Describe how force changes with distance in a spring.

Force in a spring changes with distance according to Hooke's Law, which states that force is directly proportional to displacement.

Hooke's Law, named after the 17th-century British scientist Robert Hooke, is a principle of physics that describes how the force F needed to extend or compress a spring by some distance X is proportional to that distance. This relationship can be mathematically expressed as F = kX, where k is a constant factor characteristic of the spring (its stiffness), X is the distance moved by the spring (its displacement), and F is the force applied.

The force exerted by a spring is a restoring force, meaning it acts to restore the spring to its equilibrium or natural length. If you pull a spring and stretch it, the spring will pull back, trying to return to its original length. Similarly, if you compress a spring, it will push back, trying to expand back to its original length. This restoring force is what Hooke's Law is describing.

The constant of proportionality k in Hooke's Law is known as the spring constant. It measures the amount of force required to extend or compress the spring by a certain amount. A larger spring constant indicates a stiffer spring that requires more force to stretch or compress, while a smaller spring constant indicates a more flexible spring that requires less force.

It's important to note that Hooke's Law only applies within the elastic limit of the spring. The elastic limit is the maximum distance you can stretch or compress the spring without deforming it. If you stretch or compress a spring beyond its elastic limit, it will not return to its original length when you remove the force, and Hooke's Law no longer applies.

In summary, the force exerted by a spring changes with distance in a linear, directly proportional manner as described by Hooke's Law. The force is a restoring force, acting to return the spring to its equilibrium length, and the proportionality constant is the spring constant, which measures the stiffness of the spring. This relationship holds true as long as the spring is not stretched or compressed beyond its elastic limit.