I had to do an experiment where a tiny steel ball was measured using a micrometer. There was then a series of calculations that needed to be completed and then a percent error had to be calculated. I think that my data may be incorrect or maybe I am just not doing the calculations correctly but my percent error keeps coming out to be very high.
To start off I had to use the micrometer to find the diameter D(mm) of the steel ball. 5 trials were completed. For the first trial I got 15.90 mm. The volume V=1/6(pi)D^3 had to be calculated next so to do this I plugged 15.9 into the equation 1/6(3.14)(15.90^3) and got 2019. For each trial I plugged my D value into the equation and then to calculate the average Volume I added all the numbers up and divided by 5.
So far before I continue can you please tell me if I did this correctly. Thank you for your help!!
1. Find the average magnitude of diameter
(D1+D2+D3+D4+D5)/5 ={D}
2. ΔD1 =|{D}-D1|
ΔD2=|{D}-D2|
…
ΔD5 =|{D}-D5|
Average absolute error is
{ΔD}= (ΔD1+,,,+ ΔD5)/5.
3. The relative error is {ΔD}/{D}
4. Since V~D³ the error of your result = 3• {ΔD}/{D}.
If you want it in %, multiply by 100.
It seems like you have made a mistake in your calculation of the volume. The correct formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius.
To calculate the average volume, you need to find the volume for each trial, sum them up, and then divide by the number of trials, which in your case is 5.
Let's go through the calculations step by step to ensure accuracy:
1. Trial 1: Diameter (D) = 15.90 mm
- Radius (r) = D/2 = 15.90/2 = 7.95 mm
- Volume (V) = (4/3)πr^3 = (4/3)π(7.95^3) ≈ 1678.30 mm^3
2. Trial 2: Repeat the same steps for each trial using the respective diameter.
3. Repeat the above steps for Trials 3, 4, and 5.
4. Average Volume: Add up the volumes for all 5 trials, then divide by 5. Let's say the volumes for the other trials are 1800, 1900, 1700, and 1750 mm^3, respectively.
- Sum of volumes = 1678.30 + 1800 + 1900 + 1700 + 1750 = 8828.30 mm^3
- Average Volume = Sum of volumes / Number of trials = 8828.30 / 5 ≈ 1765.66 mm^3
Now, to calculate the percentage error, you'll need to know the accepted or theoretical value for the volume. Without the theoretical value, it won't be possible to calculate the percent error accurately.
The formula for percentage error is:
Percentage Error = | (Theoretical Value - Experimental Value) / Theoretical Value | * 100%
To find the percentage error, you need to have the correct theoretical value to compare it with the average experimental value.