Question about copyright and fair use of music?

I’m working on a project that I want to include copy written music. This project is being done by me on my free time, and will not be distributed for profit. I am willing to give credit where credit is due, but I’m not going to pay royalties on something I’m going to be distributing for free.

I was of the understanding that if you used only a certain part of a song (60 seconds or less, or maybe it was 40 seconds or less) then you can claim fair use and not have to pay royalties. Does anyone know if this is correct? And does anyone know whats the most I could use of a song and not have to pay royalties? I live in Canada if that makes a difference.