I'm a bit hung up on the idea of forces at either end of a spring being equal, surely by extending the spring you are moving its centre of mass and hence applying a resultant force on it. I get it when the spring is not extending or has already extended, but while it is extending surely the force pulling the molecules apart must be greater than the force pulling them back together and hence there should be a resultant force on each molecule. And then this should accumulate throughout the spring as the force pulling on each molecule gets smaller such that though the fixed end of the spring is in equilibrium, the forces acting on it are less than the force pulling at the other end of the spring.
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I'm a bit hung up on the idea of forces at either end of a spring being equal, surely by extending the spring you are moving its centre of mass and hence applying a resultant force on it.
Yes.
If the spring is being extended then almost by definition its Centre of Mass (in the case of a massive spring) is accelerating. Being extended here means that one end moves and the other not or than one end moves faster than the other.
This means that acc. Newton's Second Law there must be a net force acting on the spring. This in turn means the forces acting on both ends cannot be the same.
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$\begingroup$ The operative word here is massive. The majority of examples consider massless springs, for which the forces at both ends must be the same, or the spring would get infinite acceleration. Springs are often much lower mass than the masses they affect, so the simplification is reasonably (usually). $\endgroup$ Commented Mar 13, 2021 at 18:29
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$\begingroup$ @KristofferSjöö I've further emphasised that. $\endgroup$– GertCommented Mar 13, 2021 at 18:31
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$\begingroup$ Ok thank you, so it sounds like I'm not wrong but just focusing too much on the laws of motion to understand something unrelated to that $\endgroup$– edwardkCommented Mar 14, 2021 at 17:32
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The forces are equal at the ends because if they were not one end or the other would move. If you replace the spring with an elastic string , it is easier to see that the tension in the string is the same all over. And also in the spring (which is a hard kind of curly string) the tension (force) is equal along the length of the spring.
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$\begingroup$ You're assuming no part of the spring or string is accelerating. When the spring begins to stretch, it must accelerate. In introductory physics classes, we make the assumption that this small difference in forces is much smaller than the other forces being considered. See the answer by @Gert $\endgroup$– Bill NCommented Mar 13, 2021 at 15:41
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$\begingroup$ @BillN It seems to me AB is assuming no motion, thereby answering a different question? $\endgroup$– GertCommented Mar 13, 2021 at 15:51
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$\begingroup$ For a long spring that weighs a lot compared to the load on its end then initially the coils will stretch more at the load end because the mass of the spring provides resistance and there will briefly be a greater force on the load end. Of course if we had a spring 1km long this would be a lot more obvious ! $\endgroup$– user291777Commented Mar 13, 2021 at 20:16