informe 2 Laboratorio de Fisica I
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Transcript of informe 2 Laboratorio de Fisica I
V. APLICACIONES
1. Grafique las siguientes distribuciones:
De la Tabla 1:
a) Grafique en una hoja de papel milimetrado V vs. i.
De la Tabla 2:
b) En una hoja de papel milimetrado grafique t vs. D. para cada una de las alturas.
c) En una hoja de papel milimetrado grafique t vs. h. para cada diámetro.
d) En una hoja de papel logarítmico grafique t vs. D. para cada una de las alturas.
e) En una hoja de papel logarítmico grafique t vs. h. para cada diámetro.
f) Haga el siguiente cambio de variables z = 1/D 2 y grafique t = t (z) en papel milimetrado.
De la Tabla 3:
g) En una hoja de papel milimetrado grafique A vs. T.
h) En una hoja de papel semilogarítmico A vs. T.
2. Hallar las fórmulas experimentales:
Regresión Lineal por mínimos Cuadrados (RLMC)
b=∑ x2∑ y−∑ x∑ xy
P∑ x2−¿¿¿
m=P∑ xy−∑ x∑ y
P∑ x2−¿¿¿
I) Obtenga las formulas experimentales usando el método de regresión lineal. para las gráficas obtenidas en los casos a), d), e), f) y h).
CASO A) V vs. i.
Voltaje (v) Intensidad(A)
Yi Xi Xi.Yi Xi2
2.18 0.5 1.09 0.254.36 1 4.36 18.72 2 17.44 4
17.44 4 69.76 16
∑Yi=32.7 ∑ Xi=7.5 ∑ Xi .Yi=92.65 ∑ Xi2=21.25
Por el método de regresión lineal por mínimos cuadrados.
Luego se calcula la pendiente y el intercepto.
m = 4 ( 92.65 )−(7.5)(32.7)
4 (21.25 )−(7.5)2 = 125.3528.75
= 4.36 y = 4.36
b = (21.25) (32.7 )−(7.5)(92.65)
4 (21.25 )−(7.5)2 = 0
28.75 = 0 b = 0
ECUACIÓN DE LA TABLA: Y = 4.36 X
CASO D)
Diámetro
D (cm)
Tiempo de vaciado t (s)
x y xy x2
log D log t log t log D ¿¿
1.5 73 0.1760 1.863 0.327 0.0309
2 41.2 0.3010 1.614 0.784 0.0906
3 18.4 0.4771 1.264 0.603 0.2276
5 6.8 0.6989 0.8325 0.581 0.4884
7 3.2 0.8450 0.505 0.426 0.714
2.498 6.0793 2.721 1.5515
H=30 cm
Para hallar el intercepto (b) y la pendiente (m) :
b=(1.5515 ) (6,0793 )−(2.498)(2.422)
5 (1.5515 )−2.4982 =3.3811.517
=2.228
m=5 (2.422 )−(2.498)(6.0793)
5 (1.5515 )−2.4982 =−3.0761.517
=−2.027
Ecuacion de la tabla:
Y = 102.228 X−2.027
H=20 cm
Para hallar el intercepto (b) y la pendiente (m):
b=(1.5515 ) (5.632 )−(2.498)(2.2)
5 (1.5515 )−2.4982 =3.24241.517
=2.137
m=5 (2.2 )−(2.498)(5.632)
5 (1.5515 )−2.4982 =−3.0687
1.517=−2.022
Diámetro
D (cm)
Tiempo de vaciado t (s)
x y xy x2
log D log t log t × log D ¿¿
1.5 59.9 0.1760 1.777 0.312 0.0309
2 33.7 0.3010 1.527 0.459 0.0906
3 1409 0.4771 1.173 0.559 0.22765 5.3 0.6989 0.724 0.506 0.48847 2.7 0.8450 0.431 0.364 0.714
2.498 5.632 2.2 1.5515
ECUACIÓN DE LA TABLA: Y = 102.137 X−2.022
H=10 cm
Diámetro
D (cm)
Tiempo de vaciado t (s)
x y xy x2
log D log t log t log D ¿¿1.5 43 0.1760 1.6334 0.2874 0.0309
2 23.7 0.3010 1.4424 0.4341 0.0906
3 10.5 0.4771 1.0211 0.4871 0.2276
5 3.9 0.6989 0.591 0.413 0.4884
7 2 0.8450 0.301 0.2543 0.714
2.498 4.9889 1.8759 1.5515
Para hallar el intercepto (b) y la pendiente (m) :
b=(1.5515 ) ( 4.9889 )−(2.498)(1.8759)
5 (1.5515 )−2.4982 =3.0541.517
=2.013
m=5 (1.8759 )−(2.498)(4.9889)
5 (1.5515 )−2.4982 =−3.0821.517
=−2.032
ECUACIÓN DE LA TABLA: Y = 102.013 X−2.032
H= 4 cm
Diámetro
D (cm)
Tiempo de vaciado t (s)
x y xy x2
log D log t log t log D ¿¿
1.5 26.7 0.1760 1.4265 0.251 0.0309
2 15 0.3010 1.176 0.3539 0.0906
3 6.8 0.4771 0.8325 0.3971 0.2276
5 2.6 0.6989 0.4149 0.2899 0.4884
7 1.3 0.8450 0.1139 0.0962 0.714
2.498 3.9638 1.3881 1.5515
Para hallar el intercepto (b) y la pendiente (m) :
b=(1.5515 ) (3.9638 )−(2.498)(1.3881)
5 (1.5515 )−2.4982 =2.9611.517
=1.434
m=(1.5515 ) (1.3881 )−(2.498)(3.9638)
5 (1.5515 )−2.4982 =−2.9611.517
=−1.951
ECUACIÓN DE LA TABLA: Y = 101.434 X−1.951
H=1 cm
Diámetro
D (cm)
Tiempo de vaciado t (s)
x y xy x2
log D log t log t log D ¿¿
1.5 13.5 0.1760 1.1303 0.1989 0.0309
2 7.8 0.3010 0.892 0.2684 0.0906
3 3.7 0.4771 0.5682 0.271 0.2276
5 1.5 0.6989 0.176 0.123 0.4884
7 0.8 0.8450 -0.096 0.0811 0.714
2.498 2.6705 0.7802 1.5515
Para hallar el intercepto (b) y la pendiente (m) :
b=(1.5515 ) (2.6705 )−(2.498)(0.7801)
5 (1.5515 )−2.4982 =2.19451.517
=1.446
m=(5 ) (0.7801 )−(2.498)(2.6705)
5 (1.5515 )−2.4982 =−2.7704
1.517=−1.826
ECUACIÓN DE LA TABLA: Y = 101.446 X−1.8260
CASO E)
D= 1.5 cm
h t H T H.T H230 73.00 1.4771 1.8633 2.7522 2.181820 59.90 1.3010 1.7774 2.3141 1.692610 43.00 1.0000 1.6334 1.6334 1.00004 26.00 0.6020 1.4149 0.8517 0.36241 13.00 0.0000 1.1205 0.0000 0.0000∑ 4.3801 7.8095 7.5514 5.2368
b=(∑ H 2∗∑ T−∑ H∗∑ H∗T )
P∗∑ H 2−∑ H2
m=P∗∑ HT−∑ H∗∑T
P∑ H2−∑ H2
T=A HB
b=(5.2368∗7.3811−4.3811∗7.5514)
5∗5.2368−4.38112 =1.1177
m=(5∗7.5514−4.3811∗7.8095)
5∗5.2368−4.38112 =0.5068
B=m=0.5068
A=10b=101.1177=13.1129
T=13.1129∗H 0.5068
D= 2 cm
b=(∑ H 2∗∑ T−∑ H∗∑ H∗T )
P∗∑ H 2−∑ H2
h t H T H.T H2
30 41.20 1.4771 1.6148 2.3852 2.1818
20 33.70 1.3010 1.5276 1.9874 1.6926
10 23.70 1.0000 1.3747 1.3747 1.0000
4 15.00 0.6020 1.176 0.7079 0.3624
1 7.80 0.0000 0.892 0.0000 0.0000
∑ 4.3801 6.5851 6.4552 5.2368
m=P∗∑ HT−∑ H∗∑T
P∑ H 2−∑ H2
T=A∗HB
b=(5.2368∗6.5851−4.3811∗6.4552)
5∗5.2368−4.38112 =0.8875
m=(5∗6.4552−4.3811∗6.5851)
5∗5.2368−4.38112 =0.4901
B=m=0.4901
A=10b=100.8875=7.7179
T=7.7179∗H 0.4901
D=3 cm
h t H T H.T H230 18.40 1.4771 1.2648 1.8682 2.181820 14.90 1.3010 1.1731 1.5262 1.692610 10.50 1.0000 1.0211 1.0211 1.00004 6.80 0.6020 0.8325 0.5011 0.36241 3.70 0.0000 0.5682 0.0000 0.0000∑ 4.3801 4.8597 4.9166 5.2368
b=(∑ H 2∗∑ T−∑ H∗∑ H∗T )
P∗∑ H 2−∑ H2
m=P∗∑ HT−∑ H∗∑T
P∑ H2−∑ H2
T=A∗HB
b=(5.2368∗4.9407−4.3811∗4.9166)
5∗5.2368−4.38112 =0.6199
m=(5∗4.9166−4.3811∗4. .8597)
5∗5.2368−4.38112 =0.4202
B=m=0.4202
A=10b=100.6199=4.1677
T=4.1677∗H 0.4202
D= 5 cm
h t H T H.T H230 6.80 1.4771 0.8325 1.2296 2.181820 5.30 1.3010 0.7242 0.9421 1.692610 3.90 1.0000 0.5563 0.5563 1.00004 2.60 0.6020 0.4149 0.2497 0.3624
1 1.50 0.0000 0.1760 0.0000 0.0000∑ 4.3801 2.7039 2.9777 5.2368
b=(∑ H 2∗∑ T−∑ H∗∑ H∗T )
P∗∑ H 2−∑ H2
m=P∗∑ HT−∑ H∗∑T
P∑ H 2−∑ H2
T=A∗HB
b=(5.2368∗2.7039−4.3811∗2.9777)
5∗5.2368−4.38112 =0.1593
m=(5∗2.9777−4.3811∗2.7039)
5∗5.2368−4.38112 =0.4352
B=m=0.4352
A=10b=100.1593=1.4431
T=1.4431∗H 0.4352
D= 7 cm
h t H T H.T H230 3.20 1.4771 0.5051 0.7460 2.181820 2.70 1.3010 0.4313 0.5615 1.692610 2.00 1.0000 0.3010 0.3010 1.0000
4 1.30 0.6020 0.1139 0.0685 0.36241 0.80 0.0000 -0.0969 0.0000 0.0000∑ 4.3801 1.14051 1.6770 5.2368
b¿(∑ H 2∗∑ T−∑ H∗∑ H∗T )
P∗∑ H 2−∑ H2
m=P∗∑ HT−∑ H∗∑T
P∑ H 2−∑ H2
T=A∗HB
b=(5.2368∗1.1405−4.3811∗1.6770)
5∗5.2368−4.38112 =−0.1113
m=(5∗1.6770−4.3811∗1.1405)
5∗5.2368−4.38112 =0.4847
B=m=0.4847
A=10b=10−0.1113=0.7739
T=0.7739∗H 0.4647
CASO F)
h = 30 cm z=1
D2
Dx i =
1
D2 y i x i y i x i2
1.51
(1.5)2=0.4444
73.0 (0.4444 )(73.0)=32.4412 (0.4444 )2=0.1974
21
(2.0)2=0.25 41.2 (0.25 ) (41.2 )=10.3 (0.25 )2=0.0625
31
(3.0)2=0.1111 18.4 (0.1111 ) (18.4 )=2.0442 (0.111 )2=0.0123
51
(5.0)2=0.04 6.8 (0.04 ) (6.8 )=0.272 (0.04 )2=0.0016
71
(7.0)2=0.0204 3.2 (0.0204 ) (3.2 )=0.0652 (0.0204 )2=0.0004
∑ x i=0.8659 ∑ yi=142.6 ∑ x i y i=45.1226 ∑ x i2=0.2742
m=5 (45.1226 )−(0.8659)(142.6)
5(0.2742)−(0.8659)2 =225.613−123.4773
1.371−0.7497=
102.13570.6213
=164.3903
b=∑ xi2∑ y i−¿∑ x i∑ x i y i
p∑ x i2−(∑ x i)
2 ¿
b=(0.2742 ) (142.6 )−(0.8659)(45.1226)
5 (0.2742 )−(0.8659)2 =39.1009−39.0716
1.371−0.7497=
0.02930.6213
=0.0471
y=164.33903 x+0.0471
}
H= 20 cm
Dx i =
1
D2 y i x i y i x i2
1.51
(1.5)2=0.4444 59.9 (0.4444 )(59.9)=26.6195 (0.4444 )2=0.1974
21
(2.0)2=0.25 33.7 (0.25 ) (33.7 )=8.425 (0.25 )2=0.0625
31
(3.0)2=0.1111 14.9 (0.1111 ) (14.9 )=1.6553 (0.111 )2=0.0123
51
(5.0)2=0.04 5.3 (0.04 ) (5.3 )=0.212 (0.04 )2=0.0016
71
(7.0)2=0.0204 2.7 (0.0204 ) (2.7 )=0.0550 (0.0204 )2=0.0004
∑ x i=0.8659 ∑ yi=116.5 ∑ x i y i=36.9668 ∑ x i2=0.2742
m=5 (36.9668 )−(0.8659)(116.5)
5(0.2742)−(0.8659)2 =184.834−100.8773
1.371−0.7497=
83.95670.6213
=135.1306
b=(0.2742 ) (116.5 )−(0.8659)(36.9668)
5 (0.2742 )−(0.8659)2 =31.9443−32.0095
1.371−0.7497=
−0.06520.6213
=−0.1049
y=135.1306 x−0.1049
Dx i =
1
D2 y i x i y i x i2
1.51
(1.5)2=0.4444 43.0 (0.4444 )(43.0)=19.1092 (0.4444 )2=0.1974
21
(2.0)2=0.25 23.7 (0.25 ) (23.7 )=5.925 (0.25 )2=0.0625
31
(3.0)2=0.1111 10.5 (0.1111 ) (10.5 )=1.1665 (0.111 )2=0.0123
51
(5.0)2=0.04 3.9 (0.04 ) (3.9 )=0.156 (0.04 )2=0.0016
71
(7.0)2=0.0204 2.0 (0.0204 ) (2.0 )=0.0408 (0.0204 )2=0.0004
∑ x i=0.8659 ∑ yi=83.1 ∑ x i y i=26.3975 ∑ x i2=0.2742
H = 10cm
m=5 (26.3975 )−(0.8659)(83.1)
5 (0.2742)−(0.8659)2 =131.9875−71.9562
1.371−0.7497=
60.03130.6213
=96.6220
b=(0.2742 ) (83.1 )−(0.8659)(26.3975)
5 ( 0.2742 )−(0.8659)2 =22.7860−22.8575
1.371−0.7497=
−0.07150.6213
=−0.1150
y=96.6220 x−0.1150
H = 4cm
D x i = 1
D2 y i x i y i x i2
1.51
(1.5)2=0.4444 26.7 (0.4444 )(26.7)=11.8654 (0.4444 )2=0.1974
21
(2.0)2=0.25 15.0 (0.25 ) (15.0 )=3.75 (0.25 )2=0.0625
31
(3.0)2=0.1111 6.8 (0.1111 ) (6.8 )=0.7554 (0.111 )2=0.0123
51
(5.0)2=0.04 2.6 (0.04 ) (2.6 )=0.104 (0.04 )2=0.0016
71
(7.0)2=0.0204 1.3 (0.0204 ) (1.3 )=0.0265 (0.0204 )2=0.0004
∑ x i=0.8659 ∑ yi=52.4 ∑ x i y i=16.5013 ∑ x i2=0.2742
m=5 (16.5013 )−(0.8659)(52.4)
5(0.2742)−(0.8659)2=
82.5065−45.37311.371−0.7497
=36.52740.6213
=58.7918
b=(0.2742 ) (52.4 )−(0.8659)(16.5013)
5 (0.2742 )−(0.8659)2 =14.3680−14.2884
1.371−0.7497=
0.07960.6213
=0.1281
y=58.7918 x+0.1281
D x i = 1
D2 y i x i y i x i2
1.51
(1.5)2=0.4444 13.5 (0.4444 )(13.5)=5.9994 (0.4444 )2=0.1974
21
(2.0)2=0.25 7.8 (0.25 ) (7.8 )=1.95 (0.25 )2=0.0625
31
(3.0)2=0.1111 3.7 (0.1111 ) (3.7 )=0.4110 (0.111 )2=0.0123
51
(5.0)2=0.04 1.5 (0.04 ) (1.5 )=0.06 (0.04 )2=0.0016
71
(7.0)2=0.0204 0.8 (0.0204 ) (0.8 )=0.0163 (0.0204 )2=0.0004
∑ x i=0.8659 ∑ yi=27.3 ∑ x i y i=8.4367 ∑ x i2=0.2742
h = 1cm
m=5 (8.4367 )−(0.8659)(27.3)
5(0.2742)−(0.8659)2 =42.1635−23.6390
1.371−0.7497=
18.52450.6213
=29.8157
b=(0.2742 ) (27.3 )−(0.8659)(8.4367)
5 (0.2742 )−(0.8659)2 =7.4856−7.30531.371−0.7497
=0.18030.6213
=0.2901
y=29.8157 x+0.2901
CASO H) A vs. t.
X LgY XLgY X²
0 2 0 0
1 1.9242 1.9242 1
2 1.8450 3.69 4
3 1.7708 5.3124 9
4 1.6901 6.7604 16
5 1.6127 8.0635 25
6 1.5314 9.1884 36
7 1.4313 10.0191 49
8 1.3802 11.0416 64
9 1.3010 11.709 81
10 1.2304 12.3040 100
∑X=55 ∑LgY=17.7171 ∑XLgY=80.0126 ∑X²=385
m = 11 (80 .0126 )−55(17.7171)
11 (385 )−(55) ² = -0.0779
b = 385 (17 .7171 )−55(80.0126)
11 (385 )−(55) ² = 2.0003
ECUACIÓN DE LA TABLA: Y = 102.0003 10−0.0779 X
II) Haciendo uso del MS EXCEL grafique y presente formulas experimentales y el factor de correlación para todos los casos desde la a) hasta la h).
CASO A)
i (A) v (V)0.5 2.181 4.362 8.724 17.44
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
2
4
6
8
10
12
14
16
18
20
Y = 4.36X
Y = 4.36XLinear (Y = 4.36X)
intensidad (A)
volta
je(V
)
CASO B)
H= 30 cm
H= 20 cm
1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
80
f(x) = 166.965437216185 x -̂2.01433568674717
ALTURA CONSTANTE EN 30cm
1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
f(x) = 135.845456256343 x -̂2.01389813238105
ALTURA CONSTANTE EN 20cm
D (cm)
t (s)
1.5 73.02 41.23 18.45 6.87 3.2
H=10 cm
1 2 3 4 5 6 7 80
10
20
30
40
50
60
70
f(x) = 135.845456256343 x -̂2.01389813238105
ALTURA CONSTANTE EN 20cm
1 2 3 4 5 6 7 80
5
10
15
20
25
30
35
40
45
50
f(x) = 94.6428242031613 x -̂1.98491646538374
ALTURA CONSTANTE EN 10cm
D (cm) t (s)1.5 59.92 33.73 14.95 5.37 2.7
D (cm) t (s)1.5 43.02 23.73 10.55 3.97 2.0
H= 4cm
H= 1
D (cm) t (s)1.5 13.52 7.83 3.75 1.57 0.8
1 2 3 4 5 6 7 80
5
10
15
20
25
30
f(x) = 58.4211089844038 x -̂1.94884532788623
ALTURA CONSTANTE EN 4 cm
1 1.5 2 2.5 3 3.5 4 4.5 5 5.50
2
4
6
8
10
12
14
16
f(x) = 27.8648097447666 x^-1.82281645529233
D (cm) t (s)1.5 26.72 15.03 6.85 2.67 1.3
CASO C)
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.000.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
f(x) = 17.4220202542866 ln(x) + 7.83696588327661R² = 0.94863709765356
ALTURA VS TIEMPO CUANDO EL DIAMETRO ES 1.5 cm
ALTURA (CM)
TIEM
PO(S
)
0 5 10 15 20 25 30 350.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
45.00
f(x) = 9.64322591830472 ln(x) + 4.82805283796686R² = 0.941446018364728
ALTURA VS TIEMPO CUANDO EL DIAMETRO ES 2 cm
ALTURA(CM)
TIEM
PO(S
)h (cm) t (s)
30 73.020 59.910 43.04 26.71 13.5
h (cm) t (s)30 41.220 33.710 23.74 15.01 7.8
0 5 10 15 20 25 30 350.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
20.00
f(x) = 4.21616416982284 ln(x) + 2.35531460191395R² = 0.935299667953378
ALTURA VS TIEMPO CUANDO EL DIAMETRO ES 3cm
ALTURA(CM)
TIEM
PO(S
)
0 5 10 15 20 25 30 350.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
f(x) = 1.48823467422729 ln(x) + 1.01798983317151R² = 0.926165117642997
ALTURA VS TIEMPO CUANDO EL DIAMETRO ES 5 cm
ALTURA(CM)
TIEM
PO(S
)
h (cm) t (s)30 18.420 14.910 10.54 6.81 3.7
h (cm) t (s)30 6.820 5.310 3.94 2.61 1.5
CASO D
H=30 cm
1 101
10
10073
41.2
18.4
6.8
3.2
t vs. D cuando H=30 cm
Diámetro
Tiem
po d
e va
ciad
o
y = -10.775x + 68.388
R² = 0.7199
0 5 10 15 20 25 30 350.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
f(x) = 0.701745428490422 ln(x) + 0.584465912980113R² = 0.946818819951521
ALTURA VS TIEMPO CUANDO EL DIAMETRO ES 7
ALTURA(CM)
TIEM
PO(S)
h (cm) t (s)30 3.220 2.710 2.04 1.31 0.8
D (cm) t (s)1.5 73.02 41.23 18.45 6.87 3.2
H=20 cm
H=10 cm
1 101
10
10059.9
33.7
14.9
5.3
2.7
t vs. D cuando H=20cm
Diámetro
Tiem
po d
e va
ciad
o y = -8.8317x + 55.977
R² = 0.7158
D (cm) t (s)1.5 59.92 33.73 14.95 5.37 2.7
H= 4 cm
1 101
10
100
26.7
15
6.8
2.6
1.3
t vs. D. cuando H=4 cm
Diámetro cm
Tiem
po d
e va
ciad
o
y = -3.9101x + 24.947
R² = 0.7172
1 101
10
100
43
23.7
10.5
3.9
2
t vs. D. cuando H=10cm
Diámetro
Tiem
po d
e va
ciad
o
y = -6.2774x + 39.846
R² = 0.7072
D (cm) t (s)1.5 43.02 23.73 10.55 3.97 2.0
D (cm) t (s)1.5 26.72 15.03 6.8 5 2.67 1.3
H= 1 cm
Caso e)
h (cm) t (s)30 73.0
1 100.1
1
10
100
13.57.8
3.7
1.5
0.8
t vs. D cuando H=1 cm
Diametro
Tiem
po
de v
acia
do
y = -1.9692x + 12.746
R² = 0.7292
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.000.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00f(x) = 1.99527972027972 x + 17.0413636363636R² = 0.958984701792988
ALTURA VS TIEMPO CUANDO EL DIAMETRO ES 1.5 cm
ALTURA (CM)
TIEM
PO(S
)
D (cm) t (s)1.5 13.52 7.83 3.75 1.57 0.8
20 59.910 43.04 26.71 13.5
h (cm) t (s)30 41.220 33.710 23.74 15.01 7.8
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.000.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00f(x) = 1.99527972027972 x + 17.0413636363636R² = 0.958984701792988
ALTURA VS TIEMPO CUANDO EL DIAMETRO ES 1.5 cm
ALTURA (CM)
TIEM
PO(S
)
0 5 10 15 20 25 30 350.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
45.00f(x) = 1.11293706293706 x + 9.81181818181818R² = 0.966480236848061
ALTURA VS TIEMPO CUANDO EL DIAMETRO ES 2 cm
ALTURA(CM)
TIEM
PO(S
)
0 5 10 15 20 25 30 350.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
20.00f(x) = 0.489510489510489 x + 4.49636363636364R² = 0.971719203293375
ALTURA VS TIEMPO CUANDO EL DIAMETRO ES 3cm
ALTURA(CM)
TIEM
PO(S
)
h (cm) t (s)30 18.420 14.910 10.54 6.81 3.7
h (cm) t (s)30 6.820 5.310 3.94 2.61 1.5
0 5 10 15 20 25 30 350.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
20.00f(x) = 0.489510489510489 x + 4.49636363636364R² = 0.971719203293375
ALTURA VS TIEMPO CUANDO EL DIAMETRO ES 3cm
ALTURA(CM)
TIEM
PO(S
)
0 5 10 15 20 25 30 350.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
f(x) = 0.174125874125874 x + 1.75636363636364R² = 0.977176981233776
ALTURA VS TIEMPO CUANDO EL DIAMETRO ES 5 cm
ALTURA(CM)
TIEM
PO(S
)
0 5 10 15 20 25 30 350.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50f(x) = 0.0804195804195804 x + 0.954545454545455R² = 0.958368056813653
ALTURA VS TIEMPO CUANDO EL DIAMETRO ES 7
ALTURA(CM)
TIEMP
O(S)
h (cm) t (s)30 3.220 2.710 2.04 1.31 0.8
CASO F)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
2
4
6
8
10
12
14
16
18
20
t vs. Z cuando h =30 cm
v (V)
Z
Tiem
po (s
)
Y = 165.77x1.0023 R2 = 0.9997
0 5 10 15 20 25 30 350.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50f(x) = 0.0804195804195804 x + 0.954545454545455R² = 0.958368056813653
ALTURA VS TIEMPO CUANDO EL DIAMETRO ES 7
ALTURA(CM)
TIEMP
O(S)
D (cm) Z = 1/D2 t (s)1.5 0.4444 73.02 0.25 41.23 0.1111 18.45 0.04 6.87 0.02 3.2
D (cm) Z = 1/D2 t (s)1.5 0.4444 59.92 0.25 33.73 0.1111 14.95 0.04 5.37 0.02 2.7
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
2
4
6
8
10
12
14
16
18
20
t vs. Z cuando h =20 cm
v (V)
Z
Tiem
po (s
)
D (cm) Z = 1/D2 t (s)1.5 0.4444 43.02 0.25 23.73 0.1111 10.55 0.04 3.97 0.02 2.0
0 2 4 6 8 10 120
2
4
6
8
10
12
t vs. Z cuando h =10 cm
Series1
Z
Tiem
po (s
)
Y = 93.95x0.9875 R2 = 0.9998
Y = 134.84x1.0019 R2 = 1
D (cm) Z = 1/D2 t (s)1.5 0.4444 26.72 0.25 15.03 0.1111 6.85 0.04 2.67 0.02 1.3
0 2 4 6 8 10 120
2
4
6
8
10
12
t vs. Z cuando h =4 cm
Series1
Z
Tiem
po (s
)
D (cm) Z = 1/D2 t (s)1.5 0.4444 13.52 0.25 7.83 0.1111 3.75 0.04 1.57 0.02 0.8
Y = 58.009x0.9696 R2 = 0.9999
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
t vs. Z cuando h =1 cm
#¡REF!
Z
Tiem
po (s
)
Caso g)
t (dias) 0 1 2 3 4 5 6 7 8 9 10A (%) 100 84 70 59 49 41 34 27 24 20 17
0.8 1 1.2 1.4 1.6 1.8 20
0.5
1
1.5
2
2.5
A vs. T
0.5
T (dias)
A (%
)
Caso h)
Y = 100.09e-0.1795x R2 = 0.999
Y = 27.714x0.9077 R2 = 0.9999
t (dias) 0 1 2 3 4 5 6 7 8 9 10A (%) 100 84 70 59 49 41 34 27 24 20 17
0 2 4 6 8 10 121
10
A vs. T
Series1
T (dias)
A (%
)
3.- Interpolación y extrapolación :
Considerando sus gráficos (en donde ha obtenido rectas)
a) Calcular el tiempo en que se ha desintegrado el 50% de los núcleos de radón, según la tabla 3.
T(dias) 0 1 2 3 4 5 6 7 8 9 10A(%) 100 84 70 59 49 41 34 27 24 20 17
T A T LogA T.LogA T 2
0 100 0 2 0 01 84 1 1.9243 1.9243 12 70 2 1.8451 3.6902 43 59 3 1.7709 5.3127 94 49 4 1.6901 6.7608 165 41 5 1.6127 8.0635 256 34 6 1.5315 9.189 367 27 7 1.4314 10.0198 498 24 8 1.3802 11.0416 649 20 9 1.3010 11.709 8110 17 10 1.2304 12.304 100
Y = 100.09e-0.1795x R2 = 0.999
∑T=55 ∑ LogA=17.7177 ∑T .LogA=80.0149 ∑T 2=385
Hallando pendiente “m”:
m=p∑ T . LogA−∑ T ∑ LogA
p∑T 2−¿¿¿
m=11 (80.0149 )−(55)(17.7177)
11(385)−(55)2
m=−0.0779
Hallando “b”
b=¿¿¿
b=385(17.7177)−55(80.0149)
11(385)−(55)2
b=2.0004
FORMULA
y=A . 10BX
DONDE
A=10b y B=m
ENTONCES TENEMOS QUE PARA A=50 “T” SERA:
50=(10¿¿2.0004 )(10−0.0779 T )¿
T=3.8694
TABLA 3
b) Halle los tiempos de vaciado de agua si:
ALTURA h(cm)
DIAMETRO d(cm)
Xi=Logdi Yi=Loghi XiYi Xi2
20 4.0 0.602 1.301 0.783 0.36240 1.0 0 1.602 0 025 3.5 0.544 1.398 0.761 0.29649 1.0 0 1.690 0 0
Hallando m y b
m=4 (1.544 )− (1.146 )(5.991)
4 (0.65 )−1.1462 =−0.68961.2866
=−0.536
b=(0.65 ) (5.991 )−(1.146 )(1.544 )
4 (0.65 )−1.1462 =2.12471.2866
=1.651
La fórmula quedaría:
Y=101.651 x−0.536
Ahora reemplazando los valores (d) en la fórmula, el cuadro quedaría de la siguiente manera :
CASOS ALTURA h(cm)
DIAMETRO d(cm)
TIEMPO t(s)
01 20 4.0 21.48402 40 1.0 44.3603 25 3.5 23.03804 49 1.0 44.36
4.- HAGA w = √hd2 PARA LAS ALTURAS Y DIÁMETROS CORRESPONDIENTES Y COMPLETE LA TABLA:
t (s) 73.0 43.0 26.7 15.0 10.5 3.9 1.5
W 2.4343 1.4054 0.8888 0.5 0.3513 0.1264 0.04
t=73.0: w ₁ = √301. 52 = 2.4343
t=43.0: w ₂ = √101. 52 = 1.4054
t=26.7: w ₃ = √41.52 = 0.8888
t=15.0: w ₄ = √422 = 0.5
t=10.5: w ₅ = √1032 = 0.3513
t=3.9: w ₆ = √1052 = 0.126
t=1.5: w ₇ = √152 = 0.04