Work -Definition, Formula, Examples, FAQs

What is Work?

In everyday language, work means doing any physical or mental activity. For example, walking, lifting a bag, or pushing a table is commonly called work. However, in physics, the meaning of work is more specific.

What is Work Done in Physics?

In physics, work is said to be done only when a force is applied to an object and the object moves (displacement occurs). If there is no movement, then no work is done, even if you feel tired.

For example, pushing a wall does not count as work in physics if the wall does not move.

Work Done - Definition

The standard definition of work done states:
"Work done by a force is equal to the dot product of the force applied and the displacement of the body."

Also read -

• NCERT Solutions for Class 11 Physics
• NCERT Solutions for Class 12 Physics
• NCERT Solutions for All Subjects

Work Done Formula

If a body is applied by some amount of force F and the body covers some displacement S then the work done by the body is written mathematically as W=F.S where W is denoted for work done.

S.I Unit and Dimensional Formula of Work Done

S.I Unit of Work Done

The S.I unit of work is joule (J).

One joule of work is said to be done when a force of one newton moves a body through a distance of one metre in the direction of the force.

$
1 \text { Joule }=1 \text { Newton } \times 1 \text { metre }
$

Thus,

$
1 J=1 N \cdot m
$

Although newton-metre $(N \cdot m)$ is equal to joule, the term joule is preferred for work to avoid confusion with torque.

Dimensional Formula of Work Done
Work $=$ Force × Displacement
We know,

Dimensional formula of Force $=$ MLT $^{-2}$
Dimensional formula of Displacement $=\mathbf{L}$
Therefore,
Dimensional formula of Work $=\mathbf{M L}^{\mathbf{2}} \mathbf{T}^{\mathbf{- 2}}$

Meaning of Work Definition Physics

Consider a block lying horizontally on the table and now it’s affected by some amount of applied force in a particular direction F and let this block gets moved to some displacement in specific direction S and the angle between the force vector and the displacement vector be then the work done by the body in order to cover this displacement is defined as W=F.S and since it’s the dot product between force vector and displacement vector so, Work done is written as W=FScos

Hence, the meaning of work done is simply that, the amount of work done by a body in order to cover a displacement of S when applied with some force of magnitude F and having an angle between force and displacement vector is calculated as W=FScos

Various Factors on which Work done by a body depends.

Some of the factors which affect the work done by a body are listed as:

1. Force. So, Work done on a body depends upon force and it’s directly proportional to the force acting on a body. On increasing the magnitude of force, the magnitude of work done is also gets increased while On decreasing the magnitude of force, the work done by a body also gets decreased.
2. Displacement. Work done by a body depends upon displacement and it’s directly proportional to the displacement covered by the body. When a body covers greater displacement the work done by the body is also greater while when the body covers less displacement, the work done by the body is also very less.

Variation of Work Done with Angle Between Force and Displacement

Work done by a force depends on the angle $(\theta)$ between the force vector and the displacement vector.
The formula of work done is:

$
W=F S \cos \theta
$

Since work is proportional to $\boldsymbol{\operatorname { c o s }} \boldsymbol{\theta}$, its value changes as the angle $\theta$ changes.
We know that:
$\cos 0^{\circ}=1$
$\cos 90^{\circ}=0$
$\cos 180^{\circ}=-1$

As the angle increases from $0^{\circ}$ to $90^{\circ}$, the value of $\cos \theta$ decreases from 1 to 0 . Therefore, work done decreases.

Different Cases
1. When $0^{\circ} \leq \theta<90^{\circ}$

Work done is positive because $\cos \theta$ is positive.
Example: Pulling a cart forward.
2. When $\theta=0^{\circ}$

Work done is maximum.

$
W=F S \cos 0^{\circ}=F S
$

Force and displacement are in the same direction.

3. When $\theta=90^{\circ}$

Work done is zero.

$
W=F S \cos 90^{\circ}=0
$

Force and displacement are perpendicular.
Example: Centripetal force in circular motion.
4. When $90^{\circ}<\theta \leq 180^{\circ}$

Work done is negative because $\cos \theta$ is negative.
Example: Friction acting opposite to motion.

Also Read:

• NCERT solutions for Class 11 Physics Chapter 6 Work, Energy and Power
• NCERT Exemplar Class 11 Physics Solutions Chapter 6 Work, Energy and Power
• NCERT notes Class 11 Physics Chapter 6 Work, Energy and Power

Examples of Work done by a Body:

In physics, work is done when a force is applied on a body and the body moves in the direction of the force. Some common examples are:

• Lifting a book from the floor: When you lift a book upward, you apply force against gravity and the book moves upward. Hence, work is done.
• Pushing a trolley: When a trolley moves forward after applying force, work is done because displacement occurs in the direction of force.
• Kicking a football: The force applied by the foot makes the ball move. Therefore, work is done.
• Pulling a bucket from a well: When you pull the rope and the bucket moves upward, work is done against gravity.
• A horse pulling a cart: The cart moves due to applied force, so work is done.

Also check-

• NCERT Exemplar Class 11th Physics Solutions
• NCERT Exemplar Class 12th Physics Solutions
• NCERT Exemplar Solutions for All Subjects

NCERT Physics Notes:

• NCERT Notes Class 11th Physics
• NCERT Notes Class 12th Physics
• NCERT Notes For All Subjects