Informes de Lab Fisica 1

UNIVERSIDAD NACIONAL SAN CRISTOBAL DE HUAMANGA FACULTAD DE INGENIERÍA DE MINAS, GEOLOGÍA Y CIVIL ESCUELA DE FORMACIÓN PROFESIONAL DE INGENIERÍA DE MINAS

CURSO

: LABORATORIO LABORATORIO DE FÍSICA

TEMA

: MEDICIÓN Y TEORÍA DE ERROR

PROFESOR

: LIC.FISICO MARCO A. CASTILLA JARA

INTEGRANTES

: HUAMANI MEZA IRVIN JUAN

AYACUCHO-PERÚ

PRESENTACION Este trabajo qe !o"s#ste e" $a %r#&era %r'!t#!a (e $aborator#o, qe ser' &) #&%orta"te %ara &'s a(e$a"te* Prese"to e$ %rese"te trabajo res%eta"(o $as %atas (a(as e" !$ase, ) se+#r $os %ro!e(#&#e"tos (e &e(#!#o"es ) teoras (e errores

INTRODUCCION Des(e -a!e &!-o t#e&%o qe se .or&aro" so!#e(a(es %r#&#t#/as, e$ ser -&a"o t/o $a "e!es#(a( (e &e(#r0 $as %r#&eras &a+"#t(es e&%$ea(as .ero" $a $o"+#t( ) &asa* Para $a %r#&era se estab$e!#1 !o&o "#(a( (e !o&%ara!#1" e$ ta&a2o (e $os (e(os ) $a $o"+#t( (e$ %#e e"tre otros* Para $a &asa se !o&%araro" $as !a"t#(a(es &e(#a"te %#e(ras, +ra"os, !o"!-as, et!* Este t#%o (e &e(#!#1" era !1&o(o %orqe !a(a %erso"a, $$e/aba !o"s#+o s %ro%#o %atr1" (e &e(#(a* S#" e&bar+o, te"a e$ #"!o"/e"#e"te (e qe $as &e(#(as /ar#aba" (e " #"(#/#(o a otro* Por eso $os est(#a"tes (e$ +ra(o (3!#&o C rea$#4a&os " $aborator#o (e &e(#(as (o"(e sa$#1 este trabajo* E" este #".or&e se re.$eja" $as !ara!terst#!as (e $o a%re"(#(o e" e$ %r#&er $aborator#o rea$#4a(o, &ostra"(o &#s !o"o!#&#e"tos ) a%$#!'"(o$os !o" &#s !o&%a2eros0 este $aborator#o se trat1 sobre $a &e(#(a qe abar!a e$ %eso, $a (e"s#(a( ) e$ /o$&e"* E" este #".or&e se &estra $a (e.#"#!#1" ) %ara q3 s#r/e" $os #"str&e"tos (e$ $aborator#o t#$#4a(os (esarro$$a"(o $a a!t#/#(a(*

MEDICION Y CALCULOS DE ERRORES

O56ETIVOS GENERALES I(e"t#.#!a $as .e"tes (e errores* Deter&#"a e$ /er(a(ero /a$or (e &a+"#t(es .s#!as &e(#(as (#re!ta e #"(#re!ta&e"te* Fa&#$#ar#4arse !o" eq#%os (e &e(#!#1" (e $aborator#o* OBJETIVO

Se %rete"(e qe e$ a$&"o se .a&#$#ar#!e !o" $os e$e&e"tos (e$ $aborator#o ) %e(a rea$#4ar %r'!t#!a&e"te (#st#"tas &e(#!#o"es, ta"to (#re!tas !o&o #"(#re!tas, $$e+a"(o a res$ta(os !o-ere"tes* De$ &#s&o &o(o se #"te"ta %o(er !a$!$ar $os errores (e &e(#!#1" !o&et#(os %ara !o"o!er $a %re!#s#1" (e (#!-as &e(#!#o"es* Ta&b#3" se %rete"(e #"tro(!#r "a .#$oso.a (e$ error* Se /er' e" $as s#+#e"tes %'+#"as qe "o so$o -a) errores (e !o"str!!#1", ta"to (e$ objeto a &e(#r !o&o (e $os #"str&e"tos t#$#4a(os %ara (#!-o %ro%1s#to, s#"o qe $a &e(#!#1" (e "a &#s&a %#e4a !o" " &#s&o #"str&e"to rea$#4a(a %or (#.ere"tes %erso"as %e(e to&ar (#st#"tos /a$ores*  A(e&'s se (esea (e&ostrar !1&o estos errores (e !$ase ) (e $e!tra to&a" !a(a /e4 &a)or #&%orta"!#a a &e(#(a qe $os !'$!$os rea$#4a(os %ara $$e+ar a " .#" 7(eter&#"ar $a (e"s#(a(8 se tor"a" &'s !o&%$ejos* As, se /e qe te"er e" !e"ta $os errores res$ta /#ta$ a $a -ora (e %re!#sar !a$q#er &e(#!#1" rea$#4a(a e" $a /#(a %ro.es#o"a$*

• • •

Fa&#$#ar#4arse !o" e$ so (e #"str&e"tos (e &e(#(a a"a$1+#!os* E9%resar e$ /a$or (e "a &e(#!#1" !o" s error o #"!ert#(&bre* E9%resar e$ /a$or (e "a &e(#!#1" #"(#re!ta !o" s error 7%ro%a+a!#1" (e errores8

MARCO TEORICO

MEDICIÓN Y TEORÍA DE ERROR MEDICIÓN Es !o&%arar $a !a"t#(a( (es!o"o!#(a qe qere&os (eter&#"ar ) "a !a"t#(a( !o"o!#(a (e $a &#s&a &a+"#t(, qe e$e+#&os !o&o "#(a(* Te"#e"(o !o&o %"to (e re.ere"!#a (os !osas: " objeto 7$o qe se q#ere &e(#r8 ) "a "#(a( (e &e(#(a )a estab$e!#(a )a sea e" S#ste&a I"+$es, S#ste&a I"ter"a!#o"a$, o S#ste&a De!#&a$* La (#&e"s#1" (e$ objeto ) $a "#(a( (ebe" ser (e $a &#s&a &a+"#t(* U"a %arte #&%orta"te (e $a &e(#!#1" es $a est#&a!#1" (e error  o a"'$#s#s (e errores )a qe to(a &e(#(a t#e"e error* A$ res$ta(o (e &e(#r $o $$a&a&os Me(#(a* Ca"(o &e(#&os a$+o se (ebe -a!er !o" +ra" !#(a(o, %ara e/#tar a$terar e$ s#ste&a qe obser/a&os* Por otro $a(o, "o -e&os (e %er(er (e /#sta qe $as &e(#(as se rea$#4a" !o" a$+;" t#%o (e error, (eb#(o a #&%er.e!!#o"es (e$ #"str&e"ta$ o a $#&#ta!#o"es (e$ &e(#(or, errores e9%er#&e"ta$es, %or eso, se -a (e rea$#4ar $a &e(#(a (e .or&a qe $a a$tera!#1" %ro(!#(a sea &!-o &e"or qe e$ error e9%er#&e"ta$ qe se %e(a !o&eter MEDIDAS DIRECTA La &e(#(a o &e(#!#1" es (#re!ta, !a"(o (#s%o"e&os (e " #"str&e"to (e &e(#(a qe $a obt#e"e, as s# (esea&os &e(#r $a (#sta"!#a (e " %"to a A " %"to B, ) (#s%o"e&os (e$ #"str&e"to qe "os %er&#te rea$#4ar $a &e(#!#1"* ERROR EN MEDICIONES DIRECTAS  A$ -a!er "a &e(#!#1" (#re!ta se (ebe" re(!#r a$ &"#&o $os errores s#ste&'t#!os qe so" (e$ t#%o te1r#!o, a&b#e"ta$, #"str&e"ta$ ) (e obser/a!#1"* E" $a %r'!t#!a e$ error s#ste&'t#!o (e "a &e(#(a (e%e"(e (e$ #"str&e"to e$e+#(o a &e(#r* S# -a!e&os " &e(#!#o"es (e "a &#s&a &a+"#t( .s#!a  x i  7#<=,>,?,@,"8 !o" e$ &#s&o #"str&e"to, e" +e"era$ se obte"(r'" $e!tras (#.ere"tes0 e9%resa&os  x i ± ∆ x s  ,(o"(e ∆ x s  es e$ error s#ste&'t#!o (e  x i * E$ !r#ter#o %r#"!#%a$ %ara est#&ar e$ error s#ste&'t#!o (e "a &e(#(a (#re!ta es e$ s#+#e"te: Sea  $a "#(a( (e $a &e"or es!a$a (e$ #"str&e"to (e &e(#!#1", e"to"!es e$ error s#ste&'t#!o e" esta es!a$a es a ±  ,B Eje&%$o: a$ &e(#r $a $o"+#t( (e "a .$e!-a (#re&os qe #"(#!a: 7B,> ± ,B8 "#(a(es (e $a &e"or es!a$a, o sea $a &e(#(a est' e"tre , ) B,

Deb#(o a $a ser#e (e " &e(#(as (e 9# 7=,**,"8 n

 X  ∑ =

i

el valor medioes : X =

i 1

n

Des/#a!#1" Sta"(ar( (e $a &e(#a o error esta(st#!o: ∆ xe

∆

E$ error ∆ X 

=

√

n

( X  − X ) ∑ =

2

i

i

1

( −1 )

n n

9 (e $a &e(#(a (#re!ta se e!"es#"$ !%":

=√ ( ∆ X  ) +( ∆ X  ) 2

s

2

e

 As $a &a+"#t( .s#!a se e9%resar' %or:

 X = X ± ∆ X 

MEDIDAS INDIRECTAS No s#e&%re es %os#b$e rea$#4ar "a &e(#(a (#re!ta, %orqe "o (#s%o"e&os (e$ #"str&e"to a(e!a(o qe "e!es#tas te"er, %orqe e$ /a$or a &e(#r es &) +ra"(e o &) %eqe2o (e%e"(e, %orqe -a) obst'!$os (e otra "atra$e4a, et!* Me(#!#1" #"(#re!ta es aqe$$a qe rea$#4a"(o $a &e(#!#1" (e "a /ar#ab$e, %o(e&os !a$!$ar otra (#st#"ta, %or $a qe esta&os #"teresa(os*

ERROR EN MEDICIONES INDIRECTAS Ca"(o e$ !'$!$o (e "a &e(#!#1" R se -a!e #"(#re!ta&e"te a %art#r (e otras qe )a !o"o!e&os qe so" $as &e(#!#o"es (#re!tas  x i ± ∆ x i  7#<=, @,/8 S#e"(o / e$ ";&ero (e /ar#ab$es #"(e%e"(#e"tes, es (e!#r R
2

√∑ ( v

∆ R=

i =1

Eje&%$o:

∂R ∂ X i

2

∆ X i )

E" " %ara$e$e%%e(o (e a$to -, a"!-o a ) $ar+o $, s /o$&e" V /#e"e (a(o %or $a s#+#e"te e9%res#1" V=V(h,a,l)=h a l 0 !o" (h ± ∆  h), (a ± ∆  a) y (l  ±

∆

 l), e"to"!es:

√

2

∆h ∆ V = √ ( a l ∆ h ) +( h l ∆ a ) +( h a ∆ l) =V  ( ) h 2

2

2

2

∆a +( ) a

2

∆l +( ) l

MATERIALES E INTRUMENTOS U"a re+$a +ra(a(a* U" !a$#bra(or /er"#er* U" &#!r1&etro* U"a ba$a"4a* U"a %#e4a !#$"(r#!a* U" je+o (e es.eras* ojas (e !a(er"o* Cro"o&etro* 6e+o (e %esas*

PROCEDIMIENTO & I(e"t#.#qe $os errores s#ste&'t#!os, !ro"o&etro, re+$a +ra(a(a, !a$#bra(or  /er"#er, ba$a"4a, (#"a&1&etro, a&%er&etro* To&e "a $e!tra ) -a$$e e$ /a$or  /er(a(ero (e (#!-a &a+"#t(* Para #(e"t#.#!ar $os errores s#ste&'t#!os se (ebe te"er e" !e"ta $a $e!tra &"#&a qe a%are!e e" !a(a #"str&e"to t#$#4a(o* Des%3s (e #(e"t#.#!a(o $a $e!tra &"#&a, (ebe&os obte"er $a &#ta( (e (#!-o /a$or %ara e"!o"trar e$ error #"str&e"ta$ qe /#e"e a ser e$ error  s#ste&'t#!o*  A !o"t#"a!#1" %rese"tare&os $os errores s#ste&'t#!os (e !a(a "o (e $os #"str&e"tos* TABLA N' &

INSTRUMENTOS CRONOMETRO REGLA GRADUADA CALI5RADOR VERNIER

LECTURA MÍNIMA *=s =&&*=!& *=&&

ERRORES SISTEM(TICOS TEÓRICOS

*Bs *B&&*B!& *B&&

5ALANHA

*=+

*B+

Para -a$$ar e$ /a$or /er(a(ero (e !a(a "o (e $os #"str&e"to, to&a&os !a$q#er &e(#(a (e re.ere"!#a (e !a(a #"str&e"to:

D1"(e: : Va$or /er(a(ero* : Va$or &e(#o* : Errores s#ste&'t#!os te1r#!os*

TABLA N' ) INSTRUMENTOS

ERRORES SISTEM(TICOS TEÓRICOS

VALORES DE

VALOR VERDADERO

REFERENCIA

CRONOMETRO

*B s

Bs

Bs

REGLA GRADUADA

*B &&*B !&

= !&

= !&

*B !&

CALI5RADOR VERNIER *B &&

B &&

B &&

*B &&

5ALANHA

B+

B+

*B +

*B s

*B +

) Me(#r !o" " !a$#bra(or /er"#er e$ es%esor (e "a %$a!a &et'$#!a (e (#.ere"tes %artes* Rea$#4ar = &e(#!#o"es ) !o$o!ar $os res$ta(os e" "a

tab$a* Deter&#"e e$ /a$or /er(a(ero (e$ es%esor (e $a %$a!a, !o&b#"a"(o errores* * Para &e(#r e$ es%esor (e $a %$a!a &et'$#!a, $o !o$o!a&os e" e$ !a$#bra(or  Ver"#er e"tre $as (os es!a$as 7es!a$a .#ja ) es!a$a &1/#$8 ) %ara saber $a &e(#(a (e$ es%esor, $a %arte e"tera "os (ar' $a es!a$a .#ja qe est3" a"tes (e$ !ero (e $a es!a$a &1/#$ ) $a %arte (e!#&a$ "os (ar' $as $"eas s%er%estas (e $a es!a$a .#ja ) $a es!a$a &1/#$* Prese"ta&os $as = &e(#!#o"es (e $a %$a!a &et'$#!a e" "a tab$a*

 ANALISIS DE DATOS =* Vo$&e" ) (e"s#(a( (e$ %ara$e$e%%e(o

=

>

?



B



J



K

=

Pro&*

=K*B   A B*>

=K*B > B*>

=K*  B*=

=K*B  B*=

=K*  B*=

=K*B  B*=

=K*B  B*>

=K*B  B*=

=K*B > B*=

=K*  B*>

=K*BB>

 ?>*?

?>*>

?>*?>

?>*?>

?>*>

?>*?

?>*?

?>*?

?>*?>

?>*?

?>*?=

L

B*=J

M >*JK

>*

>*J

>*=

>*JK

>*J

>*

>*J

>*JK

 =*?  =* 

Pro&* =*?J> B =*?J B

>*

>*BK>

>* Vo$&e" ) (e"s#(a( (e "a es.era

D &

= =*?  =* J

> =*?  =* 

? =*  =*B 

 =*?  =* K

B =*?  =* 

 =*? J =*B 

J =*  =* J

?* D#'&etro (e " !abe$$o

D

=

>

?



B



J



K

=

*B

*J

*B

*

*J

*B

*J

*

*B

*

Pro& * *BK

* Vo$&e" (e $#bro

= L >>* B  A =* 

>

?



B



J



K

=

>>*  =B* K

>>*  =B* 

>>* B =* 

>>*  =B* 

>>* B =B* K

>>* B =* 

>>*  =B* 

>>*  =B* K

>>* B =* 

Pro& * >>*K =BK*=

 >*

>*> >* >* >*> >* B* Vo$&e" ) (e"s#(a( (e " so$#(o

>*

>*

(<=*= D*? <=*= M<>?K*

RESULTADO Tab$a "= 120 100 80

L A

60

H

40

M

20 0 0

2

4

6

8

10

12

Tab$a "> 19 18 D

17

m 16 15 0

1

2

3

Tab$a "?

4

5

6

7

8

9

10

>*>

>*

>*>

D 0.1 D 0.05 0 0

2

4

6

8

10

12

Tab$a " 250 200 150

L

100

A

50

H

0 0

2

4

6

8

10

12

CONCLUSIONES &  A$ rea$#4ar $a %r'!t#!a (e $aborator#o a%re"(#&os a!er!a (e $as &e(#!#o"es (e $as (#&e"s#o"es e" .or&a te1r#!a ) sobre to(o %r'!t#!a* ) E" $a %r'!t#!a (e $aborator#o, a(q#r#&os "e/as !a%a!#(a(es qe ser'" ;t#$es e" "estro !a&%o o!%a!#o"a$ *  A(q#r#&os $a !a%a!#(a( (e #(e"t#.#!ar $as .e"tes (e error ) (eter&#"ar e$ /a$or /er(a(ero (e $a &a+"#t( !orres%o"(#e"te*

O5SERVACIONES

•

•

•

Los #"str&e"tos (e$ $aborator#o $a &a)ora so" obso$etos, ) (eja" +ra" #"sat#s.a!!#1" e" $as %ra!t#!as rea$#4a(as* Las &esas %or $as $$/#as est'" &a$o+ra(as* Fa$ta re%arar $as +oteras (e $os te!-os* E$ $aborator#o esta "o est' e" !o"(#!#o"es (e so %or $as $$/#as e" "estra "#/ers#(a(*

GLOSARIO Pa%e$ M#$#&etra(o: E$ %a%e$ &#$#&etra(o es %a%e$ #&%reso !o" .#"as $"eas e"tre!r4a(as, se%ara(as se+;" "a (#sta"!#a (eter&#"a(a 7"or&a$&e"te = && e" $a es!a$a re+$ar8* Estas $"eas se sa" !o&o +as (e (#bjo, es%e!#a$&e"te %ara +ra.#!ar ."!#o"es &ate&'t#!as o (atos e9%er#&e"ta$es ) (#a+ra&as 7/3ase +r'.#!a (e "a ."!#1"8* Se e&%$ea" e" +eo&etra a"a$t#!a ) $a e"se2a"4a (e &ate&'t#!as e #"+e"#era* Ver"#er: Es un instrumento sumamente delicado y debe manipularse con habilidad, cuidado, delicadeza, con precaución de no rayarlo ni doblarlo (en especial, la colisa de  profundidad). Deben evitarse especialmente las limaduras, que pueden alojarse entre sus  piezas y provocar daños

Para$e$e%%e(o: es " %o$#e(ro (e se#s !aras 7%or ta"to, " -e9ae(ro8, e" e$ qe to(as $as !aras so" %ara$e$o+ra&os, %ara$e$as e #+a$es (os a (os* U" %ara$e$e%%e(o t#e"e => ar#stas, qe so" #+a$es ) %ara$e$as e" +r%os (e !atro, )  /3rt#!es*

5I5LIOGRAFÍA & *&o"o+ra.as*!o& ) C#e"!#a Fs#!a E9%er#&e"ta$, Robert T LAGEMAN, E(#tor#a$ Nor&a

=K, Ca$# Co$o&b#a * Fs#!a, Vo$&e" I Me!'"#!a, A$o"soF#", E(#tor#a$ Fo"(o E(!at#/o I"tera&er#!a"a SA* + Fs#!a %ara !#e"!#as e #"+e"#era* Sera)Q5e#!-"er, E(#tor#a$ M!Gra#$$ I"tera&er#!a"a E(#tores, SA* M39#!o, #"ta e(#!#1"*

INDICE PAGINA > ?  B  K = == => =B =

CONTENIDO %rese"ta!#1" #"tro(!!#1" t#t$o objet#/os &ar!o te1r#!o &ater#a$es #"str&e"tos %ro!e(#&#e"tos a"'$#s#s (e (atos res$ta(os !o"!$s#o"es ) obser/a!#o"es +$osar#os