Supposing you were in space in a weightless environment, would it require a force to set an object in motion

Yes.  If your smartphone was floating in front of your face, motionless
relative to you, it would require a force to start it moving toward you or
away from you. 

But there's no minimum force required.  ANY force, no matter how small,
even smaller than the smallest force that you can imagine, would set it in
motion. 

The thing is, though, that the smaller the force acting on it, the smaller
acceleration it would get, and the slower it would move away from where
it is. 

So if, say, you wanted to send it across the crew compartment and over
to your sleeping bag on the wall, and you had all day to watch it mope
along over there, you might breathe on it, and the force of your breath
would set it in slow motion in that direction.  But if you wanted to throw it
at your crewmate, you'd need to give it more force.
  

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