m 2N 5

ƩXY 18.81981284N ƩXY 94.0990642ƩXƩY 86.57309302

NƩXY - ƩXƩY 7.525971189.40990642

47.0495321

43.28654651

3.762985589

2

b 0N 5

ƩXƩXY 123.820276436745(ƩX^2)(ƩY) 123.820276436745

ƩXƩXY - (ƩX^2)(ƩY) 0(ƩX)^2 43.2865465107364N ƩX^2 47.0495320997611

(ƩX)^2 - N ƩX2 -3.76298558902474ƩXƩXY - (ƩX^2)(ƩY) / (ƩX)^2 - NƩX2 0

rN 5

ƩXY 18.8198128399045ƩXƩY / N 17.3146186042946

ƩXY - (ƩXƩY / N) 1.5051942356099ƩX^2 - ((1/N)((ƩX)^2)) 0.752597117804948ƩY^2 - ((1/N)((ƩX)^2)) 28.9823163776616

ƩX^2 - ((1/N)((ƩX)^2)) * ƩY^2 - ((1/N)((ƩX)^2)) 21.8120077731393√(ƩX^2 - ((1/N)((ƩX)^2)) * ƩY^2 - ((1/N)((ƩX)^2))) 4.67033272617051

ƩXY - (ƩXƩY / N) / √(ƩX^2 - ((1/N)((ƩX)^2)) * ƩY^2 - ((1/N)((ƩX)^2))) 0.322288437218925

ƩX2

N ƩX2

(ƩX)2

NƩX2 - (ƩX)2

NƩXY - ƩXƩY /NƩX2 - (ƩX)2

i x y1 2 4 0.9609062 3 9 2.41389793 4 16 3.84362414 5 25 5.18058085 6 36 6.420804

log x log y Ʃ 18.819813

0.69314718055995 1.38629436 18.819813

1.09861228866811 2.19722458

1.38629436111989 2.77258872

1.6094379124341 3.21887582 0.4804531.79175946922806 3.58351894 1.206949

1.9218121Ʃ 6.5792512120101 13.1585024 2.5902904

3.210402

Ʃ 9.4099064 Ʃ9.4099064

Ʃ(X*Y)

Ʃ (X^2)

1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.50

5

10

15

20

25

30

35

40

Column FLinear (Column F)

1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.50

0.5

1

1.5

2

2.5

3

3.5

4

Column FLinear (Column F)

0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.5

1

1.5

2

2.5

3

3.5

4

f(x) = 2.27958308498057 ln(x) + 2.12415028825603R² = 0.981488671787423

Column FLogarithmic (Column F)

0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.5

1

1.5

2

2.5

3

3.5

4

f(x) = 2.27958308498057 ln(x) + 2.12415028825603R² = 0.981488671787423

Column FLogarithmic (Column F)

N*(Ʃ(X*Y)) ƩXƩY N*(Ʃ(X*Y)) - ƩXƩY94.099064199522 86.5730930214728 7.52597117804947

94.0990642 7.525971179

N*(Ʃ (X^2)) (ƩX)^2 N*(Ʃ (X^2)) - (ƩX)^247.049532099761 43.2865465107364 3.76298558902474

47.0495321 3.762985589

Ʃ (Y^2) N*(Ʃ(X*Y)) - ƩXƩY / N*(Ʃ (X^2)) - (ƩX)^2

1.92181205567281 2

4.82779584325033 2.000000000265757.6872482226912210.361161575920912.8416079822736

37.6396256798089

1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.50

0.5

1

1.5

2

2.5

3

3.5

4

Column FLinear (Column F)

0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.5

1

1.5

2

2.5

3

3.5

4

f(x) = 2.27958308498057 ln(x) + 2.12415028825603R² = 0.981488671787423

Column FLogarithmic (Column F)

0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.5

1

1.5

2

2.5

3

3.5

4

f(x) = 2.27958308498057 ln(x) + 2.12415028825603R² = 0.981488671787423

Column FLogarithmic (Column F)

x Ln x y Ln y (Ln X)^2 (Ln Y)^2 LnX * LnY2 0.69314718056 4 1.3862944 0.48045301 1.92181206 0.960906033 1.09861228867 9 2.1972246 1.20694896 4.82779584 2.413897924 1.38629436112 16 2.7725887 1.92181206 7.68724822 3.843624115 1.60943791243 25 3.2188758 2.59029039 10.3611616 5.180580796 1.79175946923 36 3.5835189 3.210402 12.841608 6.420803997 1.94591014906 49 3.8918203 3.78656631 15.1462652 7.573132628 2.07944154168 64 4.1588831 4.32407713 17.2963085 8.648154259 2.197224577336 81 4.3944492 4.82779584 19.3111834 9.65559169

10 2.302585092994 100 4.6051702 5.30189811 21.2075924 10.6037962Ʃ 15.1044125731 Ʃ 30.208825 27.6502438 110.600975 55.300488

-179.78412

179.78412 -1

X Ln X Y Ln Y (Ln X)^21.2 0.182321556794 3.5 1.252762968495 0.0332411500722.4 0.875468737354 27.6 3.317815772723 0.7664455100843.6 1.280933845462 93.3 4.535820107853 1.640791516454.5 1.504077396776 182.2 5.205104984826 2.2622488154935.8 1.757857917552 390.2 5.966659428189 3.0900644583026.1 1.808288771179 454 6.118097198041 3.2699082799737.3 1.987874348154 778 6.656726524178 3.951644424058.5 2.140066163496 1228.3 7.113386378545 4.5798831841429.3 2.230014400159 1608.7 7.383181678396 4.972964224917

10.4 2.341805806147 2249.7 7.718552152975 5.484054433705Ʃ 16.10870894307 Ʃ 55.26810719422 30.05124599719

N=10m b r

122.89861753 -28.746781106 122.898617527741.021956159 -41.021956159 122.89875762382.9959228919 0.70076573128 0.999998860068

3 0.7 1

(Ln Y)^2 LnX * LnY1.56941505523 0.22840569471 3.3361E-0511.0079015017 2.904643985319 3.3487E-0520.5736640508 5.810085493077 6.3739E-0627.0931179031 7.828880755524 3.0999E-0635.601024732 10.48853951718 2.6325E-07

37.4311133247 11.0632864642 2.6328E-0844.3120080177 13.23273590009 1.9583E-0750.6002657705 15.2231174966 1.3166E-0654.5113716962 16.46460146182 2.1455E-0659.5760473382 18.07535024689 3.6741E-06342.27592939 101.3196470154 8.3944E-05

σ DM DB0.003239280604 0.0102435 0.0027725

6.40483850.0015993

X Y Ln Y X^21.2 33.1 3.499533282383 1.441.7 89.9 4.498697941478 2.892.1 200 5.298317366548 4.412.6 544 6.298949246856 6.762.9 991 6.89871453433 8.413.3 2210 7.700747794512 10.893.8 5990 8.697846691109 14.444.2 13300 9.49551931421 17.644.7 36300 10.49957302025 22.095 66100 11.09892402584 25

5.6 219000 12.2968270088 31.365.9 400000 12.89921982609 34.816.2 728000 13.49805632718 38.44

N=16 6.8 2420000 14.69927809813 46.247.3 6570000 15.69802439046 53.297.5 9810000 16.09891283154 56.25

Ʃ 70.8 Ʃ 159.1771416997 374.36

m b r1954.1528556377 -1073.82165741 1954.15285564

977.12 -977.12 1954.152939771.9999108150869 1.098965999473 0.99999995695

2 1.1 1

(Ln Y)^2 X * LnY12.2467331945 4.19943993886 4.546869708E-0720.2382831687 7.64778650051 1.355912207E-0828.0721669167 11.1264664698 2.12838847E-0739.6767616145 16.3772680418 4.628012388E-0847.5922622262 20.0062721496 5.142474507E-1159.3015165947 25.4124677219 4.310213017E-0675.652537062 33.0518174262 6.090330469E-07

90.1648870465 39.8811811197 9.437851423E-06110.241033608 49.3479931952 1.053065652E-06123.186114531 55.4946201292 1.631763557E-07151.211954484 68.8622312493 2.688141126E-06166.389872122 76.1053969739 6.084274632E-07182.197524612 83.6879492285 1.272533199E-07216.068776606 99.9550910673 8.437452519E-07246.427969764 114.59557805 8.442461761E-08259.174994358 120.741846237 3.791097846E-071827.84338791 826.493405499 2.103185755E-05

σ DM DB0.0012256735 0.0049027 0.0007587

31.2589190.0001568

Tabla de Datos para calcular la pendiente, la ordenada al origen y finalmente la gravedadt d Ln t Ln d (Ln t)^2 (Ln d)^2 LnX * LnY

1.76 s 1.21 cm 0.5653 0.1906 0.3196 0.0363 0.10781.62 s 1.11 cm 0.4824 0.1044 0.2327 0.0109 0.05031.54 s 1.01 cm 0.4318 0.0100 0.1864 0.0001 0.00431.46 s 0.91 cm 0.3784 -0.0943 0.1432 0.0089 -0.03571.36 s 0.81 cm 0.3075 -0.2107 0.0945 0.0444 -0.06481.23 s 0.71 cm 0.2070 -0.3425 0.0429 0.1173 -0.07091.14 s 0.61 cm 0.1310 -0.4943 0.0172 0.2443 -0.06481.07 s 0.51 cm 0.0677 -0.6733 0.0046 0.4534 -0.04560.98 s 0.41 cm -0.0202 -0.8916 0.0004 0.7949 0.01800.82 s 0.31 cm -0.1985 -1.1712 0.0394 1.3717 0.2324

Σ 2.3525 -3.5730 1.0809 3.0823 0.1311

m 9.7168 Δm 0.1400 σ5.2748 2.29671.8421 0.0610 θ

radianesb 4.1706 Δb 0.0200

-5.2748 (2*e^B)/senθ 14.8586 g-0.7907 e^b 0.4535 sen rad

Tabla de Datos para calcular la pendiente, la ordenada al origen y finalmente la gravedad(Y-Mx-b)^2

0.00360.00000.00000.00000.00020.00450.00300.00010.00410.00020.0157

0.0443

3.50000.0611

14.85860.0610