A Grain of Rice
In an effort to apply what we learned about measurements and uncertainty, we, in our Physics lab class, decided to measure grains of rice using two different measuring tools, namely the vernier caliper and the micrometer caliper.
Measuring Devices
Before I begin, let me discuss the tools we used to take the measurements. The vernier caliper is a measuring device that allows one to take the length of objects. It is specifically useful to take the diameters of round objects as it has provisions and clamps to both accurately measure inner and outer diameters. Some vernier callipers also allow depth to be measured. A vernier caliper comes in two parts, the main scale (MS) and the fractional scale (FS). The MS works just as any ruler would, with the 0 mark on the FS being the mark you base your reading off of. Like a ruler, you're measurement won't lie exactly on one number on the MS – this is where the FS comes in. The FS is used to increase the precision of the measurement. There are many lines on the FS, each corresponding to a different fractional unit (in our 1 mm vernier caliper, the FS came in gradations of 0.02 mm). You have to find the first line on the FS that matches with a line on the MS. That is your FS reading. To get your total measurement, you add your MS reading with your FS reading.
The micrometer caliper works the same way, except that it has a circular MS and FS and its FS has gradations of 0.01 mm as the MS has gradations of 0.5 mm. You put the object in between the appropriate section and turn the dial until you hear a click that signifies that the caliper is tightened. Once this happens, you read the mark on the MS, and then you check the number on the FS that "hits" the marking line. Adding these two values up, you get your main reading.
One thing of note is that you have to make sure your instruments do not have any zero error. This is the error caused by an uncalibrated caliper and can lead to systematic error. To check for zero error, you put your caliper all the way to its lowest measurement and see if the 0 on the MS aligns with the 0 on the FS. If it does, then you are good. If it does not, the take note of how much it differs and account for this in recording your measurements. Luckily for us, there was no zero error for either of our instruments.
Measuring Rice
Actually measuring rice was a bit tricky. For the vernier caliper, it took us a while before we managed to get the rice properly between the "teeth" of the vernier caliper. It was difficult to ensure that what we were trying to measure was the entire length of the rice grain. It proved even more so with the micrometer caliper as we had to place the rice in between a rather thick compression part. Nevertheless, after a few tries, we managed to get a hang of it and proceed with our measurements.
The following is a link to our measurements and the subsequent sub results to the questions:
https://docs.google.com/spreadsheets/d/1DsqfxJWet7PCCeKjzrh4j0L5fUz7opAenDcDDEFlfLk/edit?usp=sharing
*note: the measurements listed do not show the proper significant digits of 3 for all readings as a result of limitations on excel
1. What is the length of a rice grain?
The length of a rice grain varied in between a range of measurements from 6.33 to 8.00 mm from a total of 110 different measurements of different samples. The uncertainty of the measurements varied between the two instruments used, with ±0.01 being the uncertainty of the vernier caliper and ±0.005 being the uncertainty for the micrometer caliper. This answer was obtained through direct measurement of said samples. The validity of the measured values is known to be true as it was observed firsthand by the researchers.
2. What is the average length of a rice grain?
The average length of a rice grain is 7.14±0.86 mm. This answer was obtained through the formula
AVERAGE = (SUM OF ALL MEASUREMENTS)/(TOTAL NUMBER OF MEASUREMENTS)
The uncertainty for this was taken as the maximum difference between a measured value and the mean of the set of data values.
It is known to be true because it follows a certain formula that utilises the measured data to produce its result.
3. What is the acceptable range for the length of a grain of rice?
The acceptable range for the length of a grain of rice, found through the formula Q=μ±σ, is 7.14±0.32 mm. The mean is taken as the average of the lengths of the grains of rice. The standard deviation, within which 67% of all measurements are found in, is taken through an equation utilising excel.
The precision can be commented on by comparing this to the known value of the length of a grain of this particular type of rice, l=7.09±0.36 mm taken from Hobson, Carter IMTC 2007 paper. As you can see, the values found are close to the known value, making the measurements accurate, the value for acceptable range being the most accurate as it encapsulates the known value of the actual measurement. It should also be noted that the questions are being asked in increasing orders of approximation which results in asking for an increasing level of precision.
This activity allowed me to apply what I had learned on uncertainty and measurement into an actual process.
