I have an 05 R50 and last week I noticed a short "chirp" from the serpentine belt when cold starting, this went on for about a week until the belt came off while driving. The belt was over due and should have been replaced.
Today I replaced the serpentine belt and the cold start "chirp" is still present. Prior to installing the new belt I am able to turn the alternator, tension pully, water pump and AC pully freely with no restrictions.
Any idea why the "chirp" is still present ??? I'm concerned that I'll throw the new belt and risk being stranded.
Do you think belt dressing would be helpful?

 

New belt should do the trick. Might check the tensioner to make sure it's not worn out. You can also try some 'belt dressing' on the belt to help it stick a bit better. A new belt shouldn't chirp though (as you know.)
Did the new belt break, or just come off. If it didn't break, definitely check the tensioner, and the alignment of all the pulleys. It definitely shouldn't just come off.

 

The new belt did not break, but chirps for about 2-3 seconds when its cold started.
When I got the car home when the previous belt failed on the road the belt was no where to be found, so I'm not sure if it broke or fell off due to being over streched. I'm going to search the area where it failed and see if I can locate the belt.
This week sometime I'm going to have my car looked at Greasy Garage a local MINI mechanic and get his feedback.
I was very suprised how easy it was to replace the belt, once I removed the inner wheel well.