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# Definition of Work, Formula, Faq’s with Solved Examples

Jul 12, 2022

## Work

The word work is generally one that every one of you frequently uses in your daily life. A teacher teaching in the class, a student doing his homework, a farmer ploughing his fields, a driver driving a car, an artist drawing a beautiful painting, a photographer clicking photos, etc., all are said to be working.

But, have you ever thought that Science has another perspective for the term ‘Work?’ Yes! This word, work in Physics, conversely has a definite and precise meaning. And what is work in Physics? This article will explain it to you.

This article aims to develop the understanding of a physical quantity called work in Physics.

## What is Work?

The word work contains a dictionary meaning ‘to do something which needs physical or mental efforts, to earn money or to achieve something.’ The job you do, especially to earn money, is called work.

The question ‘what is work’ in general language can be defined as an activity in which one exerts physical or mental strength or performs something. Work is a person’s function, duty, assignment, or special task. A student is learning his course for the upcoming exams; a musician is playing the flute; a businessman is thinking of a meticulous plan for his business deal; a child is riding a bicycle on the circular path in the park every day, etc. are some common examples where the subjects are performing work.

## Definition of Work in Physics

In the Physics language, the answer to the same question, ‘what is work,’ has a different meaning. Work is the connection between force and displacement.

Work in Physics is defined as the product of the component of the force in the direction of the displacement and the magnitude of this displacement. Simply put, work in Physics is the multiplicative product of force and displacement acting on the same body, or you can say that it is an approach of force over a certain distance. It is a scalar quantity. Work has only magnitude and no direction.

You can also define work in Physics as the transfer of energy to or from an object by exerting force along with the displacement.

### Examples of Work

You face a lot of examples of work in your daily life. A batsman hitting a ball, a boat sailing in the river, a cyclist paddling the cycle, a mechanic repairing a gadget, a traveller pushing her luggage from the airport, cobbler polishing shoes, etc. are some examples of work. In all these cases, the movement of objects occurs. Hence, work is done whenever a displacement occurs in the object’s position.

In some cases, like a man pushing a rigid brick wall, falling any object freely from a certain height due to gravity, etc., are not considered as possessing the ability to do work in Physics. In the first case, a man is only tiring himself by pushing the rigid wall as there is no change in the position of the brick wall after applying a lot of force. While in the second case, in terms of Physics, there is a change in the position of an object, which means work has been done. But this work is under gravity, which lets the object fall downward. Hence, in such cases, it is concluded that there is no work done.

### Mathematical Form to Define Work in Physics

Work done on a body is defined as the product of the force’s magnitude and the distance the body moves in the applied force’s direction.

Mathematically,

W = (F cos𝝧)d

Here, W = work done, F = force applied, d = displacement or distance with direction, and 𝝧 = angle between the force and displacement.

As work done is a physical quantity, in terms of vector, it is written as

W = F.d

Joule (J) is the S.I. unit of work done.

1 Joule = 1 Newton x 1 metre, i.e., J = Nm = kg m/sec2.

Although force and displacement both are vector quantities, work has no direction as it is the scalar product of both vector quantities. The dimensions of work and energy are [ML2T-2].

### Conditions When No Work is Done

As work depends on three factors, i.e., force applied on the object, displacement travelled by the body under the force, and an angle between force and displacement, there are three cases when it is called that there is no work done during the situation.

Case 1: When displacement becomes zero.

For example, a weightlifter holding a 150 kg weight for 30 sec on his shoulder does ‘no work’ on the load during this time.

Case 2: When force applied becomes zero.

For example, a ball rolling on a slippery surface is not acted upon by the horizontal force, as there is no friction. But there may be a large displacement.

Case 3: When the value of cos𝝧 or angle becomes zero.

For example, When a block is rolled down on a smooth surface, the gravitational force there does not work. It is because the force is perpendicular to displacement in this case.

### Some Solved Problems to Define Work in Physics

Example 1. A package of 100 kg is pulled up by 5m. Calculate the work done. (Given: g = 9.8 m/sec2)

Answer: Here, the mass of the body, m = 100 kg

Height by which body is lifted-up = 5m

As work done in lifting the package = (weight of the body) x (vertical distance)

W = (m) x (g) x (h)

W = 100 x 5 x 9.8

W = 4900 J

Hence, the work done is 4900 J.

Example 2. A car is being driven by a force of 2.5 x 1010 N. It reaches a certain place in 2 minutes, travelling at a constant speed of 5m/sec. Calculate the work done.

Answer: Here, force applied by the car, F = 2.5 x 1010 N

Speed of the car, v = 5m/sec

Time is taken, t = 120 sec

Now, Distance travelled = speed x time

Distance, d = 5 x 120 = 600m

Work done, W = F x d

W = 2.5 x 1010 x 600 = 1.5 x 1013

Hence, the work done is 1.5 x 1013 J.

Example 3. If the work done by a force in moving an object through a distance of 20 cm is 24.2 J, what is the magnitude of the force?

Answer: Here, work done in moving the body, W = 24.2 J

Distance travelled by the body, d = 20 cm = 0.2 m

As work done = force x distance travelled

Force, F = work done / distance travelled

F = 24.2/0.2 = 121

Hence, the magnitude of the force is 121 J.

Example 4. A cyclist comes to a crashing stop at 10 m. During this process, the force on the cycle due to the road is 200N and directly opposite the motion. How much work does the road do on the cyclist?

Answer: Here, the distance travelled by the cyclist = 10 m

The frictional force on the cycle = 200N

As work done by the road on the cyclist = work done by the frictional force on the cycle due to the road

W = Fd cos𝝧

Here, 𝝧 = 180° cos𝝧 = cos 180° = -1

W = 200 x 10 x -1

W = -2000 J

Hence, work done is 2000 J, and the negative sign means this work done brings the cycle to a halt.

### Conclusion

From the above discussion, you are now aware that there is a difference in the term ‘work’ when you talk about it while relating it to Physics. Generally, work is whatever you do, while Physics do not think so. Work in Physics is a scalar quantity and can be negative or positive. It is unlike mass and kinetic energy, as they can only be counted as positive scalar quantities.

With the help of a mathematical formula, you can calculate the work done by a force, even if the nature of the force is unknown. Also, if there is no displacement while applying force or vice-versa, there happens to be no work done.

### Q1. What are the factors that affect work?

Answer: Work is the scalar product of force and displacement. Hence,

Work = Fd cosθ

It means there are three factors that affect work, i.e., force, displacement, and angle between force and displacement. Therefore, it concludes:

• If force = 0, then work done = 0.
• If displacement = 0, then work done = 0.
• If θ = 90°, i.e., cos 90° = 1, then work done = 0.

If the work done is zero, it means no work is done during the process.

### Q2. When does a force do the work on an object negative?

Answer: When both, the force applied to an object and displacement caused by moving it, are in the opposite direction, work done is positive. For instance, to decrease the motion of a rolling football, the work is done by frictional force. It is an example of negative work done. It is because the direction of football’s motion and frictional force is opposite.

### Q3. Why is a sparrow sitting in the nest on a tree not considered as doing any work?

Answer: A sparrow sitting in the nest on a tree does not own any kinetic energy as it is not moving. The absence of kinetic energy means there is no body movement in the object. Hence, the sparrow does not hold the ability to do work in terms of the body’s motion.

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