# Spring Constant Units

## What are the Units for the Spring Constant

Spring Constant Units in the metric system (SI) are in the form of N/m representing a Newton/meter so that the spring constant is a unit of force per unit of distance.  The Spring Constant Unit when multiplied with the distance unit removes the meter (m) unit from the labeled denominator of the Spring Constant Unit so that (N/m * m) yields only a Force unit in Newtons.  Hooke’s Law shown above as (F=Kx) representing the force on a spring through extension or compression where a spring is not extended beyond its elastic breakdown point.  F represents force whilst k represents a “spring constant’ characteristic of the particular spring in use and x represents the distance traveled.  Thus, the law states that the STRAIN on an object is directly proportional to a STRESS applied within the elastic limit of that object.  When we say ‘within the elastic limit’ what is meant is that the Stress applied will not exceed the ability of the object to be deformed or it will break.

Hooke’s law originated with scientist Robert Hooke who promulgated this law in the late 17th century.  His work has been extended to other situations where bodies are deformed linearly.  It should be understood that his equation is only an approximate solution to the very complex behavior of springs and other elastic bodies having forces applied thereto.  However, Hooke’s Law has a limit based upon the physical limits of a given item in that all things have a maximum amount that can be stretched before breakage or a minimum compressible size before failure.  It is also known that many materials do not follow Hooke’s Law well before those limits are reached.

Hooke’s law originated with scientist Robert Hooke who promulgated this law in the late 17th century.  His work has been extended to other situations where bodies are deformed linearly.  It should be understood that his equation is only an approximate solution to the very complex behavior of springs and other elastic bodies having forces applied thereto.  However, Hooke’s Law has a limit based upon the physical limits of a given item in that all things have a maximum amount that can be stretched before breakage or a minimum compressible size before failure.  It is also known that many materials do not follow Hooke’s Law well before those limits are reached.

In the modern world, materials having various elastic properties play key roles in our everyday live such as the wings of an airplane, the disc platens of a disc brake and similar items.  They all help us to function safely and efficiently in our daily lives. Thus, the understanding of the elastic properties of materials has been updated by scientists from the linear Hooke’s Law to a more general understanding whereby the deformation of an object has some relation to the amount of forces or stresses to which it is being subjected.

## Applicability to More Complex Objects

Materials that are more bulky then a spring do not function according to a simple linear analysis of Hooke’s Law and these are modeled according to three dimensional tensor system of equations representing the Stresses and Strains thereupon.  Thus, materials within a car door, an engine housing, crankshaft, jet engine or similar such object are symbolized by a system of vector equation.  However, due to the complexity of the motions that are applied to a given object or portion thereof, a set of instantaneous stresses and strains are effected to infinitesimal portions of the object; thus, engineers attempt to define these so as to understand the material needs of the industrial application for fail safe operation and provide for a perfect design for final manufacture.

## Elastic Material Functionality

One would expect that Hooke’s Law and its associated Spring Constant Units would be applicable to objects that once stretched return to their original state.  Some materials do indeed exhibit Hookean behavior but only under certain stresses.  For example, steel does indeed demonstrate well defined elasticity such that it returns to its original state after being stressed in most of its industrial uses.  In fact, it can be shown that Hooke’s Law perfectly matches the characteristics of Stress-Strain that cause the steel component to return to its initial equilibrium; this is true for stresses below the breaking point know as yield strength of steel or other material.

After the yield strength the given material begins to exhibit plastic behavior where the it becomes stretched out as the word ‘plastic’ suggests.  There are other materials such as aluminum that exhibit linear proportionality similar to Hooke’s Law within a narrow margin of error.  However, once a certain point is reached the errors become to large and relation breaks down.  Thus, only a portion of the material’s range is accurate for these type of materials.