[tex]\displaystyle\\
\texttt{Se da:} \\ \\
\frac{ D_2}{ D_1} = 20~KN \\ \\
F_{2} =120~KN\\ \\
L_{2} =0,6~KJ\\ \\
\texttt{Se cere:}\\ \\
a)~~ F_{1} = ?\\ \\
b)~~ d_{1}=?\\ \\
~~~~ d_{2} =?\\ \\
Rezolvare:\\\\
a)\frac{ F_{1} }{ S_{1}}= \frac{ F_{2} }{ S_{2} } ~~\Longrightarrow~~ \frac{ F_{2} }{ F_{1} } = \frac{ S_{2} }{ S_{1} } = \Big(\frac{ D_{2} }{ D_{1} } \Big)^2= 20^{2} =\boxed{400}\\ \\
\Longrightarrow~~ F_{1}= \frac{ F_{2} }{ 400} = \frac{120.000}{400} = \boxed{300N}
[/tex]
[tex]\displaystyle\\ \\
b)~ L_{2} = F_{2} \times d_{2}\\ \\
d_{2}= \frac{ L_{2} }{ F_{2} } = \frac{0.6~KJ}{120~KN} = \frac{600}{120.000} = \frac{1}{200} =0,005~m=\boxed{5~mm}\\ \\
V_{1}= S_{1}\times d_{1} \\ \\
V_{2} =S_{2}\times d_{2} \\ \\
\texttt{Dar }V_{1}= V_{2} ~~~~~(volumele) \\ \\
S_{1}\times d_{1}=S_{2}\times d_{2} \\ \\
\Longrightarrow~~~ d_{1}= \frac{ S_{2} }{ S_{1} }\times d_1 = 400 \times 5~mm = 2000~mm =\boxed {2~m} [/tex]
