$!'!# + "o!"!#$%o. C+$o #( '&&o !$"!'o ('$'# ( o!'!$ 7!$( H +$ '(!' o #( o%$ %o. Q.-E$ #( "o$!%o& # "+#%& ( &7!' #( 'o"o&%"!#$%o # ( o!'!$ #( '&&o !$"!'o. Co$ ( ,+ # + &o7#o& o& (o %o $o ##o , o#&# ! !'Bo 'o"o&%"!#$%o # #( ##&o. O%#$ ( %( # (o %!#"o !%&o. 8.-! ( &7!' $o # ( ##& !% #( #6#&!"#$%o K'%!!# G , Q B% +# ( &!'!$ # (o %o !%&o $o '"!# #"!o. =ARTE II: 1.-=& o%#$#& ( "$!%+ # ( '#(#&'!$ #( '&&o !$"!'o* o #( "#$ # ( #$%$ # &7!''!$ H +$ '(!' #$ #( o%$ 7!% & +%& ( &7!' +$ '+& #(#''!o$$o ( o'!$ +&%!' F!%. 2.-I$%#&%# #( !$!7!'o 7)!'o # ' +$o # (o 'o#7!'!#$%# o%#$!o. A A'#(#&'!$ S
m/s ²
> V#(o'! S
m/ s
C =o!'!$ S
m
3.-D#%#&"!$# #( (o& # ( "$!%+ # ( '#(#&'!$ #( '&&o !$"!'o. a= 1.322 K cm / s ² .
CONCLUIONE: 1.-R#o&%# #( (o& # ( "$!%+ # ( '#(#&'!$ , ( #'+'!o$# o%#$! &: a= 1.322 K cm / s ² .
( ) =1. 322 t+ 0.669 ( m / s )
v=v t
()
s=s t =0 .0661 t ² + 0.669 t+ 0.195
No. 1 2 3 4 5 G Q 8 P 10
T!#"o K 0.0423 0.0305 0.025P 0.0222 0.0204 0.018G 0.01Q4 0.01G1 0.0154 0.0144
D!%$'! K'" 0.00P243P 0.00G1P54 0.0050P38 0.0042430 0.0038405 0.0034455 0.00318G3 0.002P0P2 0.002QG1G 0.002552Q
(m)
No. 1 2 3 4 5 G Q 8 P 10
%: A'#(#&'!$ K'"/ 1.322
T!#"o K 0.0423 0.0305 0.025P 0.0222 0.0204 0.018G 0.01Q4 0.01G1 0.0154 0.0144
V#(o'!K'"/ 0.2Q1P2384 0.244QQ44 0.2341P0Q2 0.225GQQQG 0.22153G32 0.21Q3P488 0.214G33P2 0.211G4288 0.21003232 0.20QQ3152
S vs T sub-title
0.01 0.01 0.01 S
0 0 0 0.01
0.02
0.02
0.03
0.03 T
0.04
0.04
0.05
# vs T
0.3 0.25 0.2 #
0.15 0.1 0.05 0 0.01
0.02
0.02
0.03
0.03 T
0.04
0.04
0.05
% sub-title
3 2.5 2
a
1.5 1 0.5 0 2
2.5
3
3.5
4
4.5
5
5.5
$
=o& (o +# '(&"#$%# # +## #& #$ ( &7!'* #7#'%!"#$%# # %&% # +$ 'o"o&%"!#$%o # +$ "o!"!#$%o '%!()$#o +$!7o&"#"#$%# '#(#&o , +# 'o"o #%$ #% &7!' # 'o"o # ##$ # 'o"o&%&# ( &7!' # #%# %!o # "o!"!#$%o. 3.-Co$ #'%o (o (o o%#$!o & ( &!#9 , o!'!$ !$!'!(#* ! ! #%o o$ #+#Wo* ! 'o&o$#$ (o (o ##&o 'o&# 'o$ ( 'o$!'!o$# !$!'!(# #( #6#&!"#$%o* #%'. !* #7!$!%!"#$%# (o (o !$!'!(# # ( o!'!$ , ( &!#9 o$ #+#W)!"o , ! o$ 'o&# ( 'o$!'!o$# !$!'!(# #( #6#&!"#$%o , o& (o %$%o ! o$ (o ##&o. 4.-Co"(#%# ( !+!#$%# %( & (o %!#"o !%&o.
% K 0.0423 0.0305 0.025P 0.0222 0.0.204 0.018G 0.0.1Q4 0.01G1 0.0154 0.0144 0.0140
1.322 K" 0.0000P2 43 0.0000G1 P5 0.000050 P3 0.000042 43 0.000038 40 0.000034 45 0.000031 8G 0.00002P 0P 0.00002Q G1 0.000025 52 0.000024 40
K"/ K"/ 0.002Q1P 0.00244Q 0.002341 0.00225G 0.002215 0.0021Q3 0.00214G 0.00211G 0.002100 0.0020G8 0.0020G8
5.-O%#$ ( !7#$'! #$% #( (o& # ( "$!%+ # ( '#(#&'!$ 'o$ #( (o& # ( 'o"o$#$%# # ( '#(#&'!$ # ( &# #$ ( !''!$ #( "o!"!#$%o* , B 'o"#$%&!o 'o$ #'%o !'B !7#$'!. L !7#$'! +# #6!%# #$% " '#(#&'!o$# # #( #&&o& #6#&!"#$%( #( '+( # ## %o ( 'o +# #%$ !$o(+'& & #( +(%o # ( # #( (o& (. A+$+# !#" # 7! +$ o&'#$%# # #&&o& #6#&!"#$%( #( '+( # '('+( # ( !+!#$%# "$#&: EEX%-#6%Y100 D# ( '+( $oo%&o o%+!"o +$ ( EEX .35X.
G.-Co$ #( &o!%o # #$%#$#& #( !$!7!'o 7)!'o # (+$o #(#"#$%o #o"H%&!'o # ( &7!'* B (o !+!#$%#: G.1 Co$ (o %o !%&o #$ ( '%!! Q # ( &%# I* #(o $+#"#$%# ( &7!' K % , %&'# +$ '+& +# o (o +$%o o%#$!o. S vs T sub-title
0.01 0.01 0.01 0.01 0.01 S
0.01 0 0 0 0 0 0.01
0.02
0.02
0.03
0.03
0.04
0.04
0.05
T
G.2 D!+# '% %$#$%# ( '+& #$ (o +$%o 'o&o$!#$%# (o %!#"o !%&o , o%#$ ( #$!#$%# # ' +$ # ( '% %&9. Z+H #$% #( (o& # ( #$!#$%# # ' '%[.
S vs T sub-title
0.01 0.01 0.01 0.01 0.01 S
0.01 0 0 0 0 0 0.01
0.02
0.02
0.03
0.03
0.04
0.04
0.05
T
G.3 Co$ (o (o # ( #$!#$%# # ( '% , #( %!#"o 'o&o$!#$%#* #(o ( '+& K %.
# vs T
0.3
0.25
0.2
#
0.15
0.1
0.05
0 0.01
0.02
0.02
0.03
0.03
0.04
0.04
0.05
T
G.4 E"(#H #( "H%oo # ")$!"o '+&o K #'+'!o$# I , II , o%#$ ( '% # +%#* ) 'o"o ( #'+'!$ +# #%#&"!$ ( &!#9 #$ 7+$'!$ #( %!#"o.
( )=1.322 t+ 0. 1744 ( m / s )
v t
G.5 Z+H #$% ( #$!#$%# # ( '% # +%#[ L #$!#$%# #$% ( '#(#&'!$.
G.G D# ( #'+'!$ o%#$! #$ #( +$%o G.4* o%#$ #( (o& # ( "$!%+ # ( '#(#&'!$ , #(o ( &7!' K %.
CONCLUSIONES:
&'! ( o7%@ , ( #'+'!$ # ( &o( +!"o o%#$#& ( '#(#&'!$ ) 'o"o + #(o'!* #"o%&$o +# #( MRUA +# +$+# &!$o #( $+(o ( '#(#&'!$ +# # o%!#$# 'o$ #%# #&"$#'# 'o$%$%# !'B '#(#&'!$. T"!H$ $o #&'%"o +# #( o7%@ (#o " #&&o # (o ##&o o& (o +# # %+o +# #%!& #( #6#&!"#$%o &! #'#. =o& o%&o (o* ( !$'#&%!+" #$ #( %!#"o %#$& o 'o"o$#$%#* #&* +$ #%)%!' K#! ( $"#&o # #'# +# # !%#$ ( "#! , o%& +# !$o(+'& #( 7'%o& B+"$o ## $o%&# +# ( #&o$ +# "!# #( %!#"o '%!& o #'%!& #( '&o$"#%&o # "$#& !7#$%# # +$ "#! o%&. =o&) 'o$!#&&# +$ %#&'#& 'o"o$#$%# +# # ( !$'#&%!+" %!o > ##'!7!' o& #( 7&!'$%# #( '&o$"#%&o* #&o H% # +## #'!& ! # %o" #$ '+#$% +# ( " $o%(# # ( +# 'o&o$# ( 7'%o& B+"$o >I>LIORAFÍA: 1.-OLAR . ?o&#* “C!$#"%!' , D!$"!' >!' & I$#$!#&o”* E. T&!((-F'+(% # I$#$!#&)* UNAM* 2\ #!'!$* MH6!'o* 1PP8. 2.-I>>ELER* R+#(( C.* “M#'$!' & I$#$!#&o* D!$"!'”* V#&!$ #$ #Wo(* R##$%'!o$# , #&!'!o # !$#$!#&)* . A.* MH6!'o* 1P84. 3.-M!'&oo7% E$'&% 2002.