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 E   E P   E P 
P
F  ( i  j  k )  gradE   E . (5.34)
P
P
x  y  z 

5.6 Energy of System. Conservation of Energy

The principle of conservation of energy states that energy cannot be

created or destroyed, although it can be changed from one form to another.
Thus in any isolated or closed system, the sum of all forms of energy
remains constant. The energy of the system may be interconvert among

many different forms; mechanical, electrical, magnetic, thermal, chemical,
nuclear, and so on
There are many ways, in which the principle of conservation of energy

may be stated, depending on the intended application. Of particular interest
is the special form of the principle known as the principle of conservation of
mechanical energy,which states that the mechanical energy of any system of

bodies connected together in any way is conserved.
The mechanical energy (or the total mechanical energy) is the sum of
the mechanic motion energy W and the energy of interactions W :
k
p
E  E  const (5.35)
P
K
The system is called conservative if all external potential forces are
stationary {aWjat - 0) and all external and internal non-potential forces do

not produce the work . In this case:
dE  d (E K  E P )  0 and E  const . (5.36)
The law of energy conservation for conservative system.The mechanical

energy of conservative system does not change with time.

5.7 Aplication of the Laws of Conservation to Collisions of Bodies

. When two bodies collide, the laws of impulse conservation and energy
conservation are both always applicable. But in some collisions a part of

the kinetic energy of the bodies is transformed into some non-mechanical
forms of energy such as heat or sound. In this case the application of the
law of energy conservation to the problem becomes exceedingly difficult

because many kinds of energy may be involved, some of which are
difficult to measure.
If a steel ball is dropped on a steel plate, the ball and the plate are

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