Where something is specifically intended to be loaded in normal use, 'unloaded' is acceptable to mean 'not loaded' / 'without load' in this sort of context (as it will not be mistaken for something from which the load has been removed, as in "the unloaded lorry drove out of the gate").

'unladen' completely removes any ambiguity — but is more commonly associated with transportation (lorries, boats, etc.)

And of course, as others have said, there's no real reason why one couldn't also say 'empty'

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