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Physics Data Analysis Tables

1. The document contains experimental data with measurements of time (t) and height (h) for different values of n. It also includes the logarithmic values of t and h. 2. The data is analyzed to calculate sums, averages, and regression coefficients. Equations are developed to model the relationship between the logarithmic values of t and h. 3. Additional experiments are described that vary the diameter (d) instead of height, and similar analyses are performed to study the relationships between the logarithmic values of time and diameter.

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Luca Vincenzo Cocchiola
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33 views11 pages

Physics Data Analysis Tables

1. The document contains experimental data with measurements of time (t) and height (h) for different values of n. It also includes the logarithmic values of t and h. 2. The data is analyzed to calculate sums, averages, and regression coefficients. Equations are developed to model the relationship between the logarithmic values of t and h. 3. Additional experiments are described that vary the diameter (d) instead of height, and similar analyses are performed to study the relationships between the logarithmic values of time and diameter.

Uploaded by

Luca Vincenzo Cocchiola
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as XLSX, PDF, TXT or read online on Scribd
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y

1.5 x
t (s) h (cm) lg t(s) lg h(cm) n
73 30 1.86 1.48 1
51.6 15 1.71 1.18 2
42.5 10 1.63 1.00 3
26.7 4 1.43 0.60 4
19 2 1.28 0.30 5
TOTAL
2
lg t(s) lg h(cm) n
41.2 30 1.61 1.48 1
29 15 1.46 1.18 2
23.7 10 1.37 1.00 3
15 4 1.18 0.60 4
10.6 2 1.03 0.30 5
TOTAL
3
t (s) h (cm) lg t (s) lg h (cm) n
18.4 30 1.26 1.48 1
12.9 15 1.11 1.18 2
10.5 10 1.02 1.00 3
6.8 4 0.83 0.60 4
4.7 2 0.67 0.30 5
TOTAL
4
t (s) h (cm) t (s) h (cm) n
10.3 30 1 1.48 1
7.3 15 0.9 1.18 2
6 10 0.8 1.00 3
3.8 4 0.6 0.60 4
2.6 2 0.4 0.30 5
TOTAL
5
t (s) h (cm) lg t(s) lg h(cm) n
6.8 30 0.8 1.48 1
4.5 15 0.7 1.18 2
3.9 10 0.6 1.00 3
2.3 4 0.4 0.60 4
1.6 2 0.2 0.30 5
TOTAL

PARTE 2
30 CM
t (s) d (cm) lg t(s) lg d(cm) n
73 1.5 1.86 0.18 1
41.2 2 1.61 0.30 2
18.4 3 1.26 0.48 3
10.3 4 1.01 0.60 4
6.8 5 0.83 0.70 5
TOTAL
15
t (s) d (cm) lg t(s) lg d(cm) n
51.6 1.5 1.7 0.18 1
29 2 1.5 0.30 2
12.9 3 1.1 0.48 3
7.3 4 0.9 0.60 4
4.5 5 0.7 0.70 5
TOTAL
10
t (s) d (cm) lg t(s) lg d(cm) n
42.5 1.5 1.63 0.18 1
23.7 2 1.37 0.30 2
10.5 3 1.02 0.48 3
6 4 0.78 0.60 4
3.9 5 0.59 0.70 5
TOTAL
4
t (s) d (cm) lg t(s) lg d(cm) n
26.7 1.5 1.4 0.2 1
15 2 1.2 0.3 2
6.8 3 0.8 0.5 3
3.8 4 0.6 0.6 4
2.3 5 0.4 0.7 5
TOTAL
2
t (s) d (cm) lg t(s) lg d(cm) n
19 1.5 1.3 0.2 1
10.6 2 1 0.3 2
4.7 3 0.7 0.5 3
2.6 4 0.4 0.6 4
1.6 5 0.2 0.7 5
TOTAL
∑▒ 〖 (𝑋𝑖𝑌𝑖) ∑128▒𝑥
ⅈ^2 Log h (cm) Log t (s) B 5 0.91
〗
2.75 2.18 1.48 1.86 5 *
2.01 1.38 1.18 1.71
1.63 1.00 1.00 1.63 A 0.91 *
0.86 0.36 0.60 1.43 5 0.83
0.38 0.09 0.30 1.28
7.64 5.02 𝑥 ̅ 0.91 𝑦 ̅ = 1.58
=
∑▒ 〖 (𝑋𝑖𝑌𝑖) ∑128▒𝑥
〗
ⅈ^2 Log h (cm) Log t (s) B 5 0.91
2.39 2.18 1.48 1.61 5 *
1.72 1.38 1.18 1.46
1.37 1.00 1.00 1.37 A 0.91 *
0.71 0.36 0.60 1.18 5 0.83
0.31 0.09 0.30 1.03
6.50 5.02 𝑥 ̅ 0.91 𝑦 ̅= 1.33
=
∑▒ 〖 (𝑋𝑖𝑌𝑖) ∑128▒𝑥
ⅈ^2
〗 Log h (cm) Log t (s) B 5 0.91
1.87 2.18 1.48 1.26 5 *
1.31 1.38 1.18 1.11
1.02 1.00 1.00 1.02 A 0.91 *
0.50 0.36 0.60 0.83 5 0.83
0.20 0.09 0.30 0.67
4.90 5.02 𝑥 ̅ 0.91 𝑦 ̅ 0.98

∑▒ 〖 (𝑋𝑖𝑌𝑖) ∑128▒𝑥
ⅈ^2 Log h (cm) Log t (s) B 5 0.91
〗
1.48 2.18 1.48 1.00 5 *
1.06 1.38 1.18 0.90
0.80 1.00 1.00 0.80 A 0.91 *
0.36 0.36 0.60 0.60 5 0.83
0.12 0.09 0.30 0.40
3.82 5.02 𝑥 ̅ 0.91 𝑦 ̅ 0.74

∑▒ 〖 (𝑋𝑖𝑌𝑖) ∑128▒𝑥
ⅈ^2
〗 Log h (cm) Log t (s) B 5 0.91
1.18 2.18 1.48 0.80 5 *
0.82 1.38 1.18 0.70
0.60 1.00 1.00 0.60 A 0.91 *
0.24 0.36 0.60 0.40 5 0.83
0.06 0.09 0.30 0.20
2.91 5.02 𝑥 ̅ 0.91 𝑦 ̅ 0.54
∑▒ 〖 (𝑋𝑖𝑌𝑖) ∑128▒𝑥
ⅈ^2 Log d (cm) Log t (s) B 5 0.45
〗
0.33 0.03 0.18 1.86 5 *
0.49 0.09 0.30 1.61
0.60 0.23 0.48 1.26 A 0.45 *
0.61 0.36 0.60 1.01 5 0.20
0.58 0.49 0.70 0.83
2.61 1.20 𝑥 ̅ 0.45 𝑦 ̅ 1.32

∑▒ 〖 (𝑋𝑖𝑌𝑖) ∑128▒𝑥
ⅈ^2 Log d (cm) Log t (s) B 5 0.45
〗
0.30 0.03 0.18 1.70 5 *
0.45 0.09 0.30 1.50
0.52 0.23 0.48 1.10 A 0.45 *
0.54 0.36 0.60 0.90 5 0.20
0.49 0.49 0.70 0.70
2.31 1.20 𝑥 ̅ 0.45 𝑦 ̅ 1.18

∑▒ 〖 (𝑋𝑖𝑌𝑖) ∑128▒𝑥
〗
ⅈ^2 Log d (cm) Log t (s) B 5 0.45
0.29 0.03 0.18 1.63 5 *
0.41 0.09 0.30 1.37
0.49 0.23 0.48 1.02 A 0.45 *
0.47 0.36 0.60 0.78 5 0.20
0.41 0.49 0.70 0.59
2.07 1.20 𝑥 ̅ 0.45 𝑦 ̅ 1.08

∑▒ 〖 (𝑋𝑖𝑌𝑖) ∑128▒𝑥
〗
ⅈ^2 Log d (cm) Log t (s) B 5 0.46
0.28 0.04 0.20 1.40 5 *
0.36 0.09 0.30 1.20
0.40 0.25 0.50 0.80 A 0.46 *
0.36 0.36 0.60 0.60 5 0.21
0.28 0.49 0.70 0.40
1.68 1.23 𝑥 ̅ 0.46 𝑦 ̅ 0.88

∑▒ 〖 (𝑋𝑖𝑌𝑖) ∑128▒𝑥
〗
ⅈ^2 Log d (cm) Log t (s) B 5 0.46
0.26 0.04 0.20 1.30 5 *
0.30 0.09 0.30 1.00
0.35 0.25 0.50 0.70 A 0.46 *
0.24 0.36 0.60 0.40 5 0.21
0.14 0.49 0.70 0.20
1.29 1.23 𝑥 ̅ 0.46 𝑦 ̅ 0.72
dh  
n m
t (s)
1,5 -2,01
30 0,50 73.0
  2,0
-2,01
15 0,50 29.0
3,0 -2,01
 10 0,50 10.5
4,0 -2,01
 4 0,50 3.8
5,0 -2,01
 2 0,50 1.6
1,5 -2,01
 2  0,50 19.0
2,0 -2,01
 4 0,50 15.0
4,0 -2,01
 15 0,50 7.3
5,0 -2,01
 30 0,50 6.8
* 1.58 - 7.63876362 = -0.43103356 0.498
0.83 - 5.02 - 0.87

7.63876362 - 1.58 * 5.02 = -0.97747135 1.13


- 5.02 - 0.87

* 1.33 - 6.49678616 = -0.43376848 0.501


0.83 - 5.02 - 0.87

6.49678616 - 1.33 * 5.02 = -0.75735886 0.87


- 5.02 - 0.87

* 0.98 - 4.89917536 = -0.43290212 0.4998


0.83 - 5.02 - 0.87

4.89917536 - 0.98 * 5.02 = -0.45459266 0.52


- 5.02 - 0.87

* 0.74 - 3.81725138 = -0.44558753 0.5144


0.83 - 5.02 - 0.87

3.81725138 - 0.74 * 5.02 = -0.23493772 0.27


- 5.02 - 0.87

* 0.54 - 2.90599088 = -0.44558753 0.5144


0.83 - 5.02 - 0.87

2.90599088 - 0.54 * 5.02 = -0.06169879 0.07


- 5.02 - 0.87
* 1.32 - 2.60940637 = 0.36231391 - 1.98
0.20 - 1.20 - 0.18

2.60940637 - 1.32 * 1.20 = -0.40463245 2.21


- 1.20 - 0.18

* 1.18 - 2.30686651 = 0.35435505 - 1.94


0.20 - 1.20 - 0.18

2.30686651 - 1.18 * 1.20 = -0.37583995 2.05


- 1.20 - 0.18

* 1.08 - 2.06944683 = 0.36333476 - 1.98


0.20 - 1.20 - 0.18

2.06944683 - 1.08 * 1.20 = -0.36134824 1.97


- 1.20 - 0.18

* 0.88 - 1.68 = 0.344 - 2.00


0.21 - 1.23 - 0.17

1.68 - 0.88 * 1.23 = -0.3096 1.80


- 1.23 - 0.17

* 0.72 - 1.29 = 0.366 - 2.13


0.21 - 1.23 - 0.17

1.29 - 0.72 * 1.23 = -0.2922 1.70


- 1.23 - 0.17
d h dh t (s)
5.477 0.4425 2.4 73
3.87 0.248 1.0 29
3.162 0.109 0.3 10.5
2.0 0.061 0.1 3.8
1.414 0.039 0.1 1.6
1.414 0.442 0.6 19
2 0.248 0.5 15
3.872 0.061 0.2 7.3
5,477 0.039 213.6 6.8

t (s)
80

70

60

50

40

30

20

10

0
0.0 50.0 100.0 150.0 200.0 250.0
h (cm) t (s)
30 73
15 51.6
10 42.5
4 26.7
2 19

0.5054
0.57
- 2.01

1.95

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