If it's the correct belt, you should have plenty of adjustment. "correct" belt meaning not mispackaged, and for the correct model and serial number for your tractor (if there is any serial number break and IF there's any differences between the 8560 cabin, Narrow, and ROPS models).
Shorter belt is simply a "band-aid". Might work-for a while-until the root problem shows it's ugly head, which normally happens at the worst possible time,..out in a field a few miles from any road, the hottest or coldest day of the year (usually the hottest in this area, contributing to overheat and/or engine failure).
I question why the alternator belt was "thrown" to begin with. Rare, outside of debris and rodent intervention-and I think there may be more to this issue, potentially also causing the "slippage" issue. Check your water pump. Have seen a few -40 series tractors with failing water pumps, causes the pulley to be "cocked", contributing to belt wear and/or failure. We've got a few of them running around with 6000+ hours last time I saw them, and they've still got original belts on them. Original everything actually other than fluids and filters-and on one of them, a/c evaporator, condenser, hoses, and compressor.
Also look into the alternator itself, make sure it turns freely. Another rare failure point but it can happen. Tight? Bearings and/or debris inside of it.
Fought with an MX5100 for the past 2-3 weeks...owner says it kept "eating" fan belts. Has put 13 belts on it since new, has 245 hours on it and was sold in 2013 January. I get tractor, inspect, find nothing wrong. Test run engine about 9 hours, nary a problem. Guy gets it back, sits overnight, gets on it next morning to feed the cows, eats a belt. Bring it back. Repeat. Talk about frustrating, both to owner and tech. So I had an idea. I threw another belt on it and left some well hidden rodent bait under the hood. Told him come get it. He picks it up, drives it home, calls me next morning and says he's found dead rats. I tell him don't move anything let me come to your barn and inspect. NO lights in the barn (of course), dark as could be, found gnaw marks on the belt and upper radiator hose, but NO gnawing on the wiring, thank goodness. He would never have believed me otherwise especially considering that he's also got a larger JD and a small MF and nothing on them was touched. Maybe the little rodents just think that orange tractor parts taste better, I don't know. They're funny like that.
I gave him a couple of my barn cats and some food, maybe they'll keep the rodents run off.
