We have a spring of spring constant $k$. If we apply force $F$ on the spring,it elongates. The restoring of by hooked law $kx$ also develops on spring. Then a time will come when $kx=F$ i.e equilibrium position is obtained. But according to Newtons 3rd law, if we apply force $F$ on th3 spring,the spring will also pull by the same force $F$ on the contact point of us and the spring. And since our force $F$ is constant,the force by which the spring pulls us(the restoring force) is also constant. But again by hookes law,restoring force is a variable which changes with extension of spring. So where is the apparent fallacy we are making?
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The thing that matters is that you think of the spring as a uniform and unified object but it's not. Every part of it does not behave as a single object and when it does( the equilibrium position) we can apply Newton's third rule easily and get the required result.
When we stretch it the part of the spring has to apply a force on the previous part and so on.that part is in equilibrium and when all parts are in equilibrium it's F=Kx.
Curious
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So where is the apparent fallacy we are making?
The fallacy is thinking that you can apply an arbitrary force on an ideal spring at any length. Newton’s 3rd law means that the force applied on the spring is equal and opposite the force the spring applies. Hooke’s law means that the force the ideal spring applies is proportional to the extension. Taken together they imply that it is possible to apply a given force on an ideal spring only if the spring is at the corresponding extension.
Dale
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