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Suppose we have two things stuck together with a glue which takes anything above $50 \,\text{N}$ of force to get it to get rid of the sticking force and anything below $50 \,\text{N}$ making no impact on it.

What would happen if we apply $50 \,\text{N}$ of force to it? Would it be stuck together or would it be separated. I do understand that the forces cancel out as they are in opposite directions but what would happen?

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Your problem may seem as a genuine mechanics problem at first, but it's not. We could formulate it in equivalent ways, such as "what happens if a tub can only be filled with 20 litres of water, not one more drop". Problems in Physics are hardly ever so precise, and the reality is there is no such "perfect" glue as the one you are talking about. Its "force capacity" would be a step function, as you would need anything over 50N to separate the glued objects, and anything below it would result in nothing at all happening. When modeling these kinds of systems, your functions will be smoother than a step function, and there will be some uncertainty as to which the limit is, you won't be able to pinpoint it at exactly 50N.

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