What happens to a spring’s force if you stretch it more?

You may stretch or compress a spring beyond a certain point that its deformation will occur. On subsequent release of the stress, the spring will return to a permanently deformed shape.

Whenever a force is applied on a spring, tied at one end, either to stretch it or to compress it, a reaction force comes into play which tries to oppose the change. This force is exerted by the spring on whatever is pulling its free end.

This is known as Hooke’s law and stated mathematically

Reaction Force ##F=-kX##,where ##k## is constant which is characteristic of the spring’s stiffness, and ##X## is the change in the length of the spring. ##-ve## sign indicates that restoring force acts opposite to the deformation of the spring.

The relationship holds good so long ##X## is small compared to the total possible deformation of the spring.

Alternatively the relationship between applied force and amount of elongation/compression is ##F=kX##

In the picture above the red line depicts a Plot of applied force ##F## vs. elongation/compression ##X## for a helical spring according to Hooke’s law.

Actual plot might look like the dashed line.

Lower part of pictures correspond to various points of the plot. At middle point the spring is in the relaxed state i.e., zero force.

If too much force is applied, one may stretch or compress a spring beyond a certain point that its deformation will occur. On subsequent release of the stress, the spring will return to a permanently deformed shape which will be different from its original shape.