# Work

In physics work is defined in a specific manner, describing what is accomplished by the action of a force on an object. Work is said to be done if the force applied on the object succeeds in moving it.If no motion takes place, no work is said to be done. For example, a horse pulling a cart does work, an engine pulling a train does work, a person lifting a stone does work, a cyclist pedalling a bicycle does work and so on.

However, a person may exert a force and yet do no work, in the specific sense of the word, because the force may not produce any motion. For example, a man pushing against a wall does no work if the wall does not move.

He may sweat and tire but he does no work if he does not succeed in moving the wall. Similarly, if you hold a heavy object in your hand and stay motionless, you do not work even though you may get tried holding it. Thus for work to be done, two conditions must be fulfilled.

- A force must be exerted, and
- The force must produce motion or displacement.

# Measurement of Work

The work done by a force on a body is given by the product of the force and the displacement produced in the direction of the force. If the force**F**is applied in such a way that the body moves in the direction in which the force acts, then the work done is given by

W = FS

Where F is the magnitude of

**F**and S is the magnitude of displacement

**S**.

**F**acting in a direction inclined at an angle Î¸ with a horizontal smooth surface along which the body moves. Let

**S**be the displacement along the surface as the body moves from position A to B. The work done by the force can be calculated in the following two equivalent ways.

- From figure (b) it is clear that the component of the displacement vector
**S**in the direction of the force is S cosÎ¸. Hence, the work done is given by,

W = Magnitude of force ï component of the displacement in the direction of the force vector**F**

**= F**ï**AC = F (S cosÎ¸)** - From figure (c) it is clear that the component of the force F in the direction of the displacement is F cosÎ¸.

W = (F cosÎ¸) S

W = Component of the force in the direction of the displacement vector**S**ï magnitude of the displacement.

Thus, measured either way, work is given by

W = FS cosÎ¸

In vector notation this is written as W =**F****S**= FS cos Î¸

i.e. work is the scalar product of force and displacement.

**Special Cases**

**Case (i):**If

**F**and

**S**are in the same direction, Î¸ = 0 then W = FS.

**Case (ii):**On the other hand, if

**F**and

**S**are at right angles to each other,

Î¸ = 90Â°, then W = FS cos90Â° = 0.

**Case (iii):**If

**F**and

**S**are in the opposite direction, Î¸ =180.

Then W = FScos180 = -FS

As an example, consider a man carrying a bucket of water, walking on a level road with a uniform velocity. Since the velocity is uniform, there can be no force in the horizontal direction, i.e. the direction in which the bucket is being carried. The force that the man exerts on the bucket is perpendicular to the direction of motion (i.e. against gravity). Since the force and displacement are at right angles to each other, no work is done on the bucket while carrying it.

# Unit of Work

Work, being a scalar product of two vector quantities is a scalar quantity. The SI unit of work is called the joule (symbol J). One joule of work is said to be done when a force of 1 newton acting on a body moves it through a distance of*1 m in the direction of the force.*