# Hooke’s Law

View Notes

## Define Hooke's Law

Many inventors have put their efforts into inventing several devices over centuries. All of them are based on the understanding of the mechanics. Operators should possess knowledge of mechanics before use. Hooke’s law is also one of them.

In this law, springs are the most used apparatus. This helps to define the laws of elasticity, torsion, and force. All of these properties come together for a play. The application of all these properties is known as Hooke's Law.

### Hooke's Law Definition

Hooke's Law is recognized as one of the finest principles of physics. This law mentions that the total force required to expand or relax a spring by a definite extent is relative to that certain amount of distance.

British Physicist Robert Hooke developed in the 17th century. He has demonstrated that the connection between the multiple forces applied to a spring and its elasticity.

### State Hooke's Law

Hooke's law explains the change in the length of the spring due to the application of a certain amount of force ‘F’. Hooke’s law equation is very easy to learn and understand.

Scientist hook stated this law early in 1660. He named it as a Latin anagram and published the law as “ut tension, sic vis” in 1678. The translated meaning of the statement is "as the extension, so the force".  Also, it is called as the extension is proportional to the force. The force of spring formula is given below:

hooke's law formula: F$_{s}$ = -kx

The above formula from Hooke’s law is also recognized as the spring constant formula.

Here, Fs = spring force

k = spring constant

x = spring stretch or compression

Hooke's law is the foremost conventional e.g. when taking into figures the phenomenon of elasticity. It can be depicted as an object's property or material that leads to the restoration of any materialistic object after it is being deformed.

This restoration property after undergoing the deformation is called the restoring force. Here, Hooke's law explains clearly that restoring force is proportional to stretch figures the material experiences.

Hooke’s law is applicable within the valid elastic limit of the spring. Elasticity property is the only one that helps the spring to remain in a confined place. When it breaks, the spring will lose its property.

However, Hooke's Law is functional within a limited frame of reference This is like the most classical law of mechanics. The reason behind this is that there is no material that can be compressed or stretched beyond a certain minimum or maximum size.

### Hooke’s Law of Elasticity

You simply can’t perform any permanent deformation or change of state to the spring. The concept of Hooke’s law is only applicable when a limited amount of force or deformation is involved. If we consider the fact, lots of materials will strikingly deviate from Hooke's law. This is because of their extreme elastic limits.

Some of the general forms of physics can relate the Hooke's Law with Newton's laws of static equilibrium as both of them are compatible with each other. When they are considered at once, you can trace the accurate relationship between strain and stress for complex objects.

This relation is totally based on the properties of intrinsic materials. For example, let’s consider a homogeneous rod that has a uniform cross-section. This rod will act as a simple spring during the stretching.

The stiffness (k) of the rod is directly proportional to the area of the cross-section of the rod. Also, it is inversely proportional to its length in the law of elasticity.

Let’s know some of the interesting factors associated with Hooke's law. This can be a perfect example of the First Law of Thermodynamics. When you compress or extend a spring, it conserves the energy so nearly.

Natural friction is the only energy that is lost due to this phenomenon. Also, Hooke's law detects the nature of a wave-like periodic function within the spring. When you release a spring from a deformed position, it will come back to its default place. The return force is the proportional force that happens in a periodic function.

You can find out the wavelength and frequency of the motion generated inside the spring.  Your observations can give you some sort of quality ideas that help you to know more regarding Hooke’s law.

A comprehensive distinction on Hooke's law can give you the idea of the modern theory of elasticity. This theory informs that the strain (deformation) of an elastic object can be proportionate with stress applied to it.

In some cases, multiple independent components are available in most of the general stresses and strains. It may have, the "proportionality factor" may no longer be just a single real number.

An example that suits well with the stress and strain factors is when you deal with wind. In this scenario, the applied stress changes with intensity and direction. But it does apply a certain force.

Q1. Find Out the Spring Force of a Stretched String of Length 4 m with a Spring Constant of 0.2.

Ans: Data given, x = 4 m

Spring constant k = 0.2

So, Spring force Fs = -k x = - 0.2 * 4 = - 0.8 N

Q2. Why is the Value of K Negative in Hooke’s Law?

Ans: K is known as the spring constant, and it is denoted as the negative one in the equation of Hooke. The negative symbol is because of the direction of the force. The return force always travels in the opposite direction when you release the applied force in spring.

Q3. Explain the Fact of Stiffer for Shorter Springs.

Ans: When you reduce the length of the spring, the spring constant is also reducing. So, you can determine from now that the length of the spring does have an impact on the spring constant is a dependent variable. When the spring is short, the number of coils is also short. So, shorter springs are stiffer springs.

Q4. Which Factor Makes Spring Stronger?

Ans: Spring index is the factor that helps the spring quality, whether it is infirm or weak condition.