UNIVERSIDAD NACIONAL FEDERICO VILLAREAL FACULT FACULTAD DE INGENIERIA INGENIER IA CIVIL
INFORME DE LABORATORIO
TEMA: PROPAGACIÓN DE ERROR
ALUMNO:
BENDEZÚ SÁNCHEZ, Nick Kei!
DOCENTE:
I!"# MISHTI INFANTES, INFANTES, $%&! '&()e*
MATERIA:
FISICA I
A+O ACADEMICO: ACADEMICO: - Se.e/)*e SECCION:
B
I.
OBJETIVOS
Re&(i0&* .e1ici2!e/ 1i*ec)&/ 3 e45*e/&* c2**ec)&.e!)e e( *e/%()&12# Re&(i0&* .e1ici2!e/ i!1i*ec)&/ 3 e45*e/&* c2**ec)&.e!)e e( *e/%()&12# A5(ic&* c2**ec)&.e!)e (& )e2*6& 1e e**2 e! /% 5*25&"&ci7! &( *e&(i0&* %!& .e1ici7! i!1i*ec)&# MATERIALES II. Re"(& "*&1%&1& M%e/)*& 1e c&*)%(i!& M%e/)*& 1e .&1e*& III. FUNDAMENTO TEORICO A) LA MEDICION
L& .e1ici7! e/ %! 5*2ce/2 89/ic2 1e (&/ cie!ci&/ %e c2!/i/)e e! c2.5&*&* (& c&!)i1&1 %e %e*e.2/ 1e)e*.i!&* 3 %!& c&!)i1&1 c2!2ci1& 1e (& .i/.& .&"!i)%1, %e e(e"i.2/ c2.2 %!i1&1# Te!ie!12 c2.2 5%!)2 1e *e;e*e!ci& 12/ c2/&/, %! 28 3 %!& %!i1&1 1e .e1i1& 3& e/)&8(eci1& 3& /e& %! /i/)e.& i!"(?/, /i/)e.& i!)e*!&ci2!&( 2 %!& %!i1&1 &*8i)*&*i& A( *e/%()&12 1e (& .e1ici7! /e ((&.& .e1i1& C%&!12 .e1i.2/ &("2 /e 1e8e @&ce* c2! c%i1&12, 5&*& ei)&* &()e*&* e( /i/)e.& %e 28/e*&*e.2/# P2* 2)*2 (&12, !2 @e.2/ 1e 5e*1e* 1e i/)& %e (&/ .e1i1&/ /e *e&(i0&! c2! &("! )i52 1e e**2*, 1e8i12 & i.5e*;ecci2!e/ 1e( i!/)*%cci2!e/ 2 & (i.i)&ci2!e/ 1e .e1i12*, e**2*e/ e45e*i.e!)&(e/, 52* e/2 /e @& 1e *e&(i0&* (& .e1i1& 1e ;2*.& %e (& &()e*&ci7! 5*21%ci1& /e& .%c@2 .e!2* %e e( e**2* e45e*i.e!)&( %e 5%e1& c2.e)e*/e# MEDICION DIRECTA: S2! &%e((&/ %e /e 28)ie!e! c2! %! i!/)*%.e!)2 1e
.e1i1&# E
1i*ec)&/ %)i(i0&!12 ;7*.%(&/ .&)e.9)ic&/, e
S2! c2!<%!)2/ 1e *e"(&/ %e 5e*.i)e!: A/i"!&* %! e**2* &( *e/%()&12 ;i!&( I!1ic&* (& i.52*)&!ci& *e(&)i& 1e (&/ 1i;e*e!)e/ .e1i1&/ 1i*ec)&/# T21& .e1i1& /e 1e8e e45*e/&* c2.2: x = x ± ∆ x
D2!1e x
: Me1i1&=.&"!i)%1 ;6/ic&>
x
:V&(2* .9/ 5*28&8(e=.e1i1& 5*2.e1i2>
∆ x:
E**2* &8/2(%)2
G*9;ic&.e!)e, *e5*e/e!)& & %! i!)e*&(2:
x −∆ x
x −∆ x
x
NOTA: E( e**2* e/)9 *e(&ci2!&12 c2! e( i!/)*%.e!)2 1e .e1i1&, e/)& .e1i1& e/ (& .9/ 5e%e& %e /e 5%e1e 28)e!e* 1e( i!/)*%.e!)2 1ii1i12 e!)*e # E( e**2* e/)9 *e(&ci2!&12 c2! e( i!/)*%.e!)2 1e .e1i1&, e/)& .e1i1& e/ (& .9/ 5e%e& %e /e 5%e1e 28)e!e* 1e( i!/)*%.e!)2 1ii1i12 e!)*e #
x=
(medidamas pequeña ) 2
P&*& %!& *e"(& "*&1%&1& %e %)i(i0&.2/, /% .e1i1& .9/ 5e%e& e/ ..# E!)2!ce/ (& .e1i1& 1e %!& (2!"i)%1 c2! (& *e"(& "*&1%&1& e! .e!ci7! /e*9:
l =2,5 cm ± 0,05 cm
E( e**2* *e(&)i2 /e 1e;i!e c2.2 e( c2cie!)e e!)*e e( e**2* &8/2(%)2 3 (& .e1i1& 5*2.e1i2 =.e1i1& *e&(i0&1&> P&*& (& .e1i1&: l=2,5 cm ± 0,05 cm
E R=
0,05 cm 2,5 cm
=0,02
E( e**2* *e(&)i2 i!1ic& %e 5&*)e *e5*e/e!)& e( e**2* &8/2(%)2 1e( &(2* 1e (& .e1i1&# Se e!)ie!1e %e c%&!12 .e!2* /e& e/)& *e(&ci7! .e<2* /e*9 !%e/)*& .e1ici7! A ece/ e/ c2!e!ie!)e e45*e/&* (& .&"!i)%1 1e( e**2* e! )?*.i!2/ 1e 52*ce!)&
( error ) = ∆ l ( 100 ) l
P&*& !%e/)*2 e
E( e**2* 52*ce!)%&(, i!1ic& e( 52*ce!)&
c2cie!)e 2 %!& c2.8i!&ci7! 1e &.82/, e( e**2* *e(&)ic2 )2)&( e/)9 1&12 52* (& /%.& 1e (2/ e**2*e/ *e(&)i2/ 1e (2/ )?*.i!2/ %e i!)e*ie!e! e! (& ;2*.%(&# IV.
DATOS EXPERIMENTALES
Te!e.2/ %! /7(i12 1e .&1e*& e! ;2*.& 1e 5*i/.& )*&5e02i1&( 12!1e /%/ .e1i1&/ %)i(i0&!12 c2.2 i!/)*%.e!)2 1e .e1ici7! %!& *e"(& .i(i.e)*&1& /2!: B&/e .&32* =
a
>
B&/e .e!2* = b > h
52 mm
24 mm
A!c@2 = k >
77 mm
A()%*& =
>
b
66 mm
h
k a
A@2*& 5&*& (& "*9;ic&:
l1
l t =l 1 + l 2
l1=57 mm l 2=52 mm
l2
V.
PROCEDIMIENTOS
l t
# P&*& (& .%e/)*& %e /e i!1ic& e! (& ;i"%*& 1e)e*.i!e /% (&*"2 )2)&( 5&*& (& c%&( .i1e c&1& %!& 1e (&/ (2!"i)%1e/ 5&*ci&(e/# E/c*i8e )%/ *e/%()&12/# S&8e.2/ %e: x = x ± ∆ x →l t =lt + ∆l t
P&*& (& "*9;ic&:
l 1=l 1 ± ∆ l 1 → l 1=57 mm ± 0.05 mm
l 2=l2 ± ∆ l 2 →l 2=52 mm ± 0.05 mm
Pe*2: A@2*&:
lt = l1 + l2 →l t =102 mm ∆ l t =0.5 mm + 0.5 mm = 1 mm
l t =102 mm ± 1 mm E!)2!ce/: # T2.&* (&/ 1i.e!/i2!e/ !ece/&*i&/ 5&*& c&(c%(&* e( 2(%.e! 1e( /7(i12 3
e/c*i8e (2/ *e/%()&12/ a =a ± ∆ a → a=66 mm ± 0.05 mm b =b ± ∆ b → b =52 mm ± 0.05 mm
h =h ± ∆ h → h =24 mm ± 0.05 mm k =k ± ∆ k → k = 77 mm ± 0.05 mm
VI. SITUACIONES PROBLEMATICAS 1. De)e*.i!e e( 52*ce!)&
.%e/)*&# I!1ic& )%/ 25e*&ci2!e/# S&8e.2/ %e: l t =l t + ∆ l t →l t =102 mm ± 1 mm A5(ic&!12 52*ce!)&
( error ) = ∆ l ( 100 ) → ( lt ) = l
∆ lt l t
( 100 )
1 mm
( lt )= 102 mm ( 100 ) =0.98 %e1&*9 &/6: l t =102 m m± 0.98 2. C2! (2/ 1&)2/ 1e (&/ .e1i1&/ 28)e!i1&/ 5&*& e( /7(i12, 1e)e*.i!&* /%
2(%.e!# Se"! (& "*9;ic& 5&*& e( 2(%.e! =V>Á*e&=A> 4 A!c@2 =k> S&8e.2/ %e:
A =
( a + b )( h ) 2
→ A=
(a + b )( h ) 2
→ A=
( 66 + 52 )( 24 ) 2
=1416 mm2
T&.8i?!: A = A +∆ A ∆ A = A ( ˄
E!)2!ce/:
∆a ∆b ∆h + + ) a b h
2
A =1416 mm ± ∆ A
∆ A =( 1416 )
(
0.5 66
+
0.5 52
+
0.5 24
)
=53.84 mm2
2
2
A =1416 mm ± 53.84 mm
E!)2!ce/ e( 9*e&:
A@2*& %e*e.2/ c&(c%(&* e( 2(%.e!, 12!1e: P2* (2 %e e( 2(%.e! 5*2.e1i2:
(
)(
V = 1416 77
V =( A ) ( k ) → V =( A )( k )
) =109032 mm
V =V ± ∆ V ∆V =V (
A1e.9/ /&8e.2/ %e:
˄
3
∆ A ∆ k + ) A k
H&((&!12 &*i&ci7! 1e 2(%.e! /e 28)ie!e: ∆ V = 109032
(
53.84 1416
+
0.5 77
)=
3
4853.68 mm
Fi!&(.e!)e 1e (& ec%&ci7! i!ici&( /e 28)ie!e e( 2(%.e!: 3
3
V =V ±∆ V →V =109032 mm ± 4853.68 mm
VII.
OBSERVACIONES Y CONCLUSIONES
L2/ i!/)*%.e!)2/ 1e .e1ici7! !2 !2/ 5%e1e! 1&* %! 1&)2 c2! e4&c)i)%1, .9/ /i )ie!e %!& &5*24i.&ci7! & (& .e1i1& i1e&(, 1e(i.i)9!12(& c2! /% .&*"e! 2 &*i&ci7! 1e e**2*# Mie!)&/ .&32* /e&! (&/ 25e*&ci2!e/ e!)*e (&/ .e1i1&/ 1i*ec)&/, .&32* /e*9 (& i!ce*)i1%.8*e &8/2(%)& 3 )&.8i?! .&32* /e*9 e( e**2* *e(&)i2 52*ce!)%&(#
L& .e1ici7! 1i*ec)& /ie.5*e /e*9 (& .e<2* @e**&.ie!)& 5&*& e!c2!)*&* (& .e1i1& .9/ &5*24i.&1&, %e & (& .e1ici7! i!1i*ec)&#
