Elementary work of force of F at infinitesimal change of position of a body of dS is called the projection of F(s) of this force to axis s increased by movement size: dA = F(s) · dS = F · dS · cos(α), where α - a corner between vectors of F and dS. Elementary work can be written down also in the form of a scalar product of the called vectors: dA = (F, dS).
Instruction
1. To find a job of a body on all way, it is necessary to break this way into infinitesimal pieces mentally. Force F on each of them can conditionally be considered as a constant. In a limit, lengths of all elementary movements direct to zero, and their number — to infinity. At addition of elementary works and transition to a limit the integral turns out: A = ∫ (F, dS).
2. So that to find the mechanical job made by a body on all way of L it is necessary to integrate its function of elementary work on L. Work is called curvilinear integral of force of F along movement of L.
3. Mechanical work — size additive. It means that at impact on a body of two or more than forces, work of the resulting force is equal to the sum of elementary works of these forces: A = A1 + A2, since F = F1 + F2.
4. Unit of mechanical work is the Joule. The physical meaning of one joule — work of force in one newton when moving a body of one meter if the directions of force and movement coincide.
5. If in a task it is required to find a mechanical job, place all mechanical forces operating on a body: gravity, reactions of a support, friction, elasticity , etc. Think what forces influence movement of a body and what — are not present.
6. Proceeding from statements of the problem, try to write down function of elementary work. You need to establish dependence of force on any changing physical quantity (time, a way, coordinate and so forth).
7. Integrate the received function on length of all trajectory. Use tabular values of the simplest integrals and a formula of integration.