Consider the following sentences
- He pushed open the door.
- He pushed the door open.
Are the two ‘pushed open’ phrasal verbs and have ‘the door’ as their objects?
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Yes, push open is a phrasal verb and in both examples in the question, the door is the direct object, not an object of a preposition. The test mentioned in Jlawler's comment is indeed an easy way to identify the particle of phrasal verbs. One substitutes a definite pronoun in for the NP. If the pronoun must precede the particle, one knows that it is indeed a particle and not a preposition. Here are more examples of how the test works:
a. He walked over the mess. b. He walked over it. c. *He walked it over. - "over" in this case is a preposition, not a particle a. We talked over the issue. b. *We talked over it. c. We talked it over. - "over" in this case is a particle, not a preposition
These examples demonstrate that over in walk over is a preposition, and over in talk over is a particle, which means talk over is a phrasal verb. The pronoun diagnostic with further examples is used in the Wikipedia article on phrasal verbs here: https://en.wikipedia.org/wiki/Phrasal_verb.
A related question concerns the phenomenon of shifting that occurs with phrasal verbs. What is it about the syntactic structure that allows shifting to occur with phrasal verbs? The relevant difference across the particle of phrasal verbs and standard prepositions is that the particle and the NP object are sister constituents in the structure, whereas when a preposition is present, the NP is the dependent of the preposition. In other words, the structure is flat with phrasal verbs, whereas it is more layered when the preposition is present. Shifting is discussed in Wikipedia here: https://en.wikipedia.org/wiki/Shifting_%28linguistics%29. The article includes examples involving phrasal verbs.