Work

If a force displaces an object, the work is said to be done. (Here force is the net force and there should be a net displacement of the object).



Magnitude of Work
The amount of work done by a force is equal to the product of the force and the displacement of the point of application of the force in the direction of force. Mathematically work is expressed as the following
     W = F × S,
Where 
     W = Work done on an object
      F = Net  force on the object
      S = Displacement of the object

If the displacement of the body, $\stackrel{}{}$$\overrightarrow{\text{S}}$  is in a direction making an angle, θ with the direction of force, $\stackrel{}{}$$\overrightarrow{\text{F}}$  the amount of work done is equal to the product of

i. Magnitude of force
ii. Magnitude of displacement and
iii. Cosine of the angle between the directions of force F and the displacement. i.e.,
                                   W = $\left|\overrightarrow{\text{F}}\right|$ $\times$$\left|\overrightarrow{\text{S }}\right|$×cos θ

Since force, $\overrightarrow{\text{F} }$  and displacement, $\overrightarrow{\text{S}}$  are the vectors and work is a scalar quantity, work done is expressed as the following in the vector form

 W = $\overrightarrow{\text{F}\text{.}}$ $\overrightarrow{\text{S}}$

Thus work is expressed as a scalar product (or the dot product) of force and displacement vectors.

Note:The Scalar product of two vecctors is a scalar.

The work done is measured in joule in the SI system after the scientist James Prescott Joule.
erg is the CGS unit of work.

Conditions for Work to be Done:
    •  A net force should act on an object.
    •  The object must be displaced in the direction of the net force.
    •  The angle between the net force acting and the Displacement of the object should not be perpendiculatr to each other.

Joule is defined as the work done when the net force of one newton acts on a body and displaces it in the direction of the force by one metre.

Work done could be either positive or negative.

    •  When both the force and the displacement are in the same direction, positive work is done.
    •  When force acts in a direction opposite to the direction of Displacement, the work done is negative.