## 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.

## What is Work and Energy ?

### Work

When a force causes motion, work is said to done. A person climbing a flight of stairs is an illustration of this. Because he is moving against the force of gravity, the person has done work in this case. Any force's work is influenced by a number of factors. The distance the body moves in the direction of the force is one of the elements. The force is the second factor. Work is defined as the product of a body's displacement and force in the direction of the force. Work equals F*S, where F stands for force and S stands for distance. Work is equal to FS Cosθ when a body is displaced by a distance with a force operating on it.

Work = force × displacement towards the force

### Energy

When you play for a long term or do quite a little physical work at your own home or out of doors you get tired, i.e., your body indicates unwillingness or reluctance towards similar play or work. at the moment you could also experience hunger. After taking a rest for some time or/ and eating something you may once more be ready for work. How does one provide an explanation for those experiences? In reality, when you do work, you expend strength and extra energy is needed to do extra work. The capability of a body to do work is decided by the energy possessed with the aid of it. i.e.,

The energy possessed with the aid of a body = overall work that the body can do. Energy has the same unit as work, i.e., joule denoted by means of J. however, conversion of 100% of energy might not usually be doable, because, within the process of conversion of energy into work a few energy may additionally remain unused or can be wasted.

### Relation between Work and Energy

The capacity to do work is referred as energy. This refers to the force that one thing will put on another object in order to displace it and cause a change in its location. Work is defined as the action of displacing an object by exerting a particular amount of force on it. One would expect a shift in position as a result of doing so. The rate at which work is completed or the amount of work completed per unit of time is referred to as power.

Based on these criteria, it is safe to conclude that energy is a fundamental requirement for completing work. The amount of work completed in a given time period is referred to as power. Work, on the other hand, is the action required to change the object's location. To do work, you require energy, and power is the rate at which you can do work, whereas energy is the capacity to accomplish work.

Work and energy are related to each other i.e, with an increase in work results increase in energy, or vice versa. Work done can be explained mathematically by:

\[W = \frac{1}{2}mv^{2}_{f} - \frac{1}{2}mv^{2}_{i}\]

in which,

W is the work achieved through an object in terms of Joules.

m is the mass of the object measured in terms of kilograms.

vi is the initial velocity in m/s.

Vf is the final velocity of an object measured by the usage of m/s.

Hence, the work-energy theorem states that total work done by the net force on an object is equal to change in its kinetic strength.

## FAQs on Relation Between Work and Energy

**1. Is there a connection between energy and work?**

Energy can be transferred in the form of force. Work or work done refers to the quantity of energy delivered by a force to move an item. As a result, Work and Energy have a direct relationship. That is, the difference in an object's Kinetic energy is work done by the item.

**2. Is the amount of work done and the amount of energy expended the same?**

To help an object move, energy must be given to it, and this energy might be delivered in the form of force. Work or work done refers to the energy transmitted by force to move any object. The difference in an object's kinetic energy is referred to as work done by the object.

**3. What is the work formula?**

The work W is equal to the force f times the distanced, or W = fd, to express this concept numerically. The work done is W = fd cos if the force is applied at an angle to the displacement.

**4. What is the formula for calculating work?**

Work is defined as the force multiplied by the distance over which it is applied. Work (joules) = force (newtons) x distance is an equation (meters), Work is measured in newton-meters in the metric system of units, where force is measured in newtons (abbreviated N) (N-m).

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

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

\[= \frac{1}{2}mv^{2}_{f} - \frac{1}{2}mv^{2}_{i}\]

Here, vf and vi 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:

\[v^{2}_{f} = v^{2}_{i} + 2ad\] . Therefore,

\[d = \frac{(v^{2}_{f} - v^{2}_{i})}{2a}\]

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

\[W = Fd = \frac{ma(v_{f}^{2}- v_{i}^{2}),}{2a}\]= ½ mv_{f}^{2} – ½ mv_{i}^{2} = KE_{f} – KE_{i} = ΔKE

**6. Describe Work, Energy, and Work-Energy Principle.**

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.