It's just a bit of intermezzo but... The words let's go and a let us go has different connotation, but the same wordings. I'm always quite confused on how they are used, which part is right and wrong. I don't know if it's just me however. We definitely can use "let's go" whenever we want to go somewhere, but it's kinda weird to use "let us go" on the same condition. What do you think about this problem?
My two cents: The contraction in "let's" takes emphasis away from the "us" and it ends up sounding less like a plea or a demand for release (or a mixture of both) than "let us go". P.S. One can still use "let us go" casually even where there's no constraint implied, but it does end up sounding overly formal, especially in contrast to the other usage (or probably because the other form is always in the back of one's mind).