Kinetic energy.  Power and Efficiency.

Learn the following words and word combinations by heart:

capacity	нагрузка; функциональные возможности, ёмкостное сопротивление
convert (into)	превращать
dissipate (to)	рассеиваться (об энергии или мощности), исчезать
efficiency     electrical ~   mechanical ~ overall ~   thermal ~	коэффициент полезного действия, КПД; отношение произведённой работы к использованной энергии полный кпд (сети); электрический коэффициент полезного действия механический кпд суммарный коэффициент полезного действия  всей установки; полная производительность, термический кпд;  КПД теплового двигателя
energy ~ output   accumulation of ~ deliver ~ depletion of ~ electrical ~ loss   large amount of ~ loss of ~ thermal ~ loss	потреблённая электроэнергия; электроэнергия выходная мощность, вырабатываемая энергия; выдача энергии накапливание энергии поставлять, передавать энергию уменьшение, расход энергии потери электроэнергии, энергетические потери большое количество энергии потери энергии потери тепловой энергии (или термической энергии)
kinetic friction	трение движения, кинетическое трение
operate uniformly	функционировать непрерывно,  постоянно
point of application of the force	точка приложения силы
power  develop a ~	питание, электроснабжение; мощность; энергия        достигать, развивать мощность
surroundings	естественные условия
total work	совокупная,  суммарная,  общая работа
unit	единица физической величины
unity	единица (число), единое целое

Ex.1. Look at Appendix 1 and read the following mathematical symbols and abbreviations.

T = ½ m v ² ;     U _1-2 = T₂-T₁ = ∆ T;   T₁ + U _1-2 = T₂;    e_{m =} P _output: P _input

 

Part 1. Kinetic energy.

The kinetic energy T of the particle is defined as

T = ½ m v ² (3)

and is the total work which must be done on the particle to bring it from a state of rest to a velocity v. Kinetic energy T is a scalar quantity with the units of N•m  or joules (J). Kinetic energy is always positive, regardless of the direction of the velocity. Equation 3 may be restated as 

U _1-2 = T₂-T₁ = ∆ T.   (4)

which is the work-energy equation for a particle. The equation states  that the total work done by all forces acting on a particle during an  interval of its motion from condition 1 to condition 2 equals the corresponding change in kinetic energy of the particle. Although T is always positive, the change ∆ Tmay be positive, negative, or zero.

When written in this concise form, Eq. 4 tells us that the work always  results in a change of kinetic energy.

Alternatively, the work-energy relation may be expressed as the initial kinetic energy T₁ plus the work done U _1-2 equals the final kinetic energy T₂ or

T₁ + U _1-2 = T₂ (4 a)

When written in this form, the terms correspond to the natural sequence of events. Clearly, the two forms 4  and 4 a are equivalent.

We now see from Eq. 4 that a major advantage of the method of work and energy is that it avoids the necessity of computing the acceleration and leads directly to the velocity changes as functions of the forces which do work. Further, the work-energy equation involves only those forces which do work and thus give rise to changes in the magnitude of the velocities.

We consider now two particles joined together by a connection which is frictionless and incapable of any deformation. The forces in the connection constitute a pair of equal and opposite forces, and the points of application ofthese forces necessarily have identical displacement components in the direction of the forces. Hence, the net work done by these internal forces is zero during any movement of the  system of the two connected particles. Thus,  Eq. 4  is ap­plicable to the entire system, where U _1-2  is the total or net work done on the system by forces external to it  and ∆Tis the change, T₂-T₁ in the total kinetic energy of the system. The total kinetic energy  is the sum of the kinetic energies  of both elements of the system. It may now be observed that a further advantage of the work – energy method is that it permits the analysis of a system of particles   joined in the manner described without dismembering the system.

Application  of the work-energy method  calls for an isolation of the particle or system under consideration. For a single particle a free-body diagramshowing all externally applied forces should be drawn.  For a system of particles rigidly connected without springs, an active – force diagram that shows only those external forces which do work  (active forces) on the entire system may be drawn.