[tex]\displaystyle \text{Se da:}\\ \\
m=100kg\\ \\
\alpha=30^\circ\\ \\
F=500N\\ \\
a=?\frac m{s^2}\\ \\ \\
\text{Formule:}\\ \\
\text{Pentru miscarea accelerata in jos:}\\ \\
\text{Pe axa O}_\text{x}:\\ \\ \\[/tex]
[tex]G_x-F_{fr}=m\times a\\ \\
G\times\sin\alpha-F_{fr}=m\times a\\ \\
m\times g\times\sin\alpha-F_{fr}=m\times a\\ \\ \\
\text{Observam ca nu avem }F_{fr}\text{, dar ea are aceeasi valoare pentru ambele}\\
\text {cazuri, de aceea o aflam folosind fortele din miscarea uniforma}\\ \\
\text{Pentru miscarea uniforma in sus:}\\ \\ \\[/tex]
[tex]\text{Pe axa O}_\text{x}:\\ \\ \\
F-G_x-F_{fr}=0\\ \\
F-G\times\sin\alpha-F_{fr}=0\\ \\
F-m\times g\times\sin\alpha-F_{fr}=0\\ \\
F_{fr}=F-m\times g\times\sin\alpha\\ \\ \\[/tex]
[tex]\displaystyle \text{Inlocuim si scoatem }a:\\ \\ \\
m\times g\times\sin\alpha-(F-m\times g\times\sin\alpha)=m\times a\\ \\
m\times g\times\sin\alpha-F+m\times g\times\sin\alpha=m\times a\\ \\
2\times m\times g\times\sin\alpha-F=m\times a\\ \\ \\
\boxed{a=\frac{2\times m\times g\times\sin\alpha-F}{m}}\\ \\ \\
\text{Calcule:}\\ \\
a=\frac{2\times 100\times 10\times\sin30-500}{100}=5\frac m{s^2}
[/tex]
