Using a Triple-beam Balance With Uncertainty Analysis

This instructable will walk you through how to make an accurate measurement with a triple-beam balance, as well as teach you how to account for measurement error with an uncertainty analysis.
Time to complete: 15-20 minutes

Important parts:
        pan
        sliding masses
        pointer
        the scale
The pan is the silver tray on which you will place your test specimen. There are three sliding masses on a triple beam balance. The largest mass represents 100 grams, the middle mass represents 10 grams, and the smallest represents 1 gram. These masses are slid along differing beams to try and determine the mass of the specimen in the pan. Next is the pointer, The pointer points towards a scale and helps you determine whenever you have the correct mass.  The scale is what the pointer uses to determine when the masses are equal. Once the pointer is directed at the 0 on the scale then your masses are equal.

Place your triple beam balance on a level surface and make sure that all of your sliding masses are on zero.

In order to reduce error in your experiment you will need to zero your triple beam balance.To do this you will want to make sure that nothing is on the pan and that all your masses are on zero. Then you will adjust a knob under the pan until the pointer is directed at zero. Image two shows a closer view of the pointer and scale.

Then you will choose a test specimen and place it on the pan.

First you start with the 100 gram sliding mass, then you move it along its beam from notch to notch until the pointer moves to below the zero on the scale. Once this happens move the slider back to the previous notch. For example if you moved the mass to the 600 gram slot and the pointer moved below zero, then you would move the 100 gram slider back to the 500 gram notch.

Repeat step five with the ten gram slider

The scale for the 1 gram slider goes from 0 to 9.9. There are also nine increments between each whole number that represent .1 grams. There are no notches for the 1 gram slider, so you will just push the slider until you get the pointer to point directly at the zero on the scale. To get the most precise measurement possible you will want to count the increments past the nearest whole number. If your 1 gram mass is pointing between two of the increments then you can add a value of .05 to your measurement. This is called the one half least squares regression method.

Once your sliding masses are in position then you will sum each of the numbers together. This will be the mass of your specimen. In the figure are the results of my measurements for an apple.

Repeat steps 5-8 with your specimen and record each of the results. The more trials you record the more accurate your measurement will be.

After collecting your data, you find the average of the measurements. Use the formula in the picture. Where Xn is your last measurement, and you add every measurement up to that point. N is the number of measurements. The value I got for my measurements is 181.

It is almost impossible to make a perfect measurement. In order to combat this we will do an uncertainty analysis to ensure that we get a range of values that include the true mass of the specimen. In order to do this we will need the standard deviation of our sample and we will need a t-value that corresponds to our confidence interval.

To calculate the standard deviation, often referred to as s, we will use the formula in the picture. My value for standard deviation was 1.36.

Level of confidence refers to the probability that the true value will be contained within the span of your uncertainty analysis. The accepted level of confidence in engineering is 95%, this is the sixth column of the table. The df value on the left hand side of the table is equal to N-1. In my experiment I had 5 trials, so my df value is 4. We will also use the two-tail portion of the table so my t-value is 2.132.

We will use the formula in the picture. my value for uncertainty was 1.30.

We will use the formula in the picture . so my measurement would have been 181±1.30.