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)


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)


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


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


H= 4 cm

Diámetro

D (cm)


x y xy x2


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


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


H=1 cm

Diámetro

D (cm)


x y xy x2


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


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


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


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


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


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


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


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


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


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(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 (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 (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(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(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(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(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(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(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


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


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


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


#¡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

LUEGO: t = mw + b

m = 7 (273 .6086 )−5.7462(173.6)

7 (9 . 0819 )−(5.7462)² = 30.0356

b = 9 .0819 (173 . 6 )−5.7462(273.6086)

7 (9 .0819 )−(5.7462)² = 0.1442

CALCULANDO LA FÓRMULA: t = 30.0356 w + 0.1442

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informe 2 Laboratorio de Fisica I