4.2. Mechanical work

The change of the mechanical movement and energy of the body occurs in the process of power interaction of this body with other bodies. To quantify this process in mechanics, the concept of work done by force is introduced.

If the force in question is constant, and the body to which it is applied, moves progressively and straightforwardly, then the work done by force with the passage of the body path call a quantity

(4.1)

where a is the angle between the force and the direction of body movement.

Work is a scalar. If the force vector and displacement vector form an acute angle i.e. then , if a then i.e. the force acting perpendicular to the movement of the body does not perform work.

In the general case, the body can move in an arbitrary, rather complicated way (Fig. 4.2). Select the elementary part of the path on which the force can be considered constant and the displacement is rectilinear. Elementary work on this site is equal to

(4.2)

Complete work on the way determined by the integral

(4.3)