# Work and Work Done By A Constant Force

## Work

Work is said to be done by a force, when the body is displaced actually through some distance in the direction of the applied force. Thus, work is done on the body only if the following two conditions are satisfied.

(I) A force acts on the body.

(II) The point of application of the force moves in the direction of the force.

Example:- Work is done when an engine pulls a train.

### Work Done By A Constant Force

Work done by the constant force is the product of component of force in the direction of the displacement and the magnitude of the displacement.

If a constant force F is applied on a body and the body has a displacement S in the direction of applied force, then

Work done on the body by the force F is given by

Work done W = F.S

Thus, work done by a force is the dot product of force and displacement.

#### Work Done When Force and Displacement Are Inclined To Each Other

Sometimes the displacement S is not in the direction of force F.

In such case, we find the work done by resolving F into two rectangular components.

Thus, work done is the dot product of force and displacement vector. Hence, work done is a scalar quantity.

Here two cases can be considered.

#### Dimensional Formula

Work = Force × Displacement

[W] = [F][S]

[W] = [MLT⁻²][L]

W = [ML²T⁻²]

#### Units Of Work

The units of work are two types.