# Why is the spring force equal to the external force?

So we are studying about springs, as of now, the assumption is that they are massless.

My teacher told me that when we extend a spring, or compress it, there is a force called the spring force which tries to reform the spring back it its original form. This force acts inwards and outwards respectively.

He also told us that the magnitude of this force is equal to the force we apply.

What I want to ask is why it this force always equal to the force we compress the spring with? Wouldn't the equality suggest that the spring will still remain deformed? If equal amount of force is coming from both sides, and if the spring is deformed then wouldnt it remain deformed?

Shouldnt the spring force be slightly greater than the external force to reform the spring?

• The spring only reforms if the applied forces are removed. – JMac Jul 4 '17 at 12:01
• but doesnt the spring force exist to reform the spring? Then shouldnt it be more than the external force to overcome it and get the spring back in its original state?? – MartianCactus Jul 4 '17 at 12:07
• The assumption that the spring is massless is an assumption. It's not actually true for any real spring. You are mixing up the "real world" and the "simplified mathematical model." The model says that if the external and internal forces are different, the spring moves infinitely fast in zero time to equalize them. Obviously that doesn't happen in the real world! If you include the spring mass in a more complete model, it doesn't happen in the model either, because the spring then has inertia and its motion depends on "F=ma" when the forces are unbalanced. – alephzero Jul 4 '17 at 12:14
• so in the "real world", the spring force doesnt have to be equal to the external force? – MartianCactus Jul 4 '17 at 12:28
• @MartianCactus The spring doesn't "overcome" the force. When you remove the force that is deforming it, it now has an unbalanced force that allows it to take its previous shape. If the spring force was actually a bit more than you were applying; you wouldn't be able to compress the spring; it would push back harder than you push it. The "springiness" of it is the fact that it resists with the same force you apply. The harder you push, the more it pushes back because you've deformed it more. It wont actually go back to it's old shape until you stop pushing. – JMac Jul 4 '17 at 12:39