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The work done by the force F during displacement dr is mathematically defined as

 (dot product)

The magnitude                = dS

dU  = F dS  cos a

= (f cos a ) dS

= f t ds

  = F cos a

Thus, the work can also be defined as the product of the force and the displacement in the direction of force or the product of the component of the force in the direction of  displacement and the displacement. Note that F n force does no work because the angle between ds and F; is 90° . As cos 90° = 0 so F n cos a. x ds


If the force F1 is in the same direction of the displacement, the work done is positive and if F1 acts opposite to the direction of displacement the work done is negative.


The unit (S.I.) of work is N-m or Joule. The unit J Goule) is applied to work and energy only and not to moment of a force which is also N-m.


In general,

And                  = area under the curve

Ft – S

Ul-2 is the work done on the body, so Ul-2 is negative.