# What is Hooke’s Law?

We can describe this Law in the Following Points:

**Robert Hooke**presents Hooke’sLaw.- Hooke’s Law is the principle of Physics that falls under
**Mechanical Physics or Mechanics**. - This Law depends upon the
**body’s elasticity**and properties like**stress**and**strain**. - In Elastic Bodies, Stress and Strain are directly related to each other, known as
**Hooke’s Law**.

## Statement of Hooke’s Law

Hooke’s Law States that;

### Hooke’s law example

Following are the Example of Hooke’s Law;

- A
**balloon**can stretch. When**molecules**of air are blown into it, it gets bigger. In the same way, when it is emptied, its size goes down. Hooke’s law says that how big or small the balloon receives depends on how hard air is pushed into it. This is how the balloon works. - Hooke’s law says that the force needed to stretch or squeeze a
**spring**by a certain distance is directly related to that distance. A constant factor characteristic of a spring is how stiff it is. The property of elasticity says that stretching a spring twice as long takes twice as much force.

### Hooke’s Law Stress

The Force applied to the body which takes it to the position of deformation is called** stress**. In Hooke’s Law equation, it is represented by **F**.

### Hooke’s Law Strain

The extent of deformation in the body that occurs when Stress or Force is applied to it is called **Strain**. In the case of spring, it is also called displacement in the loops of spring. In Hooke’s Law, it is represented by x.

### Hooke’s law stress-strain formula

**Stress = k × Strain**

where** k** is the proportionality constant and** elasticity modulus**. Hooke’s Law is true for most materials, which is important to remember.

### Elastic Limit

Elastic Limit or Elastic bodies can be stated as:

## How was Hooke’s law discovered?

**Robert Hooke** was born on July 18, 1635, in Freshwater, Isle of Wight, England. He died on March 3, 1703, in London. Hooke was an **English physicist** who discovered the law of elasticity, now called Hooke’s law. In the 1800s, when English scientist Robert Hooke was studying springs and elasticity, he noticed that many materials had the same property when the stress-strain relationship was examined. There was a straight line where the force needed to stretch the material was equal to how far it was stretched. Hooke’s Law is the name for this. He also did research in a wide range of other areas.

Robert Boyle hired Hooke in 1655 to help make the Boylean air pump. Five years later, Hooke came up with his law of elasticity, which says that the amount a solid body (like metal or wood) stretches depends on how much force is put on it. The law allowed studying stress and strain and learning about how **elastic materials** work. He used what he learned from these studies to make designs for watch balance springs, and he also tried to improve the pendulum for clock regulation, which shows how interested he was in timekeeping. In 1662, the Royal Society of London put him in charge of experiments.

## Hooke’s Law Formula

According to this Law, the stress applied to the spring is directly related to the displacement in the spring loops from its equilibrium position;

**F is directly proportional to x**

So,

**F = – kx**

Where;

- F is the applied Force (stress) on the spring
- x is the displacement of the loops in spring when stress is applied
- k is the proportionality constant which is also called the spring constant.

To deduct the formula of the spring constant:

**k = F / x**

Where;

- F is the applied force (stress) on the spring
- x is the displacement of the loops in the spring when stress is applied

By rearranging, we get the following;

**F = – kx**

### How to find force in Hooke’s law?

We can find the Force in this Law using **F = – kx**.

### In Hooke’s law, what does k represent?

**k** is the proportionality constant called **spring constant **or** elasticity modulus**.

### Why is k negative in Hooke’s law?

The **negative sign** with constant** k** in the equation represents the **direction of Force** (stress) applied on the spring, as the direction of this Force is opposite to the direction of displacement.

**NOTE**: This negative Sign doesn’t mean any negative value in the equation.

### What is the value of k in Hooke’s law?

**K **stands for the **spring constant**, which is also called the constant of proportionality. In simple terms, **Hooke’s law **(F = -kx) says that the k variable shows **stiffness and strength**. The longer it takes to stretch something to a certain length, the higher k is. Since k is the constant of a spring, it is always a **positive number**. The negative sign shows that the force being applied is going in the opposite direction of the force being restored.

## Hooke’s law experiment

Let us consider a spring with attached bodies hanging vertically downward, as shown in the figure;

The picture shows how the spring looks when there is no load on it, when it is stretched to a length of **x** under a load of **1 N**, and when it is stretched to a length of **2x** under a load of **2 N**.

Different springs have different constants, which can be worked out based on the material. The picture shows three situations: when the spring is stable when it has stretched by x under a load of **1N** and when it has stretched by **2x** under a load of** 2 N**. If we put these numbers into the equation for **Hooke’s law**, we can find the spring constant for the material in question.

### Can you always apply Hooke’s law to a spring?

**This Law** says that the force applied to an elastic object is proportional to how far it stretches. But if the object is stretched too far, it won’t bounce back. Hooke’s Law only works if the object is stretched enough. If the spring pitch (the space between coils) stays the same, the force of a conical spring will change in a way that doesn’t follow this Law. But the pitch of the spring can also be changed to make cone-shaped springs that follow the Law.

## What is Hooke’s law of elasticity?

We can’t change the shape of a spring in a way that lasts, and this Law only applies when only a certain amount of force or change is involved. According to this, there will be a lot of things that don’t follow the Law, and this is because the Elastic limits are so high. Newton’s Law of Static Equilibrium and Hooke’s Law is sometimes found to agree. This makes it easier to figure out how complex objects’ stress and strain are related. Some things make the relationship work.

Some interesting things about Hooke’s Law show the First Law of Thermodynamics in action. When a spring is compressed or stretched, it doesn’t lose any of its energy. The only energy that is lost is from the friction that happens naturally. Hooke’s Law shows that the spring has a wave-like periodic function. When the spring is released from its compressed position, it will return to its normal position. This is similar to what happens when a periodic function is changed. It is possible to figure out the wave and frequency of the movement inside the spring. This Law will be easier to understand if more observations are made about how it is used and how it can be applied.

## Hooke’s Law Graph

The **stress-strain curve** for low-carbon steel is shown in the picture below.

Up to the yield strength point, the material acts elastically. After that, it loses its elasticity and becomes plastic. Hooke’s law is shown by the straight line from the starting point to the proportional limit near the yield strength. When a material goes past the elastic limit between the proportional limit and the yield strength, it stops being elastic and becomes plastic. The elastic range is part of the curve from the start point to the proportional limit. The plastic range is the curve part from a proportional limit to where it breaks or breaks apart.

The maximum ordinate value on the stress-strain curve tells us the material’s maximum strength (from origin to rupture). At a point of rupture, the value gives the rupture strength.

## Applications of Hooke’s Law

Applications of this Law in different fields are as follows;

### In Springs

Springs are one of the most common uses of Hooke’s Law. Springs are utilized in various technologies and applications, including automobile suspension systems, shock absorbers, and door hinges. Spring can store and release energy because the amount of deformation it experiences is proportional to the force applied to it.

### In Strain gauges

Strain gauges are instruments that measure an object’s strain or deformation. They measure the resistance of a stretched or compressed wire or another conductor. By utilizing Hooke’s Law, the change in resistance can be used to compute the amount of deformation.

### In Engineering design

Engineers use Hooke’s Law extensively when constructing structures and materials. By comprehending the relationship between force and deformation, engineers can predict how a building or material will respond under different conditions and create safe, efficient designs.

### In Biomechanics

Hooke’s Law is also utilized in biomechanics to examine the behavior of biological materials, including bones, tendons, and muscles. By comprehending how these materials react to external stimuli, scientists and researchers can better understand how the human body functions and develop remedies for injuries and disorders.

### In Materials Testing

Hooke’s Law is widely employed in materials testing to assess mechanical qualities such as stiffness, elasticity, and strength. Researchers can determine how the material would behave under other conditions by applying a known force to a material sample and measuring the subsequent deformation.

## Limitations of Hooke’s Law

- This Law is only applicable to
**Elastic Materials**and is not to Non-Elastic materials. - This Law only applies to Elastic materials that show
**small deformation**under Elastic Limit when Force is applied. So assumptions of Hooke’s Law are only linear. - This Law is only applicable when the body is under
**Elastic Limit**. If the body crosses its elastic Limit, this Law will not apply. - This Law says that things should act the same in
**all directions**. But many materials, like wood or composites, behave in a way called “anisotropic,” which means that their properties change depending on how they are loaded. - This Law assumes that the material’s
**temperature**stays the same as it changes shape. But temperature changes can change how a material works and make it behave differently than this Law says it should.

## FAQ’s

### What is Hooke’s law in strength of materials?

This law says that a material’s stretch is equal to the stress that is put on it up to the material’s elastic limit. When elastic materials are stretched, the atoms and molecules change shape until stress is put on them. When the stress is taken away, the atoms and molecules go back to how they were before. This law works both when there is tension and when there is compression.

### Is Hooke’s law valid for all materials?

No, this law only works for **solid bodies** if the forces and changes are minor. This law is only a rule that applies to some things. It only works if the materials aren’t stretched past their limits. One problem with this Law is that it only works up to the elastic limit of any material. This means that material must be** perfectly flexible **for Hooke’s Law to work. Hooke’s law only works well after the elastic limit.

### Do rubber bands follow Hooke’s law?

Yes, the rubber band obeys Hooke’s Law because it moves **back and forth**. When the rubber band is laid out flat, a weight is attached, and the rubber band is pulled to the right. The rubber band acts as a restoring force, drawing the mass towards equilibrium and moving it back and forth. For minor points, in this Law, which says that **F=-kx**, describes how rubber bands stretch. This Law states that there is a limit to how much force a rubber band can take. This limit depends on the band’s physical properties, such as its cross-sectional area.

### What is Hooke’s law of potential energy?

Hooke’s law is a rule of physics that says the amount of force needed to **stretch or compress** a spring by a certain distance is proportional to that **distance**. Potential energy equals **half** the constant spring times the **square of the space**. It is equal to the amount of work done to stretch the spring, which depends on the constant of the spring (k) and how far the spring is stretched. This law says that the force to extend the spring directly relates to how much it is tested, whereas **P.E. stands for elastic potential energy**, measured in** Joule**.

### Can Hooke’s law be used in every circumstance?

No, there is some limitation to the application of Hooke’s Law, like the Body should be Elastic, which shows small deformation under Elastic Limit at a constant temperature.

### Do pendulums use Hooke’s law?

**Simple Harmonic Motion **is similar to how a simple pendulum moves (SHM). SHM happens when the restoring force is proportional to the displacement. When applied to springs, this relationship is often called Hooke’s Law. Lastly, we’ll look at the SHM behavior of a simple pendulum to determine gravity’s value in that area. The **negative sign** shows that the restoring force always moves in the opposite direction of the distortion. The constant spring k is measured in N/m and shows how stiff the spring is. k = g m/Dx.

### Does gravity affect Hooke’s law?

Yes, Hook’s law still applies here, and force is also different on different planets. But this doesn’t mean that the constant of the spring can change. In this case, how much the spring is stretched depends on the object’s weight, which depends on gravity. The spring’s point of return opposes the force of gravity pulling a mass down. Hooke’s law is an empirical physical law that says a linear relationship exists between the power a spring uses to return to its standard length and how far it is moved from that length.

### What is the conclusion of Hooke’s law?

When you plot how much the spring stretches against how much weight you add to the hanger, you get a straight line that goes through the origin. This means that a spring’s length is directly related to how much force is used to stretch it. From the experiment, it was transparent that the compressed and the stretched springs’ measurements changed the same way as the troops were altered. So, the springs followed Hooke’s law for elastic materials.

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