[tex]\displaystyle Se~da:\\ \\
x,\alpha,s\\ \\
\mu=?\\ \\ \\
Formule:\\ \\
Pe~panta:\\ \\
x=\frac{\Delta v^2}{2\times a_1}\\ \\
x=\frac{v_1^2-v_0^2}{2\times a_1},~unde~v_0=0\\ \\
x=\frac{v_1^2}{2\times a_1}\\ \\
v_1^2=2\times x\times a_1\\ \\ \\[/tex]
[tex]\displaystyle Pe~O_y:\\ \\
N-G_y=0\\ \\
N=G\times \cos\alpha\\ \\
N=m\times g\times\cos\alpha \\ \\ \\
Pe~O_x:\\ \\
G_x-F_{fr}=m\times a_1\\ \\
G\times\sin\alpha-\mu\times N=m\times a_1\\ \\
m\times g\times\sin\alpha-\mu\times m\times g\times \cos\alpha=m\times a_1\\ \\
a_1=g\times(\sin\alpha-\mu\times\cos\alpha)\\ \\ \\[/tex]
[tex]\displaystyle v_1^2=2\times x\times g\times(\sin\alpha-\mu\times\cos\alpha)\\ \\ \\
Pe~orizontala:\\ \\ \\
s=\frac{\Delta v^2}{2\times a_2}\\ \\
s=\frac{v_2^2-v_1^2}{2\times a_2},~unde~v_2=0\\ \\
s=\frac{-v_1^2}{2\times a_2}\\ \\
v_1^2=-2\times s\times a_2\\ \\ \\[/tex]
[tex]\displaystyle Pe~O_y:\\ \\
N-G=0\\ \\
N=m\times g\\ \\ \\
Pe~O_x:\\ \\
-F_{fr}=m\times a_2\\ \\
-\mu\times N=m\times a_2\\ \\
-\mu\times m\times g=m\times a_2\\ \\
a_2=-\mu\times g\\ \\ \\
v_1^2=2\times s\times (-\mu\times g)\\ \\ \\[/tex]
[tex]\displaystyle Egalam:\\ \\
2\times x\times g\times(\sin\alpha-\mu\times\cos\alpha)=2\times s\times \mu\times g\\ \\
x\times(\sin\alpha-\mu\times\cos\alpha)=s\times\mu\\ \\
x\times \sin\alpha-x\times\mu\times\cos\alpha=s\times\mu\\ \\
s\times\mu+x\times\mu\times\cos\alpha=x\times\sin\alpha\\ \\
\mu\times(s+x\times\cos\alpha)=x\times\sin\alpha\\ \\ \\ \\ \\
\mu=\frac{x\times\sin\alpha}{(s+x\times\cos\alpha)}[/tex]
