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Using the law of conservation
of energy, compare the right sides of
equalities (7.9) and (7.10)
1
P h   l д   N  . (7.11)
l
д
д
2
Using the expression of
Hooke's law l   N l EF ,
д д
determine N and substitute in the
д
formula (7.11):
1 EF
2
h   l   l  .
P
д д
2 l
(7.12)
Figure 7.3 Consider that the absolute
elongation of the rod under static load
apposition (fig. 7.3, b)
Pl
l   ,
c
EF
then dividing the left and right side of the equation (7.12) by the
stiffness of the rod EF l , come to the consolidated quadratic
equation
2
l   2 l l   2h l  .
0
д c д c
Having solved it with respect to l , we obtain
д
 2h 
2
l
l       2h l    1 1  . (7.13)
l
l
д c c c c  l  
 c 
In the last formula it should finally take the plus sign
because the minus sign does not meet the physical content of the
problem (obviously, l   ).
l
д c
Denoting the coefficient of dynamic longitudinal impact
as
2h
k  1 1 , (7.14)
д
l 
c
we obtain
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