## What is the Relation Between Work and Energy?

Energy must be transferred to an object to help it move, and the energy can be transferred in the form of force. The energy transferred by force to move any object is known as work or work done. Therefore, work and energy have a direct relationship. The difference in the kinetic energy of an object is called work done by the object. Work and energy are common terms in Physics and can be considered two sides of a coin. This article is necessary to state the relationship between work and energy.

### Work –

Work is done when force is applied for moving an object. Work can also be described as the activity that involves a movement and force in the force's direction.

The SI unit of work is Joule (J), which is a term for Newton-meter.

For example, when you kick a ball, you exert an external force called F, causing it to move at a certain distance. This change in the ball's position from A to B is called the displacement (d). Work is calculated by multiplying the force applied to the object by the movement of the object. W = F * d.

### Energy –

Energy is the capacity to do work. The formula for Potential Energy is mgh, where m is the object's mass, g is the gravitational force, and h is the height that the object covered. Below you can find the relationship between work and potential energy / Kinetic Energy.

Energy cannot be created or destroyed. Energy can only be transferred from one form to another. There are various types of energy, and all of them are either kinetic or potential. Energy in motion is termed Kinetic Energy, and the one stored in an object is termed Potential Energy.

There are other types of energy, including:

Mechanical Energy

Chemical Energy

Mechanical Wave Energy

Electric Energy

Radiant Energy

Magnetic Energy

Nuclear Energy

Elastic Energy

Thermal Energy

Gravitational Energy

Ionization Energy

Heat Energy

SI unit of Energy is Joules, named after James Prescott Joule.

### What is the Relationship Between Work and Energy?

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One can describe the relationship between work and energy using the proportionality factor; both are directly proportional to one another.

The relationship between work and energy is as follows:

W = ½ mvf2 – ½ mvi2.

Here,

W is the work done by the object and is measured using Joules.

M is the mass of the concerned object and is measured using Kg.

Vf is the final velocity of the concerned object and is measured in m/s.

vi is the initial velocity of the concerned object and is measured using m/s.

Therefore, the relation between work and energy (work-energy theorem) states:

The network that force does on an object is equal to the change in its kinetic energy. Thus, the relation between work and kinetic energy is as follows:

W = Ki – Kf = ΔK

Here,

Ki is the object’s initial kinetic energy.

Kf is the object’s final kinetic energy.

ΔK is the difference between the final and the initial Kinetic Energies.

1. Describe the Relationship Between Work and Energy Using the Work-Energy Theorem. Also, Derive its Formula.

Ans. The relationship between work and Kinetic Energy, also called the Work-Energy theorem, states that the work done by the sum of all the force acting over any particle/ object is equal to the change in the Kinetic Energy of the particle. The definition can also be extended to the rigid bodies with the definition of work of torque and rotational Kinetic Energy.

Work W done by the force on any particle/ object is equal to the change in the particle's Kinetic Energy KE.

W = ΔKE

= ½ mv_{f}^{2} – ½ mv_{i}^{2}

Here, v_{f} and v_{i} are the particle's initial and final speeds after applying the force, and m is the mass of the particle.

To simplify it, first, the case is considered where the resultant force F is constant in magnitude and direction and is also parallel to the particle's velocity. According to the second law of Newton, the particle moves with constant acceleration along a straight line, and the relation between the force and acceleration is equal to F = ma.

The displacement of the particle is d and can be determined as:

v_{f}^{2} = v_{i}^{2} +2ad. Therefore,

d = v_{f}^{2}^{ }- v_{i}^{2}.2a.

The work of a net force is calculated by finding the product of its magnitude F =ma and the displacement of the particle.

W = Fd = mav_{f}^{2} - v_{i}^{2}.2a = ½ mv_{f}^{2} – ½ mv_{i}^{2} = KE_{f} – KE_{i}_{ }= ΔKE

2. Describe Work, Energy, and Work-Energy Principle.

Ans. Work means the transfer of energy from one form to another. Work is said to be done on any particle/ object when the energy is transferred to that object. If any object transfers the energy to the other, then the first object is said to have done work on the second.

Work is the application of force over a given distance on an object. Lifting weight from the ground and then putting it on the shelf is an excellent example of work done. The force equals the object's weight, and the distance equals the height of the shelf.

W = F x d.

In contrast, energy is the capacity to do work. The simplest case of Mechanical work is when an object stands still, and you put some force to move it. The energy of any moving object is known as Kinetic Energy. For any object with mass m, moving with a velocity of magnitude v, the energy is calculated by the formula.

E = ½ mv^{2}

Furthermore, the relation between work and energy is called the Work-Energy principle. It is described as the change in Kinetic Energy of an object equals the net work done on the given object.