The preposition 'up' can be used intransitively:
a. Put your hand up if you know the answer. (toward a higher position)
The prepositional phrase 'up' here functions as complement. It's both syntactically and semantically obligatory.
However, consider these examples from OALD and Macmillan:
- Our profits are quite large when you add them up.
- She got angry and started smashing things up.
- Did you lock the house up before you left?.
- The straps are all tangled up together.
- He spent the evening wrapping up the Christmas presents.
I'm curious about the use of 'up's here. Unlike the first example, these five 'up's are optional, contributing little extra meaning to the whole sentences.
I think we could just omit these 'up' with the meanings unchanged. However, the real question is not all verbs could be paired with an omissible 'up'. In other cases, 'up' is just part of an idiomatic phrasal verb, as in 'let up', 'own up', etc.
It seems to me that these 'up's could be only paired with certain group of verbs when used in such a way.
Is there a common semantic factor licensing this particular use of 'up'?