DETERMINACIÓN EXPERIMENTAL DEL NUMERO PI
JHONAT JHONATAN DANIEL PINEDA VARGAS VARGAS () JUAN SEBASTIAN SEBASTIAN RODRIGUEZ BALLEN () ANDREA LORENA GÓMEZ FRANCO (25151595) EDUARD MAURICIO CURREA CAMARGO ()
UNIVERSIDAD NACIONAL DE COLOMBIA – SEDE BOGOT DEPARTAMENTO DE F!SICA FLUIDOS " ELECTROMAGNETISMO PARA BIOCIENCIAS AGOSTO DE 2#15 RESUMEN
E$ %&' *+,'-, .% /0*'*- &% .%'%*-$ %3%*-%$'/%$'% %/ $4%* - ,$ 0&% %$ ,-*,6$7%*%$,-& /%'*-& /& ,6/%& &% /%& %$,6%$'* &6 *.- .-+%'* 8 +*% &: -& &% ;,% 6& .% <*=,& %$ %/ -/-%'*. %/ /<*:'-, 8 %/ ,6.*-,6/. , *%7%*%$,-> PALABRAS CLAVE N4%* - +*% .% / ,-*,6$7%*%$,- *.- ,-*,6$7%*%$,-> INTRODUCCIÓ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
MTODO EXPERIMENTAL 1> V*-0/%& +*% *.-> 2> P*,%.--%$'
E$ *-%* /6<* &% '-%$% %$ ,6%$' / 7*6/ %&'0/%,-. .%/ +*% .% / ,-*,6$7%*%$,- A = π ∗r
2
*'-* .% %// &% '*$ .'& %3%*-%$'/%& .% +*% 8 *.- .%
5 ,-*,6$7%*%$,-& .-7%*%$'%& .% / &-<6-%$'% $%* 2>1> S% .-06*$ ,:*,6/& .% $%* /%'*- &0*% 6$ ; ,6.*-,6/. 8 &% -.- &6 *.- '$. , *%7%*%$,- /& ,6.*& .% #5 , ,. 6$>
2>2> P* ;//* %/ +*% &% ,$'*$ /& ,6.*& ?6% ,. ,:*,6/ *.% 8 &% 2 /-, / &-<6-%$'% 7*6/ A = no.cuadros∗(0,5 ) >
2>> P&'%*-*%$'% &% <*=,*$ /& @/*%& .% *.- @&> +*% .% /& ,:*,6/& / n ,6/ $& .- 6$ %,6,-$ .% / 7* A = c r , &-%$. * *.- 8 A +*%>
2>K> P* 0'%$%* / %,6,-$ /-$%/ .% %&'& .'& &% 6'-/- %/ %/ /<*:'-, / ?6% $& ** 6$ %$.-%$'% ,**%&$.-%$'% / %3$%$'% .%/ *.- %$ / %,6,-$ .% / ,-*,6$7%*%$,-> 2>5> U$ @% 0'%$-. &' %$.-%$'% &% <*=, / %/ +*% @&> R.-$ 0'%$-%$. %/ @/* .% , 8 =$/%$'% ,*0$. / ,%*,$: ,$ %/ $4%* > II>
RESULTADOS " DISCUSIÓN
*% (#25 ,2) D-+%'* (#5 ,) R.- (#5 ,)
R.-2 (#25 ,2)
5###
#
K#
1##
95#
11#
55
#25
112##
12#
#
##
15##
1K#
#
K9##
199##
1#
#
K##
Tabla 1. Datos obtenidos
E$ %&' *+,'-, &% %@-.%$,- / -*'$,- 8 %3,'-'6. .%/ $6%* - 8 ?6% &/%$'% ,$ %/ 6& .% %/ -/-%'*. 8 %/ /<*:'-, &% /<* ;//*/> E$ *-%* /6<* ,6$. &% -.% %/ *.- %$ '*-$& .% /& ,6.*& %3-&'% 6$ %*** .% #5 , 8 ?6% %/ $4%* .% ,6.*& $ %& %3,' 8 .%%$.% .%/ ,*-'%*- .%/ %3%*-%$'.* ,/%'* 6$ ,6.* ,$ '* 8 .%'%*-$* %&' ,$'-..> A *'-* .%/ *.- &% ,/,6/ %/ +*% / ,6/ &%% 6$ -$,%*'-.60*% .% #25 , 2 ,/,6/. &: ∆ A =±
√
2
∂r ∗∆ r ∂r
∆ A =± √ ( 2r ∗∆ r )
2
∆ A =±|2r ∗∆ r| ∆ A =±|2∗0,5∗0,25|=0,25 cm
2
E&' <*+=, ,**%&$.% / *.- ?6% %.-& .% /& 5 ,-*,6$7%*%$,-& /%'*-& %$ %/ /0*'*->
Gráfca 1. Radio vs. Área 25# 2## 15# Área (cm2) 1## 5# #
K
5
9
Radio (cm)
y =3,0602 x 2,0123
U$ @% 0'%$-. / <*+=, .% +*% %$ 76$,-$ .%/ *.- &% 6'-/- %/ %/ /<*:'-, %/ ,6/ .-=, / %,6,-$ -$-,-/%$'% '%$,-/ 6$ %,6,-$ /-$%/ /-,$. /<*-'& 8 &6& *-%..%& 0& /.& &: logA = log ( c r
n
)
logA = log ( c )+ log ( r
n
)
logA = log ( c ) + nlog ( r )
Gráfca 2. Log (r) vs. Log(A) 2>5 2 1>5
Log (A)
1 #>5 # #>5
#>
#>
#>
#>9
1
Log (r)
y =2,0178 x + 0,4843
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π ∗r >
Gráfca 3. Radion vs. Área 25# 2## 15# Area (cm2) 1## 5# # 1#
2#
#
K#
5#
#
#
Radion (cm)
y = 3,0161 x + 0,5159
S% ,*0 ?6% %/ $4%* 0'%$-. %$ %&' *+,'-, 0%.%,% / %&'0/%,-. ,$ 6$ .-7%*%$,- ,$&-.%*0/%%$'% %?6% .% #1255>
III>
CONCLUSIONES •
U$ 7* 68 %7%,'-@ .% *%$.%* *%*%&%$'* /& .'&
•
.% 6$ /0*'*- %& %.-$'% 6$ *%/,-$ /-$%/> L -$,%*'-.60*% %& 6$ @/* &,-. /& %.-.& *%/%& '.& * '%$%* 6$ *%&6/'. +& *%,-& ,%*, .% /&
•
.'&> E/ $4%* - %& 6$ $4%* ,$&'$'% 8 7+,-/%$'% &% ,*6%0 &6 @/*>
REFERENCIAS 1 M> M*:$ U*-0%> A*3-,-$ .% /& $4%*& -**,-$/%&> U$-@%*&-.. .% M%.%//:$> 2##> P+<&> 25 2>
