When teaching implicit differentiation in freshman calculus I lack good examples which might help students relate the theory to applications in other sciences.

So I'm looking for (relatively simple) examples from physics/engineering/life science/economics etc. of tow quantities $x,y$ that depend on each other in such a way, that neither $x$ is a function of $y$, nor $y$ is a function of $x$. In other words: $x,y$ should fulfil some equation such that there exists an $x$ value for which the equation has at least two solutions in $y$ and vice versa.

Equations are great, but if you have some examples where the relation between $x$ and $y$ is not easily expressed by an equation, but instead by a graph or some other data that is also fine.

My students are mainly first year engineers.