If we compare it to a rope pulled by two equal forces in each end. The net forces would be zero and you would have static equilibrium, but the rope would still break if pulled hard enough.
Additionally, wouldn’t a metal ball uniformly surrounded by powerful magnets be pulled apart as well?
I am not sure why I can’t wrap my head around this, when it comes to the center of the earth.
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The big difference is easier to understand if you simplify a little. Tension happens when two *different parts* of something are being pulled in different net directions. If we imagine only one “part” (eg, atom) of the body, its net force is zero. The part next to it also has a net force of zero. They agree on which direction to move (nowhere) and thus don’t pull against each other and experience tension.
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