what does potential energy depend on? is potential energy connected to thermal energy?

Brief Explanations:

Potential energy can be gravitational, elastic etc. Gravitational potential energy depends on mass, height and gravitational - acceleration ($U = mgh$). Elastic potential energy depends on the spring - constant and the displacement from the equilibrium position ($U=\frac{1}{2}kx^{2}$). In general, it depends on the position or configuration of the system and the relevant physical properties like mass, spring - constant etc.

Answer:

It depends on the type of potential energy. For gravitational potential energy, it depends on mass, height, and gravitational acceleration. For elastic potential energy, it depends on the spring - constant and displacement from equilibrium.