# What is the reaction force to the spring force?

Suppose we have a spring suspended downwards and a mass of block M that is pulling that spring downwards. We have the W force (that is m x g) acting upon that mass of block M and we have the spring force (Fe) (that is -k x displacement) that is acting upwards. My question would be, where is the reaction force corresponding to the spring force (Fe) in this game?

• Not sure what you mean, you've already included $F_e$ in your diagram. Nov 22 '21 at 13:05
• @Triatticus so you're saying that Fe (the spring force) is the reaction force (based on Newton's 3d Principle Law) to the W (weight force) ? That would mean that k x displacement = m x g ? Nov 22 '21 at 14:03

My question would be, where is the reaction force corresponding to the spring force (Fe) in this game?

It's the force that the block exerts on the spring. To see this, refer to the free body diagrams of the block and spring below showing the action-reaction pairs.

Per Newton'w 3rd law, the force the spring exerts on the block, $$F_e$$, is equal and opposite to the force the block exerts on the spring. At the top, the force the spring exerts on the ceiling is equal and opposite to the force the ceiling exerts on the spring, again $$F_e$$. These are the action reaction pairs.

Per Newton's 2nd law, since the block, spring and ceiling are all in equilibrium, the net force on each has to be zero. Therefore, $$F_{e}=W$$.

Hope this helps.

• "It's the force that the block exerts on the spring. To see this, refer to the free body diagrams of the block and spring below showing the action-reaction pairs." You mean the weight force W? Nov 22 '21 at 17:45
• @MrJay It only happens to be $w =mg$ because the block is in equilibrium. But suppose instead that the spring was not fully extended when the block is released. Then when it is released $w>F_e$ causing the block to accelerate downward. But the force between the spring and the block (the action-reaction pair) will still be equal and opposite, only they will be less than $w$. Nov 22 '21 at 18:37
• Also, gravity pulls the block down, and the block pulls the earth up (a bit). Nov 22 '21 at 21:10
• @R.W.Bird Aah. But suppose I support the ceiling by two columns embedded in the Earth? (LOL) Nov 22 '21 at 22:31
• If the block moves down, the earth-block center of mass is undisturbed with any kind of support. The earth moves up. Nov 23 '21 at 14:12