Work (Physics): Definition, Formula & Units

Work in Physics is defined as the transfer of energy when an object moves from one place to another. We tend to use the word ‘work’ to convey our efforts. Our parents work hard to give us a good life. We work a lot to get good marks. Some people do a lot of workouts to stay fit. But do these usages of the word ‘work’ bear the same meaning in the eyes of Physics? In this article, let’s understand the concept of work in terms of Physics in detail.

Work in Physics

Work has a precise meaning in Physics. To understand work, we need to have a clear idea about the concept of force and the concept of displacement.

Force is an external effort in the form of stretching, compressing, pushing, pulling, etc. which may move a body or stop a moving body or change its speed or change its direction or may even change its shape and size.

Displacement, on the other hand, is the shortest distance between the initial position and the final position of the body in motion.

Example: Work is said to be done when the force applied to a body displaces the body in its direction. For example, when we push a table lying on the floor, it moves to another position. This is because the table has undergone displacement due to the force applied to it. So, according to Physics, we have done some work.

Similarly, when we lift a box to some height, we have displaced the box due to the force applied to it which is greater than or equal to the weight of the box. In this case, also, we have done some work.

Now, let us push the wall with all our might. But the wall does not move or undergo any displacement. So, according to Physics, we have not done any work on the wall as there is no displacement in the wall. Therefore, if work needs to be done, then it requires both force and displacement to be non-zero.

Work: Definition and Formula

Work is said to be done when the force acts on an object, which displaces it in the direction of the force.

Work Definition in Physics: The work done by a force acting on an object is equal to the product of the force and the displacement in the direction of the force.

Work done \(\left( W \right)\) is the product of the force \(\left( F \right)\) and the displacement \(\left( s \right)\) in the direction of the force. Thus, the work done can be calculated by the below formula,

\(W = F \times s\)
If the displacement is not in the direction of force and, it is making an angle \(\theta \) with the direction of force, then work can be written as,

\(\therefore \,\,\,\,W = F \times s \times {\rm{cos}}\;\theta \;\)

where, \(\theta \) is the angle between the force and the displacement.

Unit of Work

The SI unit of force is newton \(\left( {\rm{N}} \right)\) and the SI unit of displacement is meter \(\left( {\rm{m}} \right).\) So, the SI unit of work done is \({\rm{N}}\,{\rm{m}}\) which is given a separate name called joule \(\left( {\rm{J}} \right)\) in the honour of the British scientist James Prescott Joule.

One joule work is said to be done on a body when a force of one newton displaces it by one meter along the direction of the force.

Higher units of joule are:

1. kilo joule \(\left( {{\rm{kJ}}} \right)\) where \(1\;{\rm{kJ}} = 1000\;{\rm{J}}\)
2. mega joule \(\left( {{\rm{MJ}}} \right)\) where \(1\;{\rm{MJ}} = {10^6}\;{\rm{J}}\)
3. The CGS unit of work is \({\rm{erg}}\) where \({\rm{1}}\,{\rm{erg}}\,{\rm{ = }}\,{\rm{1}}{{\rm{0}}^{ – 7}}\,{\rm{J}}{\rm{.}}\)

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Solved Examples on Work

Few solved examples on work are given below:

Q.1. A girl pushes a pencil box by applying a force of \(20\;{\rm{N}}.\) Find the work done by this force as the pencil box is displaced through \(25\;{\rm{cm}}\) along the path.
Ans: Given that, The force applied by the girl is \(F = 20\;{\rm{N}}\)
The pencil box is displaced by \(s = 25\;{\rm{cm}} = 0.25\;{\rm{m}}\)
The work done by the force is \(W = F \times s = 20 \times 0.25 = 5\;{\rm{J}}\)
Thus, the girl does \(5\;{\rm{J}}\) of work to move the pencil box.
Sol:
Given that,
The force applied by the girl is \(F = 20\;{\rm{N}}\)
The pencil box is displaced by \(s = 25\;{\rm{cm}} = 0.25\;{\rm{m}}\)
The work done by the force is \(W = F \times s = 20 \times 0.25 = 5\;{\rm{J}}\)
Thus, the girl does \(5\;{\rm{J}}\) of work to move the pencil box.

Q.2. If the work done by a force in moving a body through a distance of \(15\;{\rm{cm}}\) is \(30\;{\rm{J}},\) what is the magnitude of the force?
Ans: Given that,
The work done is \(W = 30\;{\rm{J}}\)
The displacement of the body is \(s = 15\;{\rm{cm}} = 0.15\;{\rm{m}}\)
The force applied on the body is \(F = \frac{W}{s} = \frac{{30}}{{0.15}} = 200\;{\rm{N}}\)
Thus, the magnitude of the force applied on the body is \(200\;{\rm{N}}{\rm{.}}\)

Types of Work

Work done is the product of the force applied and the displacement caused by the force in its direction. So, based on the direction of the displacement with respect to the direction of the force, work done can be mainly of three types as mentioned below:

1. Positive work In this case, the displacement caused is in the direction of the force. Thus, the angle between the force and the displacement is \(0^\circ .\)
So, \({\rm{cos}}\;\theta \; = {\rm{cos}}\;0^\circ \; = 1\;\;.\) Hence, work done is \(W = F \times s \times {\rm{cos}}\;\theta = F \times s\)

2. Negative work In this case, the displacement caused is in the opposite direction with respect to the direction of the force. Thus, the angle between the force and the displacement is \(180^\circ .\)
So, \({\rm{cos}}\;\theta \; = {\rm{cos}}\;180^\circ \; = – 1\) Hence, work done is \(W = F \times s \times {\rm{cos}}\;\theta \; = – F \times s\)

3. Zero work In this case, the direction of the displacement is perpendicular to the direction of the force. Thus, the angle between the force and the displacement is \(90^\circ .\)
So, \({\rm{cos}}\;\theta \; = {\rm{cos}}\;90^\circ \; = 0\;\)
Hence, work done is \(W = F \times s \times {\rm{cos}}\;\theta \; = 0\)
This is also possible when the force acting on the body does not cause any displacement in it.

All the above-mentioned points can be summarised in the below diagram:

Factors Affecting Work

Work done is the product of force and displacement in the direction of the force. So, work done depends on the following factors

1. The magnitude of the force form the formula of work done. It is evident that the higher the magnitude of force, the higher the work gets done and vice-versa.

2. The magnitude of the displacement form the formula of work done. It is evident that the higher the magnitude of the displacement, the higher the work gets done and vice-versa.

3. The direction between the force and the displacement If the angle between the force and the displacement is \(\theta ,\) then the value of \({\rm{cos}}\,\theta \;\) is obtained to get the magnitude of work done. So, work done depends on the value of \({\rm{cos}}\,\theta \;\)

Importance of Work

Work is associated with energy consumed to get the work done. So, the concept of work helps us to get an idea about how much energy is to be utilized for doing the work. Based on this decision, we can employ devices or agents to get the work done.

Applications of Work

Work and energy are interlinked. So, some of the applications of work are as mentioned below:

1. Work concept can be used to calculate the potential energy gained or spent by a body.
2. Work can be used to find the kinetic energy of the system utilizing the work-energy theorem.
3. Work can be utilized to calculate the power of an agent.
4. Work done may give an estimate of energy consumed.
5. Work done can help in calculating the magnitude of force applied or that of displacement caused.

Hope we could help you understand the concept of work. And this article would have quenched your curiosity to learn how science differentiates the concept of work from the work we use in our day-to-day conversations. So, next time do smile when someone sitting at a place working hard claims that they are working really hard because now you know how science will react to this case of work!

FAQs

Below are the frequently asked questions on Work:

Q.1. When is work done negative?
Ans. Work done is negative when the displacement caused is in the direction opposite to the direction of the force.

Q.2. What is work in Physics?
Ans. Work is the product of force and displacement in the direction of the force.

Q.3. How is the SI unit of work related to its CGS unit?
Ans. The SI unit of work is joule and the CGS unit of work is erg. They are related to each other by the relation, \(1\;{\rm{joule}} = {10^7}\;{\rm{erg}}\)

Q.4. When can the work do be zero?
Ans. Work done can be zero when either of force or displacement or both are zero. Work done can be zero even when force and displacement are perpendicular to each other.

Q.5. What is the SI unit of work?
Ans. The SI unit of work is joule.

Now that you are provided with all the necessary information about work. Work is usually introduced in Class 9, thus it’s crucial to master all of Class 9’s Physics topics since it creates a firm basis if you want to pursue Science as a career path. Thus to help you with that, Embibe offers Class 9 Science Practice Questions and Class 9 Science Mock Tests which can be accessed for. These will help you not only in your Class 9 exams but also helps in clearing competitive exams which are designed on the basis of 9th syllabus.