Question

what does it mean for a physical system to be in Static Equilibrium? Under what conditions is a physical system in Static Equilibrium? Provide examples of such systems.

Answer 1

You would only define "static" equilibrium to distinguish it from "dynamic" equilibrium, and dynamic equilibrium is an equilibrium that results from dynamics that cancel out -- that is, from two ongoing processes that cancel each others effects.

For example, consider your bank balance. Let us say at the end of every month it is $5000. So that's an "equilibrium," right? That number isn't changing. But there are two ways this could be true. First, it could be you make no deposits and write no checks, so there are no processes acting to change this number. That would be a "static" equilibrium.

But on the other hand, it could be your deposits always exactly equal your checks. Maybe you write $2000 of checks every month, but you also make $2000 of deposits. This would be "dynamic" equlibrium: the number doesn't change because the processes that act to change it exactly cancel each other's effects.

More physical examples: if a tank full of water always has the same level ("in equilibrium") that could be because no water goes in or out, or it could be because the same amount goes in as goes out. If the temperature of a solid does not change, it could be because it is perfectly insulated -- no heat goes in or out -- or it could be that exactly the same amount of heat flows in as flows out. And so on.