Expressing experimental error. In an experiment to measure the acceleration of gravity at the surface of the earth in the DFW Metroplex, 9.85 m/s2 (E1) and 9.73 m/s2 (E2) are obtained. The accepted local value of g = 9.80 m/s2 (A) for DFW.
What is the % difference for the measurements?
What is the % error of the first measurement E1?
What is the % error of the second measurement E2?
100(9.85 -9.73)/ (9.85+9.73)/2 = 12/9.79 = 1.23 %
100(9.85-9.80) / 9.80 = 0.51 %
100(9.73-9.80)/9.80 = -0.71 %
Well, well, well, looks like we've got some experimental error to discuss! Let's break it down with a touch of humor, shall we?
To calculate the percentage difference between two measurements, we use the formula: % difference = |(E1 - E2) / A| * 100%. Plugging in our values, we get: % difference = |(9.85 - 9.73) / 9.80| * 100%.
Now for some math magic: |0.12 / 9.80| equals around 0.01224. When we multiply that by 100% to add some drama, we get a sizzling % difference of approximately 1.22%, give or take a few clown giggles.
Moving on, let's find out the % error of the first measurement, E1. To do so, we use the formula: % error = |(E1 - A) / A| * 100%. Substituting in the values, we find % error = |(9.85 - 9.80) / 9.80| * 100%.
Now brace yourself for this one: |0.05 / 9.80| equals about 0.00510. When we slap a 100% on that bad boy, we get a % error of approximately 0.51%, give or take a few wacky honks.
Lastly, the % error of the second measurement, E2. Using the same formula as before, we get % error = |(9.73 - 9.80) / 9.80| * 100%.
Prepare yourself for the grand finale: |(-0.07 / 9.80)| equals around 0.00714. And when we multiply that by 100%, we get a % error of approximately 0.71%, give or take a few circus tricks.
There you have it, folks! The % difference between the measurements, and the % errors for both E1 and E2. Remember, even in experimental error, there's always room for some laughter!
To calculate the percent difference, percent error of the first measurement (E1), and percent error of the second measurement (E2), we can use the following formulas:
Percent Difference = |(E2 - E1) / ((E1 + E2) / 2)| * 100
Percent Error = |(Experimental Value - Accepted Value) / Accepted Value| * 100
Given values:
E1 = 9.85 m/s^2
E2 = 9.73 m/s^2
A = 9.80 m/s^2
1. Calculate the percent difference:
Percent Difference = |(9.73 - 9.85) / ((9.85 + 9.73) / 2)| * 100
= |-0.12 / (19.58 / 2)| * 100
= |-0.12 / 9.79| * 100
= 1.23%
So, the percent difference between the two measurements is 1.23%.
2. Calculate the percent error of the first measurement (E1):
Percent Error of E1 = |(9.85 - 9.80) / 9.80| * 100
= |0.05 / 9.80| * 100
= 0.51%
So, the percent error of the first measurement (E1) is 0.51%.
3. Calculate the percent error of the second measurement (E2):
Percent Error of E2 = |(9.73 - 9.80) / 9.80| * 100
= |-0.07 / 9.80| * 100
= 0.71%
So, the percent error of the second measurement (E2) is 0.71%.
To calculate the percent difference for the measurements, follow these steps:
Step 1: Calculate the absolute difference between the two measurements:
Absolute Difference = |E1 - E2|
Step 2: Calculate the average of the two measurements:
Average = (E1 + E2) / 2
Step 3: Calculate the percent difference:
Percent Difference = (Absolute Difference / Average) * 100
Let's calculate it:
Absolute Difference = |9.85 m/s^2 - 9.73 m/s^2| = 0.12 m/s^2
Average = (9.85 m/s^2 + 9.73 m/s^2) / 2 = 9.79 m/s^2
Percent Difference = (0.12 m/s^2 / 9.79 m/s^2) * 100 = 1.23%
So, the percent difference for the measurements is 1.23%.
To calculate the percent error for each measurement, follow these steps:
Step 1: Calculate the absolute error for each measurement:
Absolute Error = |Measured Value - Accepted Value|
Step 2: Calculate the percent error:
Percent Error = (Absolute Error / Accepted Value) * 100
Let's calculate it for E1:
Absolute Error E1 = |9.85 m/s^2 - 9.80 m/s^2| = 0.05 m/s^2
Percent Error E1 = (0.05 m/s^2 / 9.80 m/s^2) * 100 = 0.51%
And now let's calculate it for E2:
Absolute Error E2 = |9.73 m/s^2 - 9.80 m/s^2| = 0.07 m/s^2
Percent Error E2 = (0.07 m/s^2 / 9.80 m/s^2) * 100 = 0.71%
So, the percent error for E1 is 0.51% and for E2 is 0.71%.