1 informe de laboratorio original (1)
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BELLAVISTA, 3 DE SETIEMBRE DEL 2015
INTRODUCCIÓN
UNIVERSIDAD NACIONAL DEL CALLAOFACULTAD DE INGENIERÍA QUÍMICA
Escuela Profesioal !e I"eier#a Qu#$ica
ASIGNATURA% FÍSICA I
INFORME DE LA&ORATORIOS
INFORME 1: EL ERROR EN LA MEDICIÓN
PRESENTADO POR: BRIGGES LOAYZA, RENATO
CARRIÓN CÓRDOVA, DIEGO FERNANDO
PONTE GOÑE, JUAN MANUEL
SALDAÑA UIROZ, VALERIA BEATRIZ
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L! "#$%&'!()"! *+ !- #+*")"%(+- )&+)+ $+&#!(+('+#+('+ +( '%*%- %- )!#$%- *+ !
)"+()"! . ! '/)(")! M+*"& )%(-"-'+ +( )%#$!&!& *%- )!('"*!*+- *+ ! #"-#! #!("'*,
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O&'ETIVOS
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MARCO TEÓRICO
¿Qué es el error en la medición?
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$%*+& &+!"7!& ( +-'*"% +-'!*;-'")% U(! #!("'* *!*! -+ #+*"&> +( + !%&!'%&"%'!('!- 8+)+- )%#% -+! $&+)"-% $!&! 4+ ! +-'!*;-'")! -+! '""7!+ . + )>)% *+
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Reglas para expresar una medida y su error
T%*! #+*"*! *++ *+ "& -+"*! $%& ! ("*!*, %"!'%&"!#+('+ $%-'!*% $%& +
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1 T%*% &+-'!*% +?$+&"#+('! % #+*"*! +)! +( + !%&!'%&"% *++ *+ "&
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Medidas directas
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(! *+'+&#"(!*! +?$&+-"6( #!'+#>'")!, ! $!&'"& *+ ! #+*"*! *+ %'&!- #!("'*+- *+!- 4+ *+$+(*+ S+ '&!'! *+ )%(%)+& + +&&%& +( ! #!("'* *+&"8!*! ! $!&'"& *+ %-
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+&&%&+- *+ !- #!("'*+- #+*"*!- *"&+)'!#+('+ G+(+&!#+('+ !- #!("'*+-
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-+()"!, 4+ +- (+)+-!&"% )%(%)+&
MATERIALES
() !ali"rador de #ernier o $ie de Rey
E cali*re, '!#"/( *+(%#"(!*% cali*ra!or, car+a*, !e corre!era, -ie !e
re., -ie !e $e+ro, forc#-ula $!&! #+*"& >&%+- % Verier, +- ( "(-'&#+('%
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*+-*+ )+(';#+'&%- !-'! &!))"%(+- *+ #";#+'&%- 110 *+ #";#+'&%, 120 *+
#";#+'&%, 150 *+ #";#+'&% E( ! +-)!! *+ !- $!*!- '"+(+ *"8"-"%(+-+4"8!+('+- ! 11 *+ $!*!, ., +( - oio, *+ 112H *+ $!*!
E- ( "(-'&#+('% -#!#+('+ *+")!*% . *++ #!("$!&-+ )%( !""*!*,
)"*!*%, *+")!*+7!, )%( $&+)!)"6( *+ (% &!.!&% (" *%!&% +( +-$+)"!, !
)%"-! *+ $&%(*"*!* D++( +8"'!&-+ +-$+)"!#+('+ !- "#!*&!-, 4+ $+*+(
!%=!&-+ +('&+ -- $"+7!- . $&%8%)!& *!@%-
%& Regla met'lica de (m&L! re"la +- ( "(-'&#+('% *+ #+*")"6( )%( %&#! *+ $!()! *+!*! .
&+)'!(!& 4+ "().+ (! +-)!! &!*!*! *"8"*"*! +( ("*!*+- *+ %("'*,
$%& +=+#$% )+(';#+'&%- % $!*!- +- ( "(-'&#+('% '" $!&! '&!7!& -+#+('%- &+)'";(+%- )%( ! !.*! *+ ( %;&!% % >$"7, . $+*+ -+& &;"*%,
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-+#"&&;"*% % #. +?"+, )%(-'&"*%
*+ #!*+&!, #+'!, #!'+&"! $>-'")%, +')
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)%(-"-'+ +( (
)""(*&% &!*!*% *+ 8"*&"% 4+ $+&#"'+ )%('+(+&
;4"*%- . -"&8+ $!&! #+*"& 8%#+(+- *+ %&#!
!$&%?"#!*!
,& -alan.a de precisión&
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*+'+&#"(!& ! #!-! *+ ( %=+'% )%( (!
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++)'&%#!(/'")% . +4""&!( ! +&7!#+*"!('+ ( ++)'&%"#>( A)'!#+('+
!- #>- +?'+(*"*!- -%( !- ++)'&6(")!-, 4+ !( &++#$!7!*% )!-" $%& )%#$+'%
! !- !!(7!- *+ $&+)"-"6( #+)>(")!-
*& !ilindro sólido y /omogéneo&
0& $orción de sustancia li1uida&
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2& Es3era sólida y ta"la&
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PARTE E2PERIMENTAL
() De+er$ie el error sis+e$1+ico !e% re"la $e+1lica0 el cali*ra!or !e Verier0 la-ro*e+a "ra!ua!a . !e la *ala/a)
K!!#%- + +&&%& *+ )!*! "(-'&#+('% 8"+(*% ! #+*"*! #;("#! 4+ $%-++( +-'%-. +% *"8"*"&% +('&+ *%-
REGLA% M;("#! #+*"*!: 1 ##, +('%()+- !)+#%-:ESIST) 1##2 0,5 ##
CALI&RADOR : M;("#! #+*"*!: 0,02 ##, +('%()+- !)+#%-ESIST) 002 ##
PRO&ETA% M;("#% 8%#+( *+ )!$!)"*!*: 1 #, +('%()+- !)+#%-:ESIST) 1#20,5 #
&ALAN3A% M;("#! )!('"*!* 4+ -+ $+*+ $+-!&: 5, +('%()+- !)+#%-
ESIST) 52 2,5TA&LA 4(%5
6) Co el Verier $i!a% el !i1$e+ro 7!8 !e la esfera0 la al+ura 798 . el !i1$e+ro D!el cili!ro !e $a!era)
ESFERA%
4atos
E&&%& -"-'+#>'")%:ESIST 0,02 #
V!%& P&%#+*"% *+ ! N #+*")"%(+- 9:63+60.58+59.1
3 0H
CILINDRO%
ALTURA% 4atos
E&&%& -"-'+#>'")%: ESIST 0,02 ##
INSTRUMENTO
REGLACALI&RADO
R PRO&ETA &ALAN3A
E) SISTEM) : 40(; $$ : 4046 $$ : 40; $l : 60; "
M+*"*! *##1 <=2 <4);>3 ;?)(
M+*"*! ##1 (4@)(2 (4=);
3 (4@)(
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V!%& P&%#+*"% *+ ! N #+*")"%(+- 9:104.1+103.5+104.1
3 103DIMETRO%
Datos:
E&&%& -"-'+#>'")%: ESIST 0,02 ##
V!%& P&%#+*"% *+ ! N #+*")"%(+- 9:
53.02+53+52.6
3 52,H
=) Co la re"la $e+1lica $i!a los la!os 7280 7B80 738 !e
la -laca $e+1lica%
728 %
4atos
E&&%& -"-'+#>'")%: ESIST 0,5 ##
V!%& P&%#+*"% *+ ! N #+*")"%(+- 9:
150+150,5+150
3 150,1
7B8%
4atos
E&&%& -"-'+#>'")%: ESIST 0,5 ##
V!%& P&%#+*"% *+ ! N #+*")"%(+- 9:
151+150.5+150
3 150,50
738%
4atos
E&&%& -"-'+#>'")%: ESIST 0,5 ##
M+
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##
1
5
302
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3
3
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9
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(;4);
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V!%& P&%#+*"% *+ ! N #+*")"%(+- 9:5+4+3
3
@) Co la *ala/a aal,"ica $e!ir la $asa !e ca!a uo !e los cuer-os
TA&LA 4=%
CUE
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Cili!
ro
Esfer
a
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;) Co la *ala/a aal,"ica $e!ir la $asa !e ca!a uo !e los cuer-os)
7PRO&ETA8%
4atos
E&&%& -"-'+#>'")%: ESIST 2,5
V!%& P&%#+*"% *+ ! N #+*")"%(+- 9:
60+85.5+110
3 H51
V(
m
(
g
)
60
60
80
8
5
.
5
10
1
1
0
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CUESTIONARIO
() alle el alor -ro$e!io !e ca!a uo !e los !a+os $e!i!os ue se $ues+rae la +a*la NH6) Calcule el error co$e+i!o e ca!a -ro$e!io)
TABLA N02
N
9
Y
Z
*
D
V
#
(
1
1
5
1
5
6
1
1
1
5
H
H
=
1
1
3
5
1
5
1
1
a) Calculando el Promedio:
X =
N °1+ N ° 2+ N ° 3
3
X =150+150.5+150
3=150.17 d=
63+60.5+59.1
3=60.87
Y =151+150.5+150
3=150.5h=
104.1+103.5+104.1
3=103.9
Z =
5+4+3
3 =4 D=
53.02+53+52.6
3 =52.87
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12
m=60+85.5+110
3=85.17
b) Calculando el Error cometido en cada promedio:
eS
¿¿e¿
∆ X =√ ¿
- Para calcular el error co$e+i!o e ca!a -ro$e!io -ri$ero !e*e$os calcular elerror !e !is-ersi,)
X e D=
√(150.17
−150
)
2
+(150.17
−150.5
)
2
+(150.17
−150
)
2
3 (3−1) =0.17
Y e D=√(150.5−151)2+(150.5−150.5)2+(150.5−150)2
3(3−1) =0.29
Z e D=√(4−5)2+(4−4)2+(4−3)2
3(3−1) =0.58
d e D=√(60.87−63)2+(60.87−60.5)2+(60.87−59.1)2
3 (3−1) =1.14
h e D=√(103.9−104.1)2+(103.9−103.5)2+(103.9−104.1)2
3(3−1) =0.2
D e D=
√
(52.87−53.02)2+(52.87−53)2+(52.87−52.6)2
3(3−1)
=0.43
- De la +a*la NH4( se +ie+:
eS=mínima medición
2
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ReglaeS=0.5mm
2=0.25mm
Calibrador eS=0.02mm
2=0.01mm
Probeta eS =1ml
2=0.5ml
Balanza eS=5g
2=2.5g
- Ree$-la/a!o los !a+os%
0.25mm ¿
2
+(0.17 mm)
2
¿¿
∆ X =√ ¿
0.25mm ¿
2
+(0.29mm)
2
¿¿
∆ Y =√ ¿
0.25mm ¿2+(0.58mm)2
¿¿
∆ Z =√ ¿
0.01mm ¿2+(1.14mm)2
¿¿
∆ d=√ ¿
0.01mm
¿¿¿2+(0.2mm)2
¿∆ h=√ ¿
0.01mm
¿¿¿2+(0.43mm)2
¿∆ D=√ ¿
6) E la+a*la
TA&LA NH46
N
9
Y
Z
*
D##
1
1
1
5
1 5302
2
1
1
1 53
3
1
1
3
5
1 52
1
1
0
1 52H
Q
0.45
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NH @ escri*a e -ul"a!as i ca!a uo !e los !a+os ue -rese+a !e la+a*la NH 6)Calcule el error co$e+i!o e -ul"a!as i)
TA&LA NH 4(
I
s+ru$e+o
R
e"la
Cali*ra!or
P
ro*e+a
&
ala/a
Es
is+
4)6;$$
4)4($$
4);$L
6
);"
TA&LA NH 46
2
B
3
!
9
D
V
$
15
1
5
1
5
15
1
1
5
H
H
15
1
3
5
1
5
1
1
!5L!6L7S :
No+a% 1## 0033 "(
E 2%
0.03937∈ ¿
1mm
150mm x ¿ 5055
"(
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15
0.03937∈ ¿
1mm
150.5mm x ¿ 5251H
"(
0.03937∈ ¿
1mm
150mm x ¿ 5055
"(
E B%
0.03937∈ ¿
1mm
151mm x ¿ 5H
"(
0.03937∈ ¿
1mm
150.5mm x ¿ 5251H5
"(
0.03937∈ ¿
1mm
150mm x ¿ 5055
"(
E 3%
0.03937∈ ¿
1mm
5mm x ¿ 01H5
"(
0.03937∈ ¿
1mm4 mm x ¿ 015H
"(
0.03937∈ ¿
1mm
3mm x ¿ 011H11
"(
E !%
0.03937∈ ¿
1mm
63mm X ¿ 2H031
"(
0.03937∈ ¿
1mm
60.5mm x ¿ 23H1H "(
0.03937∈ ¿
1mm
59.1mm x ¿ 232
"(
E 9%
0.03937∈ ¿
1mm
104.1mm x ¿
0H1 "(
0.03937∈ ¿
1mm
103.5mm x ¿
05 "(
0.03937∈ ¿
1mm
104.1mm x ¿ 0H1
"(
E D%
0.03937∈ ¿
1mm
53.02mm x ¿ 20H
"(
0.03937∈ ¿
1mm
53mm x ¿ 20H "(
0.03937∈ ¿
1mm
52.6mm x ¿ 201 "(
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16
TA&LA NH 4@
9
Y
Z"
*
"
D
5
5
0
2
2
5
5
0
2
2
5
5
0
2
2
0
0
0
0
0
0
=) Co los !a+os -ro$e!ios !e la +a*la NH 60 9alle el 1rea !e la cara !e la +a*la. calcule el error co$e+i!o al !e+er$iar el 1rea)
TA&LA NH 4(
I
s+ru$e+o
R
+!
C
!"
& !*%&
P
& % +'!
B
!!(7!
Es
is+
4
)6;$$
4
)4($$
4
);$L
6
);"
TA&LA NH 46
N
2
B
3
!
9
D
V
$
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17
(
1
1
5
H
5
6
1
1
H
5
H
H
=
1
1
3
5
H
5
1
1
!alculando el 'rea de la l'mina de aluminio
A !'&! ?
!()&! A A ∆
A
alla!o 1rea NH(%
? ? ∆ ? ? 150## 025 ##
. . ∆ y . 151 ## 025##
150 ##
025## ? 151 ## 025## 2250 ## A
Sa"emos 1ue
A ? .
∆ x√ !X
X
2
+ !Y
Y
2
∆
22650mm2 x √
(
0.25mm
150mm
)
2
+
(
0.25mm
151mm
)
2
5321 ##2
alla!o 1rea N H 6%
? ? ∆ ? ? 1505 ## 025 ##
. . ∆ y . 1505## 025##
1505## 025## ? 1505 ## 025## 225025 ##
2
A Sa"emos 1ue
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18
A ? .
∆ x√( !X
X )2
+( !Y
Y )2
∆
22650.25 mm2 x √(
0.25mm
150.5 mm)2
+( 0.25mm
150.5mm )2
5135
alla!o 1rea N H =%
? ? ∆ ? ? 150 ## 025 ##
. . ∆ y
. 150 ## 025##
150## 025## ? 150 ## 025## 22500##2 A
Sa"emos 1ue
A ? .
∆ x ( !X
X )2
+( !Y
Y
2
) ∆
22575mm2 x √(
0.25mm
150mm )2
+( 0.25mm
150mm )2
532 mm2
@) Calcule el olu$e !e la +a*la !e la -re"u+a N= . calcule el error co$e+i!o)Lue"o !e+er$ie la !esi!a! !e la +a*la)
$ara /allar el 8olumen de la ta"la de"emos usar la 3órmula
" = B # $
D6(*+:
B= X #Y % ∆ B
$ =Z =Z% ∆ Z
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19
( X = ´ X % ∆ X
´ X =
150mm+150.5mm+150mm
3=150.17mm
∆ X =√ (eS )2
+( e D )2
e D=√(150.17mm−150mm )
2
+(150.17mm−150.5mm )2
+(150.17mm−150mm)2
3#2
e D=0.17mm
∆ X =√ (0.25mm )2+ (0.17mm )2
∆ X =0.31mm
(2) Y = Y % ∆ Y
´
Y =
151mm+150.5mm+150mm
3 =150.5mm
∆ Y =√ ( eS )2+(e D )
2
e D=√(150.5mm−151mm )2+(150.5mm−150.5mm)2+ (150.5mm−150mm )2
3#2
e
D
=0.17 mm
∆ Y =√ (0.25mm )2+(0.17 mm )2
∆ Y =0.3mm
(3) B= X #Y
B=150.17 mm #150.5mm
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20
B=22600.585 mm2
(4) ∆ B= B #
√(∆ X
´ X
)
2
+(∆ Y
Y
)
2
∆ B=22600.585mm2
#√( 0.31mm
150.17 mm )2
+( 0.3mm
150.5mm )2
∆ B=64.85mm2
R++#$!7!#%-
B= ´ X # Y %∆ B
B=22600.585 mm2
%64.85mm2
A%&! $%*+#%- )!)!& + 8%#+( *+ ! $!)!
" = B # $
1 B=22600.585 mm2
%64.85mm2
2
$ = ´ $ % ∆ $
´ $ =5
mm+4
mm+3
mm3 =4mm
∆ $ =√ ( eS )2+(e D )
2
e D=√(4mm−5mm)2+( 4mm−4mm )2+(3mm−4 mm)2
3#2 0.5773mm
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21
∆ $ =√ (0.01mm )2+(0.5773 mm)2
∆ $ =0.58
mm
$ = ´ $ % ∆ $
$ =4mm %0.58mm
(3 ) " = B# $
" =22600.585 mm2
#4mm
" =90402.34 mm3
(4 ) ∆ " =" #√( ∆ B
´ B )
2
+( ∆ $ ´ $ )
2
∆ " =90402.34 mm3
#√( 64.85mm
2
22600.585 mm2 )
2
+(0.58mm
4 mm )2
∆ " =2160.109198mm3
" =90402.34 mm3
%2160.109198 mm3
C!)!#%- ! *+(-"*!* *+ ! $!)!
&=m
" % ∆ &
1
m= m % ∆ m
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22
m=85.16 g %2.5g
2
&= m"
&=
85.16 g
90402.34 mm3=0.000942
g
mm3
3
∆ &= &#
√(∆ m
m
)
2
+
( ∆"
"
)
2
∆ &=0.000942 g
mm3 #√(
2.5g
85.16g )2
+(2160.109198 mm3
90402.34 mm3 )
2
=0.0000282 g
mm3
F"(!#+('+
&= &% ∆ &
&=0.000942
g
mm3
%0.0000282 g
mm3
;) Co los alores -ro$e!ios !e 9 . D e la +a*la N60 9alle el 1rea !e la *ase .el olu$e el cili!ro !e $a!era) Calcule el error co$e+i!o e ca!a caso)
El área de la base debemos usar la formula
B=' # r2
D%(*+
r= D
2
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23
1 D= ´ D % ∆ D
´ D=
53.02mm+53mm+52.6mm
3=52.87mm
∆ D=√ ( eS )2+(e D )
2
e D=√(52.87mm−53.02mm)2+ (52.87 mm−53mm)2+(52.87mm−52.6mm)2
3#2
e D=0.1368 mm
∆ D=√ (0.01mm)2+(0.1368mm )
2
∆ D=0.1371mm
D= ´ D % ∆ D
D=52.87mm %0.1371mm
(r= D
2=
52.87mm %0.1371mm
2
r=26.435mm %0.06855 mm
2 B=' # r2=' # r # r
B=' #26.435mm #26.435 mm=698.809 ' mm2
3 ∆ B= B #√(∆ X
´ X )2
+(∆ Y
Y )2
∆ B=698.809 ' mm2
#√(0.06855 mm
26.435 mm )2
+(0.06855mm
26.435mm )2
=25.6mm2
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24
R++#$!7!#%-
B=' # r2
B=685.91' mm2
%25.6mm2
A%&! $%*+#%- )!)!& + 8%#+( *+ )""(*&%
" = B #h
( h=h % ∆ h
h=
81.9mm+81.88mm+81.82mm
3=81.87mm
∆ h=√ (eS )2
+( e D )2
e D=√(81.87mm−81.9mm)2+(81.87mm−81.88mm )2+(81.87mm−81.82 mm)2
3
#2
e D=0.024mm
∆ h=√ (0.01mm )2+ (0.024mm)
2
∆ h=0.026mm
h=´h % ∆ h
h=52.38mm %0.44mm
6 " = B #h
" =685.91 ' mm2
#52.38mm
" =112871.03mm3
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25
= ∆ " =" #√(∆ B
´ B )
2
+( ∆ h
h )2
∆ " =112871.03mm3
#√( 25.6 mm
2
685.91 ' mm2 )
2
+( 0.44 mm
52.38mm )2
=1642.4mm3
" =112871.03mm3
%1642.4 mm3
<) Co el alor -ro$e!io !e ! e la +a*la N60 calcule el olu$e !e la esfera .
el error co$e+i!o al !e+er$iar es+e olu$e• El volumen para calcular el volumen de la esfera es
" =4
3# ' # r
3
D%(*+
r= D
2
• Entonces podemos allar el volumen de la si!uiente manera
( r= r % ∆ r
´ D=
63mm+60.5mm+59.1mm
3=60.87mm
∆ D=√ ( eS )2+(e D )2
e D=√(60.87mm−63mm )
2
+(60.87mm−60.5mm )2
+ (60.87mm−59.1mm)2
3#2
e D=1.135mm
∆ D=√ (0.01mm)
2
+(1.135mm)2
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26
∆ D=1.135mm
D= ´ D % ∆ D
D=60.87mm %1.135mm
(r= D
2=
60.87mm %1.135mm
2
r=30.44 mm% 0.5675 mm
6
" =43
# ' # r 3% ∆ "
" =4
3# ' #(31mm)3
" =124725mm3
∆ " =124725mm3
#
√(9 )#(
0.5675mm
2
30.44mm2
)2
∆ " =6975.83mm3
" =124725mm3
%6975.83mm3
J) Calcule la !esi!a! !el cili!ro . !e la esfera) alle el error co$e+i!o al
calcular la !esi!a! !e ca!a cuer-o)
eS=mínima medición2
Calibrador :eS=0.02mm
2=0.01mm
Balanza :∆ m=5g
2=2.5g
2&(& !alculando la densidad del cilindro
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27
! C!)!(*% + $&%#+*"% *+ !'&! . *">#+'&% *+ )""(*&%
h=104.1mm+103.5mm+104.1mm
3=103 .9mm
D=53.02mm+53mm+52.6mm
3=52.87mm
• C!)!(*% + +&&%& )%#+'"*% +( )!*! $&%#+*"%:
eS
¿¿e¿
∆ X =√ ¿
- P!&! )!)!& + +&&%& )%#+'"*% +( )!*! $&%#+*"% $&"#+&% *++#%- )!)!& + +&&%& *+
*"-$+&-"6(
h e D=√(103.9−104.1)2+(103.9−103.5)2+(103.9−104.1)2
3(3−1) =0.2
D e D=√(52.87−53.02)2+(52.87−53)2+(52.87−52.6)2
3(3−1) =0.23
- E&&%& -"-'+#>'")%
eS=mínima medición
2
Calibrador eS=0.02mm
2=0.01mm
- R++#$!7!(*% %- *!'%- $!&! !!& + +&&%& )%#+'"*% +( )!*! $&%#+*"%
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28
0.01mm¿¿
¿2+(0.2mm)2
¿∆ h=√ ¿
0.01mm¿¿
¿2+(0.23mm)2
¿∆ D=√ ¿
C!)!(*% + 8%#+( *+ )""(*&% $!&! !!& ! *+(-"*!*
" = ba)e # h" =' ´
D
2
4# h
" =' (52.87mm)
4
2
#103.9mm
" =227983.7144 mm3
- C!)!(*% + +&&%& )%#+'"*% +( + 8%#+(
" = * ´ D
n#h
m∆"
" x
√n2 !D
´ D2
2
+m2 !h
h2
2
∆ "
0.2mm¿¿
¿2¿
22¿
227983.7144 mm3 x √ ¿
∆ " =1725.97627 mm3
) C!)!(*% ! *+(-"*!* *+ )""(*&%
&=m
+
&cilindro= 155 g
227983.7144 mm3
# 1000mm
3
1ml =
0.67987 g
ml
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29
- C!)!(*% + +&&%& )%#+'"*% +( ! *+(-"*!*
&= m
"
∆ &= &√(∆ m
2
m2 )+∆
" 2
" 2
179.5437 m3
¿¿¿2¿¿
2,5g2
155g2+¿
∆ &=0.6798 g
ml √ ¿
2&%& !alculando la densidad de la es3era! C!)!(*% + $&%#+*"% *+ *">#+'&% *+ ! +-+&!
d=63+60.5+59.1
3=60.87
• C!)!(*% + +&&%& )%#+'"*% +( )!*! $&%#+*"%:
eS
¿¿e
¿∆ X =√ ¿
- P!&! )!)!& + +&&%& )%#+'"*% +( + $&%#+*"% $&"#+&% *++#%- )!)!& + +&&%& *+
*"-$+&-"6(
d e D=√(60.87−63)2+(60.87−60.5)2+(60.87−59.1)2
3 (3−1) =1.14
- E&&%& -"-'+#>'")%
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30
eS=mínima medición
2
Calibrador eS=0.02mm
2=0.01mm
- R++#$!7!(*% %- *!'%- $!&! !!& + +&&%& )%#+'"*% +( )!*! $&%#+*"%
0.01mm ¿2+(1.14mm)2
¿¿
∆ d=
√ ¿
C!)!(*% + 8%#+( *+ ! +-+&! $!&! !!& ! *+(-"*!*
" =4
3' r
3
" =4
3' ( 60.87mm
2 )3
=118028.8658mm3
- C!)!(*% + +&&%& )%#+'"*% +( + 8%#+(
" = * dn∆ " " x √n
2 !d
d2
2
∆ " 118028.8658mm3 x√3
2 1.14
60.872
2
=6631.394869 mm3
) C!)!(*% ! *+(-"*!* *+ ! +-+&!
&=m
+
&e),era= 150g
118028.8658mm3 #
1000mm3
1ml =
1.27g
ml
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31
- C!)!(*% + +&&%& )%#+'"*% +( ! *+(-"*!*
&= m
"
∆ &= &√∆ m
2
m2
+∆ "
2
" 2
∆ &=1.27 g
ml √ (2.5g )2
(150g )2+
(6631.394869 mm3 )2
(118028.8658mm3 )2
0.02g
ml
>) Calcule la !esi!a! !el l#ui!o -ara ca!a olu$e . $asa !e la +a*la NH6)
De+er$ie el error co$e+i!o al calcular la !esi!a!)
&=m
+
TA&LA NH 46
NH
9
Y
Z
*
D
V
#
(
1
1
5
1
5
6
1
1
1
5
H
H
=
1
1
3
5
1
5
1
1
eS=mínimamedición
2
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32
Balanza e )b=5 g
2=2.5 g
ProbetaeS=1ml
2=0.5ml
C!)!(*% + +&&%& *+ ! #!-! 4+ + !!*%, &+-'!(*% ! #!-! #+*"*! )%( !
!!(7! *+ ! $&%+'! +(! . ! #!-! #+*"*! *+ ! $&%+'! 8!);!
∆ - =√ (e ) b )2+( e)b )
2
∆ - =√ (2.5 g )2+(2.5g )2=3.5g
a) C!)!(*% ! *+(-"*!* N1
&= 60g
60ml=1
g
ml
*) C!)!(*% + +&&%& *+ ! *+(-"*!*
&= m
"
∆ &= &√∆ -
2
´ - 2
+∆ "
2
" 2
∆ &=1 g
ml √(3.5 g)2
(60 g )2 +
(0.5ml )2
(60ml )2 =
0.06 g
ml
c) C!)!(*% ! *+(-"*!* N2
&=85.5 g
80ml =1.06875
g
ml
!) C!)!(*% + +&&%& *+ ! *+(-"*!*
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33
&= m
"
∆ &= &
√∆ -
2
´ - 2 +∆ "
2
" 2
∆ &=1.06875 g
ml √ (3.5g )2
(85.5g )2+
(0.5ml )2
(80ml )2 =
0.04 g
ml
e) C!)!(*% ! *+(-"*!* N3
&= 110g
100ml=1.1
g
ml
f) C!)!(*% + +&&%& *+ ! *+(-"*!*
&= m
"
∆ &= &√∆ -
2
´ - 2 +
∆ " 2
" 2
∆ & =1.1 g
ml √ (3.5 g )2
(110g )2+
(0.5ml )2
(100ml )2=
0.04 g
ml
?) alle el -ro$e!io !e la !esi!a! . calcule el error co$e+i!o al !e+er$iar
es+e -ro$e!io)
´ &=
1g
ml +
1.06875 g
ml +
1.1 g
ml
3=1.05625 g
ml
- C!)!(*% + +&&%& )%#+'"*%:
S+ '+(;! "(")"!#+('+:
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34
∆ &=0.06 g
ml
∆ &=0.04 g
ml
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∆ &=0.04 g
ml
∆ &=√(0.06g
ml )2
+(0.04 g
ml )2
+(0.04 g
ml )2
=0.08
(4) Grafiue el error -orce+ual EK e el ee B0 el olu$e e el ee 20 !e ca!a
alor $e!i!o !el olu$e !el l#ui!o) E-liue sus coclusioes !e la"r1fica)
55 60 65 70 75 80 85 90 95 1001050
0.2
0.4
0.6
0.8
1
Error Porcentual E%
Error Porcentual E%
. =∆ X
X
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A #!.%& 8%#+( #+(%& +- + +&&%& $%&)+('!
(() E-liue ua al+era+ia -ara $e!ir el es-esor
co ua re"la . la $asa co ua *ala/a !e ua9oa !e -a-el *o! co el $eos error -osi*le)
Para allar el espesor de las o"as bond:
P&"#+&% $&+$!&% ( $!4+'+ *+ $!$+ *+ #>- *+ 100
%=!- )!('!- #>- +- #+=%& . )+('! )>('!- %=!- '"+(+
B-)! +( + +(8%'%&"% *+ %- %"%- - &!#!=+: -++ -+& *+
0 #2 % *+ H0 #2 C%#$&"#+ + $!4+'+ *+ $!$+ )%(
(! $!)! 4+ )&! '%*! ! -$+&")"+, *+=!(*% ( $+4+@%
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!"*% (! *"+&+()"! -"("")!'"8! E-'% -+ *++ ! 4+ + 8!%& '+6&")% +- + 8!%& "*+!
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DISCUSIÓN
P!&! $%*+& +('+(*+& #+=%& %- &+-'!*%- %'+("*%- +( (+-'&!- '!!-, +( !
$&+-+('+ $&>)'")!, *++#%- $&"#+&% )%(%)+& ! *"+&+()"! *+ +?!)'"'* . $&+)"-"6( L!
+?!)'"'*, "#$")! &+!"7!& #+*"*!- ).%- &+-'!*%- +-'/( )+&)! ! 8!%& &+! % !)+$'!*%
+- )>( )+&)!(! +-'> +-! #+*"*! *+ 8!%& +-'>(*!& +-'!+)"*% P%& %'&% !*%, !
$&+)"-"6(, +- %'+(+& (! -+&"+ *+ #+*"*!- +?$+&"#+('!+- 4+ -+!( &+$+'"*!- !=% !-
#"-#!- )%(*")"%(+- . 4+ !- #"-#!- +-'/( (!- "+( )+&)! *+ !- %'&!- E- + &!*% *+
"*+"*!* )%( 4+ -+ %'"+(+ (! #+*"*! D+ %&#! &>")!, ( +=+#$% +-: A%&! $%*+#%- *+)"& 4+ (+-'&%- *!'%- %'+("*%- -%( +( ! #!.%&;! *+
)!-%- $&+)"-%-, $%&4+ +#%- %'+("*% *!'%- &+$+'"*%- % &+-'!*%- #. )+&)!(%- ! %-
%'&%- F"(!"7!*% + '&!!=% $&>)'")% $%*+#%- !$&+)"!& 4+ $!&! ! &+!"7!)"6( *+
#+*")"%(+-, %- "(-'&#+('%- '""7!*%- -%( "#$%&'!('+-, .! 4+ *+ !)+&*% ! '""7!*%,
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+ 8!%& %'+("*% 8! ! -+& *+ #!.%& % #+(%& +?!)'"'* E- "#$%&'!('+ '+(+& +( )+('!
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#+*")"6( )%( +?!)'"'*, #"+('&!- #>- -+ !$&%?"#+ ! )+&%, #>- +?!)'% -+&> ! #+*"*!
REFERENCIAS &I&LIOGRFICAS
1 ANÓNIMO U("*!*+- *+ )%()+('&!)"6( D"-$%("+ +(:
''$:&%*!--+-("*!*+-$!"(!0'# !&';)% + C%(-'!*! + 2 *+
-+'"+#&+ *+ 20152 ANÓNIMO E&&%&+- +( ! #+*"*! D"-$%("+ +(: ''$:%)(")!(+-E&&%&+-
20+(20!20#+*"*!-$* !&';)% + C%(-'!*! + 1 *+ -+'"+#&+ *+2015
3 C+&(-)", F G&+)%, F 1H #eor$a de errores de mediciones B+(%- A"&+-:E*"'%&"! U("8+&-"'!&"!
FWSICA Y UWMICA E&&%&+- +( ! #+*"*! D"-$%("+ +(:
''$:"-")!.4"#")!+(!-+-)%()+$'%-+&&%&+-'# !&';)% + C%(-'!*!+ 1 *+ -+'"+#&+ *+ 2015
5 GALEONCOM C!"&!*%& 8+&("+& D"-$%("+ +(:
''$:)!"&*%&8+&("+&!+%()%# !&';)% + C%(-'!*! + 1 *+ -+'"+#&+ *+2015
S+!&-, F Z+#!(-X., M 200 %$sica &niversitaria M/?")%: P+!&-%( IIPEDIA E&&%& *+ #+*")"6( D"-$%("+ +(:
''$:+-"X"$+*"!%&"X"E&&%&*+#+*")"C3B3( !&';)% + C%(-'!*!+ 2 *+ -+'"+#&+ *+ 2015
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ANE2O
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ERR7RES 9R7SER7S C%(-"-'+ +( +4"8%)!)"%(+- +( !- +)'&!- . &+"-'&%-
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- Errores !e M+o!o: -+ %&""(!( +( + $&"()"$"% *+ ()"%(!#"+('% *+ %-
"(-'&#+('%- *+ #+*")"6(- Errores !e a-reciaci, !e la i!icaci,: + #+*"% +?'+&(% +( 4+ -+
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%&#! )!&!)'+&;-'")! *+ !$&+)"!& %- +(6#+(%-, . +( $!&'")!&, *+ ++)'!&
+)'&!- +( !- #+*")"%(+-
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*+ &+$+'"'"8"*!* +( ! &+-$+-'!, *+"*% (*!#+('!#+('+ ! &%7!#"+('%-
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