CUADRO2.docx
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TARUGO ESFERA PLACA
Medid
a
dt(mm)
H
(mm)
mt
(g)
de(mm)
me(g)
a(mm)
hp(mm)
l(mm)
m p
(g)
01 15.06 101.65 15.6 15.07 5.4 50.0 0.15 54.045 0.7
0! 15.0! 101.0" 15.6 15.06 5.5 51.015 0.1 54.04 0."0 15.05 101.07 15.6 15.07 5. 50.005 0.1 54.05 0.7
04 15.06 101.06 15.7 15.065 5.4 50.0! 0.1 54.0 0."
05 15.04 101.05 15.7 15.06 5. 50.01 0.! 54.0 0."´ x 15.05 101.1"! 15.64 15.065 5." 50.016 0.1 54.06 0.76
Es= El 0.01 0.01 0.05 0.01 0.05 0.01 0.01 0.01 0.05
σ 0.01! 0.! 0.04 0.004 0.07 0.00" 0.04 0.005 0.04
Ea 0.006 0.4 0.07 0.006 0.105 0.1! 0.06 0.075 0.06
∆ X 0.006 0.4 0.0" 0.01 0.11 0.1! 0.06 0.075 0.07
Medid
a´ x ± ∆ x
(mm)
15.046± 0.0
!!
101.1"!± 0.
4
15.64± 0.
0"
15.065± 0.01
5."± 0.1
1
50.016± 0.1!
0.1± 0.
06
54.06 ±
0.01!5
0.76± 0
.07
#$%&me' (#t)
(c m3)
Maa
mt
(g)
#$%&me'
'
(m)
me(g)
#$%&me' (#*)
(c m3)Maa
m*
Medida
́z ± ∆ z
71.++"+ ± 0.6!!
+740"
15.64± 0.
0"
0.7+0!1"4 ± 0.00564 0.5146
± 0.160+160.76± 0
.07
Medid
a´ ρ ± ∆ ρ
( g
c m3)
0.!117 ± 1.0"!"
71.++"+ ± 0.6!!+
!.166 ± 0.4565
Solución:
Tarugo:
Diámetro:
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ERROR ,EL -STRUMETO ( Ei )
Ei=1
2(0.02 )=0.01mm
PROME,-O ( ´ x)
´ x=15.06+15.02+15.05+15.06+15.04
5=15.05
,ES#-AC-O ESTA,AR ,E LA ME,-A ( σ )
σ =√ (15.05−15.06)2+(15.05−15.02)2+(15.05−15.05)2+(15.05−15.06)2+(15.05−15.04)2
5
σ =√ (−0.01)2+(0.03)2+(0)2+(−0.01)2+(0.01)2
5
σ =√0.0001+0.0009+0.0001+0.0001
5=√
0.0012
5=√ 0.00024=0.015491
σ =0.02
ERROR ALEATOR-O ( Ea )
Ea= 3σ
√ 5−1=
3(0.0)2
Ea=0.03
ERROR A/SOLUTO ( ∆ x )
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∆ x=√ (0.01)2+(0.03)2=0.031622766
∆ x=0.03
ME,-,A
´ x ± ∆ x=17.47±0.03
Altura:
ERROR ,EL -STRUMETO ( Ei )
Ei=1
2(0.02 )=0.01mm
PROME,-O (´ x)
´ x=101.65+101.08+101.07+101.06+101.05
5=101.182
,ES#-AC-O ESTA,AR ,E LA ME,-A ( σ )
σ =√(101.182−101.65)2+(101.182−101.08)2+(101.182−101.07)2+(101.182−101.06)2+(101.182−
5
σ =√ (−0.468)2+(0.102)2+(−0.112)2+(0.122)2+(0.112)2
5
σ = 0.219+0.01+0.0125+0.0148+0.0125
5=
0.2688
5=√ 0.05376=0.02318
σ =0.23
ERROR ALEATOR-O ( Ea )
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Ea= 3σ
√ 5−1=
3(0.2318)2
=0.3477
Ea=0.34
ERROR A/SOLUTO ( ∆ x )
∆ x=√ (0.01 )2
+(0.34 )2
=0.34
∆ x=0.34
ME,-,A
´ x ± ∆ x=101.182±0.34
Masa del tarugo:
ERROR ,EL -STRUMETO ( Ei )
Ei=1
2(0.1)=0.05g
PROME,-O (´ x)
´ x=15.6+15.6+15.6+15.7+15.7
5=15.64
,ES#-AC-O ESTA,AR ,E LA ME,-A ( σ )
σ =
√(15.64−15.6)2+(15.64−15.6)2+(15.64−15. 6)2+(15.64−15.7)2+(15.64−15.7)2
5
σ =√ (0.04)2+(0 .04)2+(0.04)2+(0 .06)2+(0.06)2
5
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σ =√ 0.0016+0.0016+0.0016+0 .0036+0.00365 =√ 0.125 =√ 0.0024=0.0489σ =0.04
ERROR ALEATOR-O ( Ea )
Ea= 3σ
√ 5−1=
3(0.0489)2
=0.07335
Ea=0.07
ERROR A/SOLUTO ( ∆ x )
∆ x=√ (0.05)2+(0.07)2=0.086
∆ x=0.08
ME,-,A
´ x ± ∆ x=15.64±0.08
VOLUMEN DEL TARUGO:
,imet$2 15.046 ± 030!! mm 1.5046 ± 0.00!! m
A%t&a2 101.1"! ± 0.4 mm 10.11"! ± 0.04 m
V t =(1 .5046±0.0022)2
× π
4×(10.1182±0.034)
V t =[(1 .5046)2× π 4 ±(1.5046)2× π 4 ( 0.00221.5046 )×2]×(10.1182±0.034 )
V t =(1.778±0.00519952 ) ×(10.1182±0.034)
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V t =(1.778)(10.1182)±(1.778)(10.1182)√(0.005199521.778 )2
+( 0.03410.1182)2
V t =(17.99±0.058 ) c m3
DENSDAD DEL TARUGO:
ρ=m
V = 15.64 ±0.08
17.99±0.058
ρ=0.869±0.869
√( 0.0815.64 )
2
+(0.05817.99 )2
=0.2117±0.006
ρ=0.2±0.006 g
c m3
!laca:
Longitud:
ERROR ,EL -STRUMETO ( Ei )
Ei=1
2(0.02 )=0.01mm
PROME,-O (´ x)
´ x=54.045+54.04+54.035+54.03+54.03
5=54.036
,ES#-AC-O ESTA,AR ,E LA ME,-A ( σ )
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σ =√ (54.036−54.045)2+(54.036−54.04)2+(54.036−54.035)2+(54.036−54.03)2+(54.036−54.03
5
σ =
√(−0.009)2+(−0.004)2+(0.001)2+(0.006)2+(0.006)2
5
σ = 0. 000081+0.000016+0.000001+0.000036+0.000036
5=
0.00017
5=√ 0.000034
σ =0.00583
σ =0.005
ERROR ALEATOR-O ( Ea )
Ea= 3σ
√ 5−1=
3(0.005)2
=0.0075
Ea=0.0075
ERROR A/SOLUTO ( ∆ x )
∆ x=√ (0.01)2+(0.0075)2=0.0125
∆ x=0.0125
ME,-,A
´ x ± ∆ x=54.036±0.0125
Anc"o:
ERROR ,EL -STRUMETO ( Ei )
Ei=1
2(0.02 )=0.01mm
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PROME,-O (´ x)
´ x=50.03+50.015+50.005+50.02+50.01
5=50.016
,ES#-AC-O ESTA,AR ,E LA ME,-A ( σ )
(50.016−50.015)¿
(50.016−50.005)¿
(50.016−50.02)¿
(50.016−50.01)
¿¿2¿¿¿¿
(50.016−50.03)2+¿¿
σ =√ ¿
σ =
√
(−0.014 )2+(0.001)2+(0 .011)2+(−0.004)2+(0.006)2
5
σ =√ 0.000196+0.000001+0.000121+0.000016+0.0000365 =√ 0.000375 =√ 0.000074σ =0.0086
σ =0.008
ERROR ALEATOR-O ( Ea )
Ea= 3σ
√ 5−1=
3(0.008)2
=0.012
Ea=0.02
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ERROR A/SOLUTO ( ∆ x )
∆ x=√ (0.005)2+(0.012)2=0.12
∆ x=0.012
ME,-,A
´ x ± ∆ x=50.016±0.012
Altura:
ERROR ,EL -STRUMETO ( Ei )
Ei=1
2(0.02 )=0.01mm
PROME,-O (´ x)
´ x=0.15+0.1+0.1+0.1+0.2
5=0.13
,ES#-AC-O ESTA,AR ,E LA ME,-A ( σ )
σ =√ (0.13−0.15)2+(0.13−0.1)2+(0.13−0.1)2+(0.13−0.1)2+(0.13−0.1)2
5
σ =√ (−0 .02)2+(0.03)2+(0.03)2+(0.03)2+(0.07)2
5
σ =√ 0 .0004+0.0009+0.0009+0.0009+0.00495 =√ 0.0085 =√ 0.0016=0.04σ =0.04
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ERROR ALEATOR-O ( Ea )
Ea= 3σ
√ 5−1=
3(0.04)2
=0.06
Ea=0.06
ERROR A/SOLUTO ( ∆ x )
∆ x=√ (0.01)2+(0.06)2=0.06
∆ x=0.06
ME,-,A
´ x ± ∆ x=0.13±0.06
Masa de la #laca:
ERROR ,EL -STRUMETO ( Ei )
Ei=1
2
(0.1)=0.05mm
PROME,-O (´ x)
´ x=0.7+0.8+0.8+0.7+0.8
5=0.76
,ES#-AC-O ESTA,AR ,E LA ME,-A ( σ )
σ =√ (0.76−0.7)2+(0.76−0.8)2+(0.76−0.8)2+(0.76−0.7)2+(0.76−0.8)2
5
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σ =√ (0.06)2+(0 .04)2+(0.04)2+(0 .06)2+(0.04)2
5
σ =
√0.0036+0.0016+0.0036+0 .0036+0.0016
5
=
√0.012
5
=√ 0.0024=0.04
σ =0.4
ERROR ALEATOR-O ( Ea )
Ea= 3σ
√ 5−1=
3(0.4)2
=0.06
Ea=0.6
ERROR A/SOLUTO ( ∆ x )
∆ x=√ (0.05)2+(0.06)2=0.07
∆ x=0.07
ME,-,A
´ x ± ∆ x=0.76±0.7
VOLUMEN DE LA !LA$A:
V p=(50.016±0.12 )× (0.13±0.06 ) ×(54.036±0.0125)
V p=[6.50208±6.50208√( 0.1250.016 )2
+(0.060.13 )2
]×(54.036±0.0125)V p=(6.50208±2.99 )×(54.036±0.0125)
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V p=[351.346±351.346√( 2.996.50208 )2
+( 0.012554.036 )2
]V p=351.346±160.916mm
3
Saem$ &e2 1cm 10 mm
1c m3=1000m m3
E't$'e2
V p=0.351346±0.160916c m3
DENSDAD DE LA !LA$A:
ρ=m
V =
0.76±0.7
0.3513±0.16
ρ=2.1714 ±2.1714√( 0.070.76 )2
+( 0.160.3513 )2
=2.1633±0.987
ρ=2.2±1 g
c m3