Funnily enough, there are some applications for converting mechanics problems to analogous electricity problems to leverage circuit simulation software such as PSPICE to help solve things like transcendental equations.
Yes, but the mapping doesn't change the relationship between the units of measure, which is the actual meaning as far as the type system is concerned. It's just a change of names.
Sure, I wasn't meaning to detract from the comment above, just to point out what I thought was an interesting related fact.