Force of gravity on magnetically levitating object?

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KidSix
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I just had a question regarding magnetic levitation..
If an object were to have a great enough magnetic force (via magnets of unequal strengths) to cause an object to be lifted while being held together by something that isn't rigid, like string, would putting force on the top object project force downward?
As in if I had higher grade magnets on the bottom object, would pressing down on the top object make the bottom object more difficult to lift?
Apologies if this is a bit vague or obvious. I have little experience with magnets.
 
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hi there
welcome to Physics Forum

just having a little difficulty visioning what you are trying to do

how about drawing and posting a pic of your setup :)

Dave