Coke contains phosphoric acid, which is why it cleans metal and acts as a rust remover - most commercial rust converters are based on this substance that changes rust (ferrous oxide) to ferrous phosphate.
It is also an excellent reason not to drink the stuff. As for McDonalds, well..........
When us Brits visit Europe and talk to the natives, they cannot understand why we feed our kids on such crap instead of the same diet we have!
Cheaper way to clean copper or brass is to soak it in vinegar or lemon juice.