I've only taken two semesters of calculus-based physics as part of my general education credits at university. Please keep this in mind when reading this question and framing answers.
Today I observed a gecko on a ceiling and began wondering how it managed to stay put. A bit of googling revealed that the magic is actually van der Waals forces, not an unusually high coefficient of static friction or something.
So I tried to draw a mental free body diagram of a gecko at rest on the ceiling. I drew a downwards arrow representing the gravitational force, and an upwards arrow for the van der Waals force. And then I wondered -- is that it? Is the van der Waals force upwards equal to the downwards force of gravity?
When I studied physics at university, we always drew a normal force perpendicular to the surface the object in question was resting on. We were told this represented the force exerted "upwards" by the surface to counteract gravity. By doing this we could calculate the magnitude of an unknown force by having the normal counteract gravity.
In my gecko situation, my unknown force is acting counter to gravity. Is there a normal force at play here too? Or is the van der Waals force taking its place?