Some years ago I helped a talented young boy do a project for his elementary school science fair. He wanted to build an electric motor and “see how fast it would go with different batteries.” After building the usual wobbly paper-clip-and-toothpick type motor that needed careful jiggling to get it to move, he suggested using Lego Technics, with which he had hours of experience building cool vehicles and devices with winches and little pneumatic drives. Lego blocks are solid and precise, the fluted axles spin true and fast in their plastic bearings with a little oil, and with an 8-32 steel screw wrapped with wire and mounted through a Lego T-piece slipped onto the axle, 2 round refrigerator magnets and 2 brushes cut from a flat bronze spring, the result was a high quality DC motor. To measure “how fast it would go,” I had him tie a small fishing weight to one end of a string and tie the other end onto the axle. He started a stopwatch upon connecting the D-cell battery, stopping it when all the string wound up on the axle and the weight hit the top. Because of the small diameter of the axle and the long string (about 15 or 20 inches), it took a while to raise the weight so his time measurements were pretty accurate. I came across a photocopy of his hand-drawn chart yesterday, and have replotted and attached it. The y axis is the speed or, more precisely, the length of string in inches divided by the number of seconds it took the weight to travel from bottom to top. He was able to present “how fast it would go with different batteries” and won a ribbon from the judges (teachers). He didn’t realize that, because of how I had him measure “speed”, he was actually measuring power; indeed horsepower was originally measured by seeing how long it took a horse to raise a known weight a known distance. I naively expected to see something like a quadratic curve, since we are accustomed to thinking that P is proportional to V^2 in common situations. I was surprised to see that the power of this motor depends linearly on voltage! I've thought about why this might be, but I’m curious to hear from any experts out there who can explain it.