For a few hundredths of a dollar, you can weigh a few thousandths of a gram.
Using simple, inexpensive materials, this balance is sensitive enough to weigh items of only a few milligrams, allowing you to find the approximate masses of objects and substances so light that they show no weight at all on ordinary kitchen or postal scales.
In the use of this balance, we’ll be dealing with mass, in grams. The distinction between weight and mass is critical in physics, but even in scientific settings it’s sometimes common to talk about "weighing" things on an analytical balance, rather than "massing" them. When that happens here, your forgiveness is appreciated!
One 3 inch x 8 inch (8 cm x 20 cm) piece of corrugated cardboard or sturdy matboard (for the base)
Two 1.5-inch (4-cm) pieces 1/2-inch PVC pipe
Hot-glue gun and hot-glue sticks
Four wooden craft sticks
Two mini binder clips
Two 3 x 5 index cards
Matte-finish tape or glue stick
Black pen or fine-point marker (not shown)
Scale or balance accurate to the nearest whole gram
Ten sheets of copy paper
Optional: notepaper and pencil (or similar) to record findings
Cut two slits, each about 1/2 inch (1.5 cm) long, on opposite side walls of the flexible end of the straw. Use a pencil or the straightened end of a paper clip to poke the top flap back into the straw so that it blocks the tube (see photo below). The bottom will form a small trough or pan to hold the object being weighed; the part poked into the tube will prevent that object from sliding down into the straw.
Hold the straw horizontally, with the trough facing upwards, and stick the pin crossways through the straw, about 2 inches (5 cm) away from the non-flexible end. (Be sure to stick the pin through so that it’s nearer the upper edge of the straw!) Then, slide a jumbo paper clip onto the end of the straw near the pin, with the small part of the paper clip inside the straw (see photo below).
Using hot glue, attach one piece of PVC pipe to the cardboard base. The edge of the pipe should be about 1/2 inch (1.5 cm) from the end of the base and centered between the two sides, as shown below.
Hot glue two of your craft sticks to opposite sides of the pipe, with their ends resting on the base (the other two craft sticks will be used in Step 10). When dry, attach a mini binder clip at the center of each craft stick. The bottoms of the binder clips should be about 2 inches (5 cm) above the base, as shown below.
Bend the flexible end of the straw to a roughly 150° angle, with the open trough pointing up. Then suspend the straw so that the pin rests across the handles of the two binder clips (click to enlarge the photos below). The binder-clip handles will act as low-friction bearings for the pin, making it very sensitive to forces producing any rotation of the straw. Carefully set the whole apparatus aside to make your index scale that will display the calibration values.
To make your scale, overlap the two 3 x 5 cards by 3 inches (7.5 cm) and, using tape or a glue stick, attach them together to make a single card that is 3 inches tall x 7 inches wide (7.5 cm x 18 cm).
Hot-glue the 3 x 7 card to the side of the second piece of PVC pipe. Then, position the card-pipe assembly on the base so the swing of the straw will allow calibration marks to be made on the card (see photos below). The straw should be close to the card, but not touching it. Placing the back edge of the pipe approximately 1/2 inch (1.5 cm) from the edge of the base is a good starting point in the process. Note: Do not glue the card-pipe assembly to the base until all you complete the adjustments in Step 8.
Before attaching the card-pipe assembly to the base, you’ll need to align the tip of the straw so that it sits near the top of card. There are several ways to do this. You can slide the paper-clip counterweight in or out of the straw (being sure that the end of the paper clip doesn't hit the table), adjust the bend of the flexible section of the straw, adjust the position of the card-pipe assembly, and/or move the position of the pin on the straw. When the card-pipe assembly is properly positioned, use hot glue to attach it to the cardboard base.
Once the tip of the straw is resting somewhere near the top of the card, and the card-pipe assembly has been glued to the base, use a pen or marker to make a mark on the index-scale card alongside the resting point at the end of the straw. Label this mark with a zero.
To continue calibrating the balance, you’ll need to handle very small pieces of paper, so a pair of tweezers will be handy. To make them, tape the ends of the remaining two craft sticks tightly together, and insert a jumbo paper clip between the sticks, just above the taped joint (see photo below).
Use a scale to weigh a stack of ten identical sheets of paper to determine their mass in grams. Then find the mass of a single sheet by diving the total mass in grams by 10 (the number of sheets). Note your findings.
Measure the length and width of a single sheet in centimeters, and multiply the two measurements together to find the area in square centimeters. Note your findings.
Divide the mass of a single sheet by the area of a single sheet. This will give you the mass, in grams, of a single square centimeter of paper. Note your findings.
Use scissors to cut out one square centimeter of paper.
Use the tweezers to place this square centimeter of paper on the trough end of the balance (it may be easier if you fold or crumple the tiny paper square). Make a mark on the card alongside the resting point of the far end of the straw. Label this mark with the mass of the square centimeter of paper (first mark below zero on the photo below). Repeat the process, using two, three, four, and five square centimeters of paper, or however many are feasible with your balance. (Rather than handling individual squares of paper, you may find it easier to cut strips of paper 1 cm wide and 2, 3, 4, and 5 cm long, folding them before using the tweezers to place in the tip of the straw.) Mark your scale each time, removing any calibration masses and making sure your balance goes back to zero between measurements. You have now calibrated the balance.
To Do and Notice
Place a small object on the balance and use your calibration marks to find its mass. Readings between the marks can be estimated. You might try different spices—a single peppercorn, a rosemary leaf, a red-pepper flake, a mustard or sesame seed, a sea-salt crystal, and so on. Try finding the mass of a dead insect, a small flower petal, a grain of birdseed—anything within the range of your balance. It's up to you!
What’s Going On?
This balance lets you find the approximate masses of things that are too small to even attempt to weigh on an ordinary balance. It also allows you to detect the differences in mass between objects whose masses are in the order of several thousandths of a gram. However, the limitations of the microbalance and its calibration process put its accuracy in question. That is, you may be able to tell that the mass of an object of 4 milligrams is lighter than one of 8 milligrams, but you can’t really be sure how accurate those masses are. Still, you're definitely in the ballpark and, considering the cost, it’s an impressive capability.
Familiarize yourself with the following measurement terms: sensitivity, precision, accuracy, and deviation. See if you can apply them to your balance.
Making and/or using this microbalance can provide unique hands-on insight and experience in the measurement of very small things, but with limitations on precision and accuracy affecting its use as an everyday working tool. There are, however, relatively inexpensive digital balances with exceptional capabilities currently available, which provide a very useful working tool for many aspects of science education.
A similar balance using different materials appeared as part of the original PSSC Physics text created by MIT’s Physical Science Study Committee in the 1960s, and is the inspiration for the version presented here.