[tex]\displaystyle \alpha=30^o\\\\m=50~kg\\\\F=294~N\\\\F_x+G_t=ma\\\\ cos\alpha=\frac{F_x}{F}\Rightarrow Fcos\alpha=F_x\Rightarrow F_x=Fcos\alpha\\\\F_x+G_t=ma\Rightarrow Fcos\alpha+mgsin\alpha=ma\Rightarrow\\\\\Rightarrow 294\cdot cos30^o+50\cdot10\cdot sin30^o=50a\Rightarrow294\cdot\frac{\sqrt{3}}{2}+500\cdot\frac{1}{2}=50a \Rightarrow\\\\\Rightarrow147\cdot1,73+250=50a\Rightarrow 254,31+250=50a\Rightarrow504,31=50a\Rightarrow\\\\\Rightarrow a=\frac{504,31}{50} \Rightarrow \mathbf{a\approx10\frac{m}{s^2}}[/tex]
[tex]\displaystyle N+F_y=G_n \Rightarrow N=G_n-F_y\\ \\ sin\alpha=\frac{F_y}{F} \Rightarrow Fsin\alpha=F_y \Rightarrow F_y=Fsin\alpha\\ \\ N=G_n-F_y \Rightarrow N=mgcos\alpha-Fsin\alpha \Rightarrow \\ \\ \Rightarrow N=50 \cdot 10 \cdot cos30^o-294 \cdot sin30^o \Rightarrow N=500 \cdot \frac{\sqrt{3} }{2} -294 \cdot \frac{1}{2} \Rightarrow \\ \\ \Rightarrow N=250 \cdot 1,73 -147 \Rightarrow N=432,5-147 \Rightarrow \mathbf{N=285,5~N}[/tex]
