You Can Make Your Own Scale With a Rubber Band and a Ruler

Did you know you can measure an unknownmass with arubber band? You pretty much can.

The first thing you should do with any project is to play. So, go get a rubber band and play with it. What happens when you stretch it? Perhaps you can feel that it takes a greater force the farther you pull it. Or try this: Hold the rubber band at one end and hang a mass on the other end. Noticehow far down it stretches. What if you put a heavier mass on the rubber band? It stretches farther. So, here is our plan: see if there is a a mathematical relationship between the stretch distance and the stretching force.

Now that you have played with the rubber band, it's time to collect some data. I'm going to start with a very simple rubber band measuring device that I built. Here is what it looks like.

My original plan was to get the bottom ruler aligned so that part of the paper clip at the bottom would line up with the "zero" of that ruler. That didn't work and I was too lazy to fix it. Actually, I think it's better this way. Now I can just hang some known masses on the end of the rubber band and measure the position of the paper clip.

Here is the data I get using different known masses.

Yes, technically I should put the mass on the horizontal axis since it's the independent variable. However, I'm not going to do that. Putting the mass on the vertical axis is going to make the next step easier.

The first important thing about making a graph is that I can see that the mass and the rubber band stretch distance have a linear relationship. That's important. It says that I can make a linear function to fit the data.

The next thing is to actually get an equation that fits this data. The linear fit for this plot gives the following equation.

That's it. Now I can use this rubber-band-and-ruler combo to find some unknown masses. All I need to do is to hang the mass from the rubber band and record the stretch distance (in centimeters). Once I have that value, I put it in as "x" in the equation above to calculate the mass in grams. Boom—I just made scale. From a rubber band. Oh, and a ruler.

Homework

Now for some homework questions.

• Make one of these yourself. You can surely find a rubber band and a ruler (and maybe some paperclips and string). The one thing you might not have is some known masses. If you need to make a substitution, you can use some other standard. What about a bunch of hex nuts of the same size? These are about the same mass so that you could calibrate your rubber band scale in units of nuts instead of grams.
• The rubber band is not a spring. In fact, when you stretch it the rubber band warms up. If you keep it stretched, it cools back down to room temperature. A warm rubber band behaves differently than a cool rubber band. So, how big of an effect does the temperature have on your rubber band scale?
• Suppose you want to measure something much more massive than the stuff you used for your rubber band. How could you use two rubber bands to increase the mass range of your scale?
• Replace your ruler with a new scale that doesn't measure in centimeters, but instead measures grams. Now you can directly measure the mass without any calculations.
• Pick a mass that makes the rubber band stretch some reasonable amount. See if you can convert your scale into a vertical accelerometer. You might need to make a new scale that reads in meters per second squared (the units for acceleration). Take your new accelerometer in a nice elevator. Estimate the acceleration based on the travel time and distance between floors. Now use your new rubber band accelerometer to get a separate value for the acceleration. Are the two values close?

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