VIII The law of conservation of energy.

LCE. for conservative systems:

If the system are only conservative forces, the total energy of the system remains constant.

W = const.

LCE.for dissipative systems (not conservative systems):

If the system dissipative forces, the change in the total mechanical energy equal to the work of these forces.

ΔW = A_Fdiss

In the case of the dissipative forces are converting mechanical energy into other forms of energy (with the force of friction - in the heat: contact body heat). However, if any transformations, energy conversions performed universal natural law - the law of conservation of energy: energy can change from one form to another, and redistributed within the system, but its total in a closed system must remain constant. If the system is not closed, then the change of its energy in the interaction with the environment is equal to the energy that the system receives from the outside.

IX. Is elastic and inelastic collisions.

Stroke is called a significant change in the speed for the very small amount of time.
Central strike called at which the velocity vector direction of colliding bodies in a straight line connecting their centers. In the collision of two bodies is difficult to analyze and take into account all the forces acting on them. Often the solution of problems of a clash of bodies with these initial conditions it is important to know just the end result. This can be obtained using the law of conservation of momentum and energy conservation.

Problem is usually stated as follows:

the known momentum and energy bodies before the collision to determine the values of these quantities after the collision.

There are two extreme types of stroke: a completely elastic and completely inelastic.
Is called the elastic impact such a hit, in which the mechanical energy of the bodies is not transferred to other non-mechanical forms of energy.

With this impact kinetic energy is transferred in whole or in part to the potential energy of the elastic deformation. Then the body returns to its original shape, pushing each other. As a result, the potential energy of the elastic deformation again converted to kinetic energy of the body and fly at speeds of magnitude and direction of which is determined by two conditions – L.C.E. and L.C.M.
Is called inelastic impact, in which: 1) the strain energy does not arise. 2) The kinetic energy of a fully or partially transferred to the inside. 3) After the shock of the body move at the same speed or at rest.

L.C.M.:                                             

x:                                                       

L.C.E.:                                                          

Application:
1) The collision of identical spheres (in molecular physics):

m₁ = m₂, then  

ie body exchange speed.

2) Hit the ball on the massive wall.

Speed after the impact of the massive body changes slightly. As a result of hitting the wall from the increase in momentum, a relatively small amount of energy

Inelastic collision:

L.C.M.:                                             

L.C.E.:                                                          

- energy transformed into other forms of energy

If        

then

If m₂ >> m₁, then u << v₁ and almost all W_K1 striker converted into heat.

At absolutely elastic collision u₁ - u₂ = - (v₁ - v₂), ie relative speed of the balls after the collision is equal in magnitude and direction opposite to their relative velocity before impact. When completely inelastic collision the relative velocity after the collision is equal to 0, because u₁ = u₂ = u. When partially inelastic collision the relative velocity after the collision is equal to a percentage of the relative velocity before impact

where ε (0 ≤ ε ≤ 1), the coefficient of restitution of the relative velocity at impact. When you hit a steel balls ε = 0,9; balls of ivory ε = 0.89; for lead ε = 0,2; glass ε = 0.95.

X. Power.

The work done per unit of time is called power. The instantaneous power is the ratio of the unit work to a small period of time during which the work is performed.

The average power is the ratio of work for the entire period of time during which the work is performed