Consider a piano sitting in a stationary freight elevator. Draw a force diagram

Question

Consider a piano sitting in a stationary freight elevator.  Draw a force diagram for the piano alone and for the elevator alone.  For all the forces in the two force diagrams, identify and list the action-reaction pairs. (Hint: Think carefully!  There are some forces here that are equal and opposite, but are NOT action-reaction pairs!)

For the piano its just the gravitational force down and normal force up correct? Then for the elevator, a gravitational force down and a tension force up (something must be holding it in place)? For the action-reaction pairs, I'm not really sure what to do here since the elevator is suspended (ie- no normal force up on the elevator). I know its about the interaction of the 2 objects with each other, but I'm not quite sure how it fits together. Help me out!

Explanation / Answer

Fg for the piano alone points vertically down, Fn points vertically up, and they are an action/ reaction pair. They will be equal at (m piano) x g.

When the piano is in the elevator, its Fg will still be pointing down, and Fn from the elevator floor points up, and are an action/ reaction pair. They will be (m piano) x g, and equal, as above.
But then Fg for both combined acts down, and Fn for the combined pair points up, and are another separate action/ reaction pair. They are equal and are (m lift + m piano) x g.

There's no Ff acting that needs to be considered.

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