Geometry While You Wait

Have you ever waited at the gas pump while filling your gas tank? Did you pass the time by fiddling with the gas-tank filler door? You may have noticed that the door was controlled by a spring, so that if you put it in the fully open position, if stayed open. If you closed it, it stayed closed. In some other positions, it either closed or opened. How convenient!

The next step in your thinking may have been to locate the expected spring. Perhaps you wondered how the door assembly was engineered, and if the engineering has anything to do with highschool geometry and algebra.

Being an algebra and geometry teacher, the author wondered the same thing and hoped that his students had enough interest in the world around them to wonder about the geometry and physics of the gas-tank door. Why just wonder? Why not investigate?

The gas-tank filler door pictured in Figure 1 can be found on a 1989 Chevrolet Caprice and other GM cars. In the drawing, the gas-tank door is in the open position. You can see the gas-tank cap, the door hinges, and the spring.