Răspuns:
40 newtoni
Explicație:
[tex]\displaystyle{ \eta = \frac{sin \ \alpha}{sin \ \alpha + \mu \cdot cos \ \alpha} = 50 \ \% }[/tex]
[tex]\displaystyle{ \frac{1}{2} = \frac{\frac{1}{2}}{\frac{1}{2} + \mu \cdot \frac{\sqrt{3}}{2}} }[/tex]
[tex]\displaystyle{ \frac{1}{2} + \frac{1+ \mu \sqrt{3}}{2} = \frac{1}{4} }[/tex]
[tex]\displaystyle{ \mu = | -\frac{1}{2} \cdot \frac{1}{\sqrt{3}}| }[/tex]
[tex]\displaystyle{ \mu = \frac{\sqrt{3}}{6} = aprox. \ 0,28 }[/tex]
[tex]\displaystyle{ N = Gn = mg \cdot cos \ \alpha }[/tex]
[tex]\displaystyle{ N = 10 \cdot 10 \cdot \frac{\sqrt{3}}{2} = 86,5 \ N }[/tex]
[tex]\displaystyle{ Ff = \mu \cdot N = \frac{\sqrt{3}}{6} \cdot 50\sqrt{3} = \frac{50 \cdot 3}{6} = 25 \ N }[/tex]
[tex]\displaystyle{ F - Gt - Ff = 0 \rightarrow F = Gt + Ff }[/tex]
[tex]\displaystyle{ F = mg \cdot sin \ \alpha + Ff }[/tex]
[tex]\displaystyle{ F = 10 \cdot 10 \cdot \frac{1}{2} + 25 = 15 + 25 = 40 \ N}[/tex]
