UNIVERSIDAD NACIONAL DE INGENIERÍA FACULT FACULTAD DE INGENIERÍA INGENIER ÍA MECÁNICA
INFORME DE LABORATORIO Nº1:
MEDICIÓN INTEGRANTES: CHAVEZ CHAVEZ FERNANDEZ JOVANI JOVANI JESUS SAGASTEGUI CALDERON DAVID DAVID ORLANDO DIAZ RUIZ ROBERTH ERICK ROJAS CALLE MARIO ENRIQUE MOSQUERA GUTIERREZ PEDRO JOSE
CURSO:
FSICA I
SECCION:
E
FECHA:
0!"0!"15
PROFESOR:
V A S Q U E Z A L VA D A R I O
20151308I 20152652E 20151053K 20152636J 20151362C
INDICE
1 2 3 $ 5 6 & 8 ! 10
RESUMEN TITULO ANTE ANTECE CEDE DENT NTE E E#PE E#PERI RIME MENT NTA AL FUND FUNDAM AMEN ENTO TO TE%R TE%RIC ICO O PARTE RTE E#PE E#PERI RIME MENT NTA AL CUESTIONARIO DISC DISCUC UCI% I%N N DE DE RES RESUL ULT TADO DOS S CONCLUSIONES SUGERENCIAS REFERENCIA REFERENCIAS S BIBLIOG BIBLIOGRAFIC RAFICAS AS
RESUMEN E' ()*+,-.( /--/' 4+ +,+ +/+-7+,( + 4+,+7- +' +( -+,-497)+ 4+ 9 79+, 4+ :-*('+ 9,-'-;4( ' 9. 4+ 4-,-)9-< (7' 7=,(4( +,4>,-( (7( ' 4+.--< +,?4@ L( 7,+-'+ 9,-'-;4( :9+( :-*('+ 9 ,;< +' 9' 7+4-,+ +,-(+ +/+,-,-. 9+ )+ + 9 /94( /94( + +,*( +,*( 100 .++ .++ /(+4-7( /(+4-7( (,' (,'( ( '9+( (,9-7( (,9-7( 9 9 ,)' ,)' +,4>,-@ A4+7? A4+7? + -;( +' 7-7( +/+-7+,( ( /''+ '+,+*@
A' :-'-; 4-( +/+-7+,( ('9-7( 9+ +' /(+,*+ 4+ +( +,? /++,+ + 9'9-+ 7+4--< 4+7? ' + +' +/+-7+,( ( /''+ '+,+* (,7( 9+ +' +( .-) (-4+)'+7+,+ ( 4-7( 9+, 9+ + /( +' ,7( 4+ ' 79+,@ P( '( ,,( +7/'+7( ' 7+4- -,7=,- ' 4+.--< +,?4 9+ ( (/+-(+ 9+ ( 94 /+-)- 4+ 7+ 4+,''4 '( '( +9',4( (),+-+4( ' 9. 4+ 4-,-)9-< (7'@
P') '.+ -
E( +/+-7+,' C9. 4+ 4-,-)9-< (7' I+,-497)+ (7' M+4--< +/+-7+,'
MED ICIÓ N Y ERR OR EXP
1 ANTECEDENT ANTECE DENTES ES EXPERIMEN EXPER IMENTA TALES: LES: A EXPERIMENTO EXPERIME NTO DE MEDICIÓN Y ERROR EXPERIMENTAL EXPERIM ENTAL LOS OBJETIVOS OBJETIVOS DE ESTE E#PERIMENTO E#PERIMENTO SON 1D+,+7- ' 9. 4+ 4-,-)9-< (7' + 9 /(+( 4+ 7+4--< (+/(4-+,+ ' 7+( 4+ :+*('+ 9+ )+ + 9 /94(@ 2D+,+7- ' -+,-497)+ + +,+ /(+( 4+ 7+4--<@ MATERIALES @U ,;< 4+ :+*('+ @U ,;< 7+4-( 4+ /'?,-( PROCEDIMIENTO D+/(-,+ '( :-*('+ + +' ,;<@ C(* 9 /94( 4+ :-*('+ 4+' +-/-+,+ 9 (, .+; , '( 9 /94( /94( (7' 9 /94( /94( - 79 /+,4( /+,4( - 79 79 9+',(@ D+/9= (* 9 /94( (7' 9+,+ +' 7+( 4+ ( (),+-4(@ (),+-4(@ A/9,+ +' +9',4( +/-, ' (/+-< /( '( 7+( -+ .++ ''+4( 9 ,)' (7( ' -4-4 + +' +*+7/'( 4+' '-)( 4+ +/+-7+,( 4+' ')(,(-(@ R+-,( 4+ '( :-*('+ (,4( &2 6! 6! &1 66 6! &5 66 &6 &2 62 &2 &1 && 63 &6 &1 &3 &0 &$ &8 &$ && &3 && &8 6! &1 &! &8 && &5 &6 &$ 6! &3 68 &0 &3 &1 &3 6! 6! &$ &$ 68 &1 &6 &8 6& &! 6$ 65 &5 && &! &5 &! &3 &0 L 7+4- -,7=,- 4+ +,( 4,( + &2@2!
2. FUNDAMENTO TEÓRICO:
60 &$ &$ &6 &1 &1 &0 &! &$ &2
6$ &$ 68 && &8 &1 &$ &1 &6 6!
6$ &8 6! &3 &3 &0 68 &3 &1 &6
6$ && 6$ && &8 &6 &1 6! 6! &&
S+ 4+)+ ,++ + 9+, / '( ?'9'( ' 4+:---(+ -9-+,+ :>- @E,+ +,( ,++7( L(-,94 L(-,94 MEDICIÓN E ' 7+4-4 9,-,,-. 4+ 9 7-,94 :>- ,-+7/( 7 +,@ P 7+4- + ++-( ((+ -+, ( (7(
MEDIA ARITMÉTICA: E +' .'( 9+ (+/(4+> 4 9( 4+ '( 4,( 4+ ' 4-,-)9-< - 9 97 ,(,' + +/,-+ /( -9'@ D4( '( 7+( a1 ,a2 , ... , a n ' 7+4- -,7=,- +? -9'
INCERTIDUMBRE NORMAL O DESVIACION ESTANDAR: L 4+.--< 4+.--< +,?4 +,?4 + 9 7+4-4 7+4-4 4+' 4( 4+ 4-/+4-/+-< < 4+ '( 4,( 4+' .'( .'( /(7+4-( /(7+4-(@@ D-( 4+ (, 7+ ' 4+.--< +,?4 + -7/'+7+,+ +' /(7+4-( ( .--< +/+4 ( +/+,( 4+ ' 7+4- -,7=,- U 4+.--< 4+.--< +,?4 4+ -4- 9+ '( /9,( +,? +,? '+*( 4+ ' 7+4- 9 4+.--< 4+.--< /+9+ -4- 9+ '( 4,( +,? 9/4( + 4+ ' 7+4-@
PROBABILIDAD: E ' /())-'-44 4+ 9+ ' +,+ 9 /94( +,+ + 4+ '+
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CAUSAS DE ERRORES DE MEDICION A99+ + -7/(-)'+ ((+ ,(4 ' 9 4+' +( + (.+-+,+ ((+ ,(4 ' 9 -7/(,,+ ,++ 9 -4+ 9+ /+7-, +.'9 '( +(+ 7? :+9+,+@ L /--/'+ 9 9+ /(49+ +(+ + /9+4+ '-:- + •
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. PROCEDIMIENTO: C(* 9 /94( 4+ :-*('+ :-*('+ 4+' +-/-+,+ +-/-+,+ 9 (, .+; , '( 9 /94( (7' 9 /94( - 79 /+,4( - 79 9+',( .+ :-9 2 4+/9= (* 9 /94( (7' 9+,+ ' 7+( 4+ ( (),+-4(@ A/9,+ +' +9',4( +/-, ' (/+-< /( '( 7+( 100 .++ ''+4( + 9 ,)'@
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Σ de d e
mnp = 7229 / 100 mnp = 72.29 2.
D*0*"-'* / -'3*"0-+,"* ')"/ ) +*$=-3-4' *$0<'+"# '0*"-)". S* 3/3/ $:
∆
(mnp
%# +* /
*+-3-4'
∆ (
mnp ) = ( 1/100
Σ (
2 1/2 NK - mnp ) ) k=1
D+ ' ,)' + /9+4+ ()+. 100 Σ (
2 NK - mnp ) =1931.91 k=1 ∆ (
mnp ) = (1931.91/100) 1/2
= 4.12492947
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TABLA TABLA 1. MEDICION DE PUJADO PUJADO DE FRIOLES K
NK
1 2 3 4 5 6 7 8 9 10 11
72 69 69 71 66 69 60 64 64 64 75 75
NK – 72.29 -0.29 -3.29 -3.29 -1.29 -6.29 -3.29 -12.29 -8.29 -8.29 -8.29 2.71
(NK – 72.298)2 0.08 10.82 10.82 1.66 39.56 10.82 151.04 68.72 68.72 68.72 7.34
"# " 2 .
12 13 14 15 16 17 18 19 20
66 76 72 62 72 74 74 74 74 78 78 77
K
NK
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
71 77 63 76 71 73 73 74 74 68 69 64 70 74 74 78 78 74 77 73 73 76 77 73 73 77 77 78 78 69 71 79 78 78 71 78 78 73 73 78 78 77 75 75 76 74 74
-6.29 -13.71 -0.29 -10.29 -0.29 1.71 1.71 5.71 4.71 NK – 72.29 -1.29 4.71 -9.29 3.71 -1.29 0.71 0.71 -1.29 -3.29 -8.29 -9.29 1.71 5.71 -1.71 4.71 0.71 3.71 4.71 0.71 4.71 4.71 5.71 -3.29 -1.29 6.71 5.71 -1.29 5.71 0.71 5.71 4.71 2.71 3.71 1.71
39.56 187.96 0.08 105.88 0.08 2.92 2.92 32.6 22.18 (NK – 72.298)2 1.66 22.18 86.3 13.76 1.66 0.5 0.5 1.66 10.82 68.72 86.3 2.92 32.6 2.92 22.18 0.5 13.76 22.18 0.5 22.18 22.18 32.6 10.82 1.66 45.02 32.6 1.66 32.6 0.5 32.6 22.18 7.34 13.76 2.92
55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
69 73 73 71 71 70 76 68 70 73 73 71 73 73 69 70 74 74 68 71 69 74 74 74 74 68 71 76 79 71 73 73 69 78 78 67 79 64 65 75 75 74 74 76 71 69 77 79 75 75 79 73 73 70 72 69 76
-3.29 0.71 -1.29 -1.29 -2.29 3.71 -4.29 -2.29 0.71 -1.29 0.71 -3.29 -2.29 1.71 -4.29 -1.29 -3.29 1.71 1.71 -4.29 -1.29 3.71 6.71 -1.29 0.71 -3.29 5.71 -5.29 6.71 -8.29 -7.29 2.71 1.71 3.71 -1.29 -3.29 4.71 6.71 2.71 6.71 0.71 -2.29 -0.29 -3.29 3.71
10.82 0.5 1.66 1.66 5.24 13.76 18.4 5.24 0.5 1.66 0.5 10.82 5.24 0.5 18.4 1.66 10.82 2.92 2.92 18.4 1.66 13.76 45.02 1.66 0.5 10.82 32.6 27.98 45.02 68.72 53.14 7.34 2.92 13.76 1.66 10.82 22.18 45.02 7.34 45.02 0.5 5.24 0.08 10.82 13.76
100
77 77
4.71
22.18
TABLA TABLA 2. NUMERO DE EXTRACIONES EXTRACIONES VS FRECUENCIA
NUMERO DE !RECUEN EXTRACIO CIA NE 60 1 62 1 63 1 64 5 65 1 66 2 67 1 68 4 69 11 70 5 71 12 72 4 73 9 74 10 75 4 76 8 77 9 78 7 79 5
7 /94( 7 /+9+( 60 M /94( 7 4+ &!
mnp =7229/ 100 mnp = 72.29
∆
) = (1931.91/100) 1/2
4.12492947
0.1 0.09 0.08 0.07 0.06 0.05
Moving average ()
0.04
Polynomial ()
0.03 0.02 0.01 0
F-9 $@ C9. 4+ 4-,-)9-< (7'
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'
D+/9= 4+ +'-; +' +/+-7+,( (* U4@ 9 /94( 4+ :-*('+@ WQ9= /9+4+ U4@ :-7 ()+ +' 7+( 4+ :-*('+ :-*('+ (,+-4( + ,' /94( ,+ 4+ (,X@ Q9+ +' 7+( 4+ :-*('+ +? 9 .'( +( ( -9' 53 9+ + +' /(7+4-( 4+ +,-(+
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DISCUSIÓN DE RESULTADOS: • • • •
P (),++ 9 )9+ 7+4--< 4+' 7+( 4+ :-*('+ 4+ 9 /94( + ,+> 9+ (+ 9 (, .+; , 9+ + /9+4 (),++ 9 /94( (7' 4+ :-*('+@ S- '( :-*('+ :9+ )-+ '-( +,( /94-+ +)' ' (+'( -+4( ' +/+-7+,-< 7? ,+4-(@ L :(7 4+ '( :-*('+ ( + ' 7-7 /+( + /(-7) +,+ - '( 9+ > .- ' 7+4--<@ E ++-( 7,++ +' -,7( 4+94( / ( (7),- +' -(@
CONCLUSIONES:
•
•
A' +'-; ' 7+4--(+ ('9-7( 9+ +' /(+,*+ 4+ +( +, /++,+ + 9'9-+ 7+4--< /( '( ,,( +7/'+7( ' 7+4- -,7=,- ' 4+.--< +,?4 9+ ( (/+-(+ (/+-(+ +,4>,- +,4>,- 9+ ( 79+, 79+, 4+ 9 7+ 7? 4+,''4 4-.+( 4-.+( 4,( 9 ()+.-(+@ R+'-;4( R+'-;4( +' +/+-7+,( +/+-7+,( + /9+4+ (, 9+ ' 7( ( + 9 9-44 4+ 7+4-4 +, ( (:-)'+@
SUGERENCIAS: •
P +.-, 9+ ( ,+ 79 4-:++- +,+ 9 /94( (,( ,, 9+ '( :-*('+ ,+ +' 7-7( ,7(@
REFERENCIAS BIBLIOGRÁFICAS: BIBLIOGRÁFICAS: • • • •
,,/""+@]-^-/+4-@("]-^-"E(_4+_7+4--C3B3 A,++4+,+ +/+-7+,'+ ,,/""+@-)4@(7" ,,/""+@-)4@(7" I:(7+ 4+ ')(,(-(\M+4--<\ T9,(-' T9,( -' G:-( 4+ D-,-)9-< D-,-)9-< N(7' + + E+' ,,/""]]]@(9,9)+@(7"],X._R8^`N]/6BA FISICA UNIVERSITARIA UNIVERSITARIA .('97+ 1@ S+ Z+7^ a I+,-497)+ -: --:-,-.@ E4-,(-' P+(
