# Work

## Work

When a body is displaced by applying a force on it, then work is said to be done. Example., a girl pulls a trolley and the trolley moves through a distance. In this way, she has exerted a force on the trolley and it is displaced. Hence, work is done.

If a body is displaced by a distance (s) on applying a force (F) on it, then the work was done

W= F.s

Thus, work can be defined as ‘work done by a force on an object is equal to the magnitude of the force multiplied by the distance moved in the direction of the force.

The SI unit of work is newton-meter (N-m) or joule (J) and its CGS unit is erg. It is a scalar quantity, it has only magnitude and no direction.

If F=1 N and s=1 m, then work done by the force will be 1 J.

1 joule = 107 erg

### Work done by a Force Acting at an angle

When force F acts on an object in such a direction that it makes an angle θ with the direction of displacements the work done by the force

W=Fscosθ

Value of work will be maximum at θ=0º and minimum at θ=90º

### Types of Work

There are three types of work

### Positive work

When the force and displacement are in the same direction, then work done will be positive (i.e., work is done by force).

e.g., a boy pulls an object towards himself.

#### Negative work

When the force and displacement are in opposite directionthen work done will be negative (i.e., work is done against force.)

e.g., a body is made to slide over a rough horizontal surface, then frictional force acts in the direction opposite tot he direction of displacement, so work done by friction will be negative.

#### Zero Work

When the force and displacement are in perpendicular direction, then work done is zero e.g.,

• If a coolie is moving forward carrying load on his head, in this case force is acting vertically downward (weight of load) and displacement is along horizontal direction, so work done is zero.
• If a body is moving on circle, then after completing one circle work done is zero, because of zero displacement.