Work, Power and Energy

Work 
Work is said to be done by a force if the point of application of force moves in the direction of force.

                                                OR

Work is said to be done by a force when it actually moves the body through  a certain distances.


                                      
 Mathematically,          

Work done = Force (in the direction of motion)  × Distance through which Force acts.
                                                                                           
Let a force F   displaces a body placed on a horizontal surface through displacement  R,  in the direction of force  (F), then work done is given by,

 Work done = Force (in the direction of motion)  × Horizontal displacement
i.e.,        W = F.R

But when force (F) acts along a direction making an angle θ  with the direction of displacement (R), then work done is found by resolving the force.  

Since force is a vector quantity and can be resolved into two mutually perpendicular components-

(i)                        Fx = F Cos θ  
(ii)                       Fy = F Sin θ

Since  Fy component is perpendicular to the direction of motion of the body, hence it has no effect on the motion of the body i.e., No work is done by Fy component, it just balances the weight of the body. Only Fx component does work and moves the body (horizontally),

hence,       W =   Fx .R

              =   F Cos θ.R

OR            W =    F.R

Hence work may also be defined as the dot product of applied force (F) and the displacement (R) produced by force in the body.

Work is a scalar quantity and its dimensional formula is [M¹L²T^-2].

S.I. Unit of Work : The unit of work depend upon the units of force and the units of distance.
In S.I. system the unit of force is newton and unit of distance is metre.

∴         Unit of work  = newton × meter
                              = Nm
                              = Joule
The S.I. unit of work is newton metre or joule.

One Joule (or 1 Nm) is the work done by a constant force of 1 N, if it moves the body on which it acts through a distance of 1m in the direction of force.

C.G.S Unit of Work : In C.G.S system, unit of work is erg.

                                  1 erg = 1 dyne × 1 cm

One erg work is said to be done by a constant force of 1 dyne, if it moves the body on which it acts through a distance of 1 cm in the direction of force.

 S.I. units  and C.G.S units of work are related to each other by the relation.

                                  1 Joule = 10⁷ ergs.

courtesy:engineeringarchives.com