Why is it that a transformer rated at 60Hz cannot be operated at 50Hz? Doesn't hysteresis increase with frequency? What is the relationship between frequency rating and the amount of iron required for the core?
The iron in the core defines the volts/Hertz capability of the transformer. You can operate the transformer at 50 Hz, but at a reduced voltage (5/6 of the 60 Hz value). The reason is that transformers are typically designed close to the saturation point in order to conserve iron (typically capable of operating with rated capacity at around 105% V/Hz and with reduced rating and for short times at up to around 110% V/Hz).
If you operate at nominal voltage with reduced frequency, the transformer will be saturated and the increased iron losses will lead to overheating and eventual failure.