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physics the word work is used in a restricted and carefully defined
method.
External forces cause the alteration of mechanical motion.
 A
The elementary work  A of the force F on the small

displacement dr of the point of
force application is the scalar
product of vectors F and dr (Fig.

4.3)
 
A  (F ) r d  (5.9)

or in scalar form

Figure 5.3   FA  dS  cos  , (5.10)
where dS is elementary distance

dS  r d and  angle between

force end displacement
(Note that we use designation A , because A is not the total
differential of continuous function , i.e. there is no sense to define work in

a point without displacement)
Work is measured in joule (J): 1J = N m. One joule is the work done
when a force of one newton acts through a distance of one meter.

The work is not produced if     when the force vector is
2
perpendicular to the direction of the velocity .

If force is variable quantity given by function S  f (t ) work done
by this variable force can calculated as definite integral

S 2
A   f (S )ds (5.11)

S 1
i.e sum of elementary work
A  f ( S) dS (5.12)

Suppose, force-distance graph
is arbitrary curve as shown in

fig.5.4
Consider so small distance dS that
force F is constant , then we can
assume that elementary work

 A  FdS is numerically equal
area of thin strip with height F
and initially small width dS

Obviously , the total work done by
Figure 5.4

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