Question

those MIT problem sets are challenging; they lecture you on basic things, and then have you prove something really hard like Newton's second law of thermodynamics. How do I approach those kinds of problems?

Answer 1

you mean cooling laws?

Answer 2

I haven't looked at the Mechanics part, since I took AP in high school, so I just skipped to E&M.
I know what you mean though, those problem sets are not to be taken lightly. You need to think "outside the box" at times (though that phrase has been used far too often). Draw on every trick in math and science you know is the only general advice I can give...