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Hooke’s Law

Last updated date: 20th May 2024
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What is Hook'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 it in the 17th century. He has demonstrated 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


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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 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 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.


For centuries, we have seen a lot of inventions of a lot of devices and each invention involves some kind of Mechanism.  A basic idea of the Mechanism is required. Hooke’s Law is one of these, and the main device used here is Spring. This helps in the definition of Elasticity, Torsion and Force Laws., and these all come together for a play.  The properties of these applications are known as Hooke’s Law. 


The Hooke’s Law has been named after the 17th-century British scientist, Robert Hooke who has established a link between the many Forces applied to a string, and its Elasticity. He has also demonstrated the connection between the many forces that are applied to a string and its Elasticity.


Being recognized as one of the best principles of Physics, Hooke's Law states that the total Force required to expand a spring by a particular amount of distance is relative to that particular amount of distance. 


The Hooke’s Law spring formula is: F8 = -kx, and is recognized as the ‘Spring Constant’ formula. The Law is applicable only within the spring’s valid electric limit and Elasticity allows the spring to remain in the limited capacity. If it breaks the spring will lose its property. Like most of the Classical Laws of Mechanics, the spring formula too is functional within a limited frame. No material can be stretched or compressed beyond a certain size and limit.


Hooke’s Law of Elasticity

There is no permanent way in which we can modify or distort a spring’s state and the relevancy of Hooke’s Law is when only a particular amount of Force or distortion is involved. According to this, we will come across a lot of materials that will actually deviate from the Law, and this is because of extreme Elastic limits. Newton’s Law of Static Equilibrium and Hooke's Law is sometimes found to be compatible with each other and with the help of this, the relationships between stress and strain for complex objects can be accurately traced.


The relation is based on certain inherent properties.


Some of the interesting factors associated with Hooke's Law that can be a perfect Example of the First Law of Thermodynamics. When a spring is compressed or extended, it conserves the energy, and the only energy that is lost is the natural friction. Hooke’s Law ascertains a wave-like periodic function within the spring. When the spring is released from a compressed position, it will come back to its usual position, and the returned proportional Force is similar to what happens to a periodic function.


The wave and frequency of the motion inside the spring can be determined. More observations on the applications and uses of this Law will give clearer ideas regarding a better understanding of Hooke's Law.

FAQs on Hooke’s Law

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

Data given, x = 4 m

Spring constant k = 0.2

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

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

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.

3. Explain the Fact of Stiffer for Shorter Springs.

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

4. Which Factor Makes Spring Stronger?

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

5. What are some applications of Hooke’s Law?

Hooke’s Law can be applied to various situations. It can be applied to every discipline of Science and Engineering. It is the supporting and underlying principle of spring scales, manometers and clock balance wheels. The molecular, seismological and acoustics Mechanics are built on this foundation. An all-inclusive distinction on Hooke's Law gives an idea of the Modern Elasticity theory. This theory explains how the deformation of an Elastic object can be proportionate with the required amount of stress applied to it. 

6. What is Hooke's Law?

Hooke’s Law, invented by British scientist Robert Hooke is basically about the stress and strain relationship of certain materials. When the Force that is required to stretch a material is proportional to the extension of the material, a linear region is noticed, and Hooke's  Law is based on this. Stress and strain are varied according to situations and for certain deformations, the stress and strain are always proportional to each other. This is what Hooke's Law is about. 

7. What is the reason for the negative value of k in Hooke’s Law formula?

The formula for Hooke’s Law is F8 = -kx, and the ‘k’ is negative.  The value of ‘k’ is constant. When a certain amount of stress is involved or any kind of strain is applied to any material, the return Force is always in the opposite direction when the applied Force is released in the string. The spring constant ‘k’ is always denoted as the negative value, and this is because of the direction of the Force.

8. What is the concept of stiffer strings?

When the length of a spring is reduced, the spring constant is also reduced at the same time. From this, it can be determined that the length of the spring has an impact on the spring constant and is a dependent variable. The number of coils is short if the spring is short. Therefore, we can say that shorter springs have stiffer strings. Stiffer strings denote more control, less power and also less comfort.

9. What are the disadvantages of Hooke’s Law?

Hooke’s Law comes with certain disadvantages. This Law does apply past the Elastic level of a material and is applicable only to a certain level. It is only accurate and gives proper reading only for solid bodies provided the deformations and the Force are small. The application of Hooke’ Law is not a universal principle and only applies to those materials which are not stretched beyond their capacities.