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Lab Exercise 1: Experimental Errors and Uncertainty
Introduction: what is the purpose of this laboratory experiment?
The purpose of this lab experiment was to show that experiments are not always 100% correct and it provided the mathematical means to calculate how much error there are in the measurements that were taken. The experiment also asked for different ways that the measurements could have errors and ways that we can minimize the errors to get better measurements.
QUESTION 1 Imagine that your team has been assigned by a construction company to measure the dimensions of an empty lot in a subdivision. Briefly give examples of the 6 types/sources of errors described above and explain what you would do to minimize them.
1. If using a measuring tape with a limited accuracy, such as being accurate to the nearest centimeter, this could introduce errors in measuring the dimensions of the lot. To minimize this, consider using more precise instruments, like a laser distance measurer accurate to the nearest millimeter.
2. Calibration of your equipment is very important. If the GPS device used for mapping the lot is not properly calibrated, it could result in inaccurate measurements. To minimize this, ensure that all measurement instruments, including GPS devices, are regularly calibrated to known standards. Additionally, use redundant measurements or cross-verify with other calibrated instruments. 3. When measuring the lot dimensions with a surveying instrument, incorrect interpretation of readings or inaccuracies due to instrument fluctuations may occur. To minimize this, use instruments with digital displays for clear and precise readings. Make sure when you are reading a value that you are looking at the reading head on and not from an angle. Reading from an angle can cause the reading to be off because of the angle of your view.. Additionally you can take multiple readings and average them to reduce the impact of occasional fluctuations.
4. Slight temperature or humidity changes can affect the dimensions measured, especially for materials like metal tapes that may expand or contract. To minimize this, measure during stable weather conditions and, if possible, choose measuring tools that are less affected by environmental changes such as laser measuring devices.
5. In the real world, achieving a perfectly flat and obstacle-free lot may be challenging. To minimize errors
from over-simplifications, acknowledge the limitations and potential obstacles in the lot and adjust the measurement strategy accordingly. Account for irregularities and use appropriate measurement techniques to compensate.
6. Reading the measurement incorrectly, recording the wrong number, or experiencing parallax errors. To
minimize these errors, provide training to the measurement team, use digital instruments with clear displays, cross-verify measurements, and ensure proper alignment and positioning to avoid parallax errors.
Copyright © 2017 by Thomas Edison State University. All rights reserved.
QUESTION 2
A certain gas is known to have a pressure of 9 psi. We are asked to take measurements using two different sensors. These are the results that we obtained after measuring the pressure of the gas 7 different times.
Sensor 1: 9.8 10.0
10.3 9.7 9.9 10.1 9.8 Sensor 2: 9.3 9.5 8.6 9.0 8.9 9.2 8.5
Do you believe one of the sensors is more accurate than the other? What about precise? Explain your reasoning.
Sensor 1 is consistently higher with an average of 9.94 psi while sensor 2 has an average of 9 psi. Sensor 2 is accurate but not precise while sensor 1 is not accurate but it is precise.
QUESTION 3 Calculate the mean and standard deviation from the values using Sensor 2. Show all your work step by step. Sensor 2 values: 9.3 9.5 8.6 9.0 8.9 9.2 8.5
QUESTION 4 If we were able to perform totally accurate and precise measurements, what would be the standard deviation in these conditions?
The standard deviation would be zero because there would be no error in the measurements.
QUESTION 5 By inspecting the mean and standard deviation values from Sensor 1 and Sensor 2, what can you say about the accuracy of each sensor. What about its precision?
Copyright © 2017 by Thomas Edison State University. All rights reserved.
Sensor 2 has a mean that is exactly the actual measurement while sensor 1’s mean is .94 psi higher than actual. This means that sensor 2 is more accurate. The standard deviation shows that sensor 1 has a lower standard deviation of 0.207 while sensor 2 is 0.365. This shows that sensor 2 is more precise than sensor 1.
QUESTION 6 Calculate the Mean ¿
and Standard Deviation for each time completing the table below.
Distance (y) at different time intervals in free-fall
experiment
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
Mean
Std. Dev.
Time (s)
Y1 (m)
Y2 (m)
Y3 (m)
Y4 (m)
Y5 (m)
(Y (m))
σ
0.00
0
0
0
0
0
0
0 0.50
1.0
1.4
1.1
1.4
1.5
1.28
.217 0.75
2.6
3.2
2.8
2.5
3.1
2.84
.305 1.00
4.8
4.4
5.1
4.7
4.8
4.76
.251
1.25
8.2
7.9
7.5
8.1
7.4
7.82
.508
QUESTION 7 Using the spreadsheet or plotting program of your choice, plot ¿
vs. t (that is, plot ¿
in the vertical axis and t in the horizontal axis.
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Copyright © 2017 by Thomas Edison State University. All rights reserved.
Copyright © 2017 by Thomas Edison State University. All rights reserved.
CONCLUSION:
In this lab I relearned the calculations for standard deviation. It has been awhile since I have used these calculations. This was the area that I struggled with the most as well. I have always
struggled to remember the formulas and the formula for standard deviation will be a part of that too.
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