# Can Hooke's law go along with Newton's 3rd law & how is momentum conserved in case of spring?

Let there be a spring in its relaxed state- that is neither compressed nor extended. One end is fixed on the left and other end is free in the right. Now, I stretch the spring by pulling the free-end towards right. As soon as I do it, the spring exerts force ie. the restoring force on me towards left. But, I willn't move on the left but rather expand the spring towards right & it will exert more restoring force acc. to Hooke's law. So, in this spring-me system , is the linear momentum conserved?? If so, how??? And also, is Hooke's law saying about Newton's 3rd law? That is, if I exert force on the spring, the spring exerts restoring force on me; then can I say by Newton's third law,at any instant $$\text{restoring force} = - \text{my applied force}$$ ??? Please help me explaining these two: how the momentum is conserved and whether the relation above is true.

The above relation is correct. Regarding momentum, you need to consider the momentum of the entire system, including the wall, because the spring is not isolated. Just imagine the wall is very heavy but not infinitely so. And suppose both you and the wall are in a frictionless surface, otherwise there will be additional friction forces and momentum will not be conserved. In the frictionless case, when you pull the spring to the right, it will move to the right togetre with your hand, but the rest of you body will slightly move to the left to compensate (because of the reaction force), Also, the wall will move slightly to the left, minimally if it is too heavy, so the string will actually expand. If you take into account all these motions, momentum is conserved (because no external forces act on the whole system). Momentum will not be conserved if you are standing on a regular floor because friction (an external force) will act.

• Momentum is conserved even if you are standing on regular floor, but the floor now has to be included in the system as well. Nov 27 '14 at 5:59
• yes, thanks! you are right, I know momentum is always conserved, I meant the momentum of the wall-sring-person system only
– user65081
Nov 27 '14 at 6:00
• Sir, the restoring force of the spring is different from the reactive force that the spring applies on me . This is evident: When I displace the spring to the right & remove my hands, the spring will move back to its inititial point, due to what?? The restoring force!! So, restoring force is not same as reactive force . Am I right or am I right?? THANKS.
– user36790
Nov 27 '14 at 9:08
• I know it sounds confusing, let me think a more didactic way to explain it
– user65081
Nov 27 '14 at 14:47
• When you attach a mass, the spring will interact with the mass, and make force on the mass because of the restoring force. And the value of the restoring force with the mass attached will be equal to the reaction force of the mass. There is no way around that. When two objects interact the force the first makes on the second is equal but opposite to the force that the second makes on the first. But when you analize a dynamical sytem as I did in my answer, you generaly do not have to consider the internal forces.
– user65081
Nov 27 '14 at 14:56