I have a logical misconception about resultant force/potential energy that has been bugging me for a while.
Consider lifting a book with a constant force against gravity. I think I understand that when we consider the system as only the book, no resultant force acts on the book and thus no resultant work is done on the book (no change in KE). However, when we consider the system as the book+earth we can begin to include potential energy gained in the system by lifting (with the gravity forces being internal).
Here is my issue though: when providing a single external force (say equal to the weight of the book) on the book (in the book+earth system), does this force separate the two bodies or does it simply accelerate the centre of mass of the system? I read another answer on the site that said, in fact, two equal and opposite forces are required to separate two bodies and increase the potential energy (it is just that, as W = F.x, the displacement of the earth is negligible and we consider the work done to be zero). The precise quote was:
"The only external force is F and let this force have the same magnitude as the weight of the body. That single force F cannot move the body further away from the Earth. To separate the body and the Earth two forces of magnitude F but opposite in direction must act on the body and the Earth."
This seems to make sense to me as, when we lift a book, we are actually providing two forces, the weight of the book is transferred through our body and this provides the increased opposite contact force to push against the earth (though this may be incorrect).
However, if you always need two equal and opposite forces on each body in the system to separate them, how does a rocket leave the earth (from the ground and once in space)? It does not "push" against the earth yet in my mind I consider its thrust to be an single external force on the rocket+earth system which, by the previous statement, should not separate the two bodies in the system, but rather just accelerate the entire earth+body system.
Where is my logical misunderstanding? My apologies if this is too long-winded but thanks for your time!