As an engineer you quickly learn to appreciate how any dynamic system is just a series of energy connections. For example: any driver knows what the brake pedal does; a technician understands how it works, with the caliper pressing the pads against the disc; an engineer, however, understands that deceleration is nothing but a conversion of energy: from kinetic to heat. The car will lose velocity by the same rate as the brakes heat up. Power simply has to go somewhere.
As an engineer I'va always been confused about potential energies though.
I don't know what flavor of engineering you are in. I am in between mechanical and electrical, so I try to see any potential energy as a the behavior of a capacitor or a spring (the two are equivalent). Gravity is like a constant force spring pulling you towards the center of the planet. Heating up and cooling down a pizza stone is like charging and discharging a capacitor. Bond graphs helped me understand these equivalences:
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