Table of Contents

**Introduction:**

The stamina, power, energy, or potency as an aspect of physical action or movement is called force. In other words, any push or pull upon an object resulting in its movement is force. A force has both magnitude and direction, therefore, making it a vector quantity.

Hence, it can be said that force is energy that causes an object to move.

Sir Isaac Newton was one of the first scientists to study force and gravity. Any kind of push or pull can be defined as a force. It can be defined as pushing or shoving on a mass or an object.

Aristotle symbolizes power/force as anything that makes something “move unnaturally”.

Pushing or pulling an object is considered as a force. Interaction of one object with another gives rise to pushing and pulling. Words like stretching and squeezing can also be used to indicate a strength that is Force.

In Physics, Force is defined as:

Pushing or pulling an object with a weight causes it to change its speed.

Force is an external agent that can change the state of rest or movement of a particular body. It has size and direction. The direction in which energy is used is known as the direction of energy and energy consumption is the area in which energy is used.

Force is represented as F and its SI unit is Newton.

Force is given as the product of mass and acceleration because whenever a force is applied to any object it results in the object’s motion with its weight, therefore,

**F=mass×acceleration**

** F=m×a**

Work done by a constant force is defined as:

“Work performed with infinite energy can be defined as the product of the movement of an object (where energy is used) and part of the constant energy associated with the direction of motion.”

It is important to note that the work done with constant energy is directly proportional to the product of the amount of energy used and the movement of the object in which the energy is used.

In physics, motion is defined as a change in position relative to time. In simple terms, movement refers to physical activity. Generally, movement can be defined as:

- Change in the speed
- Change in route or direction

### Some of the different effects of force are:

- It can make the body move from a relaxing state.
- It can stop the moving body or slow it down.
- It can accelerate the speed of the moving body.
- It can also change the direction of the moving body and its shape and size.

**Integration and Formula for Variable Force:**

Functional activity of magnitude of force F in the area of displacement d on the energy side of the product is

**W=Fd**

To calculate the function performed by the dynamic/variable force and the function performed by the variable force, a method of integration calculation can be used.

SI unit of work is a joule.

Also, non-SI work units include kilowatt-hour, erg, the foot-pound, foot-poundal, liter-atmosphere, and horsepower-hour.

If change in displacement is ∆x then work done by a constant force is given by:

**W=F∆x**

In the case of a dynamic force, integration is required to calculate the work performed.

As per Hooke’s law, the regenerative power (or spring force) of a perfect elastic material or spring is equal to its extension or compression but contrary to the direction of extension or compression. So, the spring power applied to the object connected to the horizontal spring is given by:

**F _{s}=-k x**

Thus, the spring force is directly proportional to its displacement in x direction but the direction of displacement is opposite to the direction of force applied.

All the infinitely smaller contributions to the work done during the infinitely shorter periods dt (or equally, at intervals of infinitely shorter dx = v x dt) must be added for variable force. In other words, the important thing to consider is:

**W _{s}=^{0}∫_{t}F_{s}.vdt**

**= ^{0}∫_{t}-k x v _{x }d t**

**= ^{x}∫_{x0}-x s dt**

**=-12 k∆x ^{2}**

If the force applied is in the same direction as of direction of motion, then

**W _{a}=^{0}∫_{t }F _{a }. v d t**

**= ^{0}∫_{t}-F _{s }.v d t**

**=12 k∆x ^{2}**

Where W _{a} is the energy stored in spring, F_{a }is the force applied on spring, and F _{s} is the spring force.

**Integration calculation of Constant Force:**

The same method of integration can also be applied to work with constant energy. This suggests that combining energy output with distance is a common way of determining the dynamic activity of a moving body.

Consider the case of a closed gas piston, an important subject in Thermodynamics. In this case, Pressure (Pressure = Strength / Location) does not change and can be excluded from the integral value, therefore

**W= ^{a} ∫_{b }P d V**

**=P ^{a} ∫_{b }d V**

**=P∆V**

Because gravitational force is also a constant force then work done by gravitational force can be given by:

**W= ^{t1}∫_{t2}F.v dt**

**= ^{a} ∫_{b }m g v_{y}dt **

**=mg ^{y1}∫_{y2}dy**

**=mg∆y**

**Revising Hooke’s Law:**

Hooke’s law states that the type of material is proportional to the pressure applied within the elasticity of the material i.e., When elastic objects are stretched, atoms and molecules decompose into stress, and when the stress is removed, they return to their original state.

According to statistics, Hooke’s law is as follows:

**F=-kx**

In the equation, F is the force, x is the length of the extension, k, the equilibrium of the equation known as the constant in spring, and the unit is N / m.

### The following are some of the applications of the Hooke’s Law:

- It is used as a basic principle behind the manometer, spring scale, and clock balance wheel.
- Hooke’s law lays the foundation for seismology, acoustics, and molecular machinery.

### The following are some of the disadvantages of Hooke’s Law:

- Hooke’s law ceases to apply the expansion limit of the object.
- Hooke’s law is only valid for strong bodies when power and conversion are limited.
- Hooke’s law is not a general rule and only applies to consumables as long as they do not expand beyond their capacity.

Also read: **Centripetal Force**

**Frequently Asked Questions (FAQs):**

**Question: 1: When did Hooke’s Law fail?**

**Answer: **Hooke’s law applies to completely flexible objects and does not work beyond the elastic limit of any object. i.e., as long as they do not expand beyond their capacity.

**Question: 2: Why do we need Hooke’s Law?**

**Answer: **Hooke’s law is important because it helps us to understand how an extended object will behave when it is stretched or compressed.

**Question: 3: ****What is the work done by a constant force?**

**Answer: **It is the product of the component of the force in the direction of motion and the magnitude of the displacement. It is expressed by the equation

**W=F d**

**Question: 4: Does Hooke’s Law apply to all building materials?**

**Answer: **Hooke’s spring rule applies to any stretch of the subject’s undisputed complexity, as long as one number can indicate deterioration and stress.

**Question: 5: What is K in Hooke’s Law?**

**Answer: **K stands for spring constant. It represents how stiff the spring is. The higher the value of k lesser the elasticity of the material and the greater the force required to displace it.