ANSWER:
0.66
STEP-BY-STEP EXPLANATION:
Free body diagram:
Therefore:
[tex]\begin{gathered} F_v=86\cdot\sin 57 \\ F_h=86\cdot\cos 57 \end{gathered}[/tex]
Vertical:
[tex]\begin{gathered} F_v=mg+N \\ N=F_v-mg \end{gathered}[/tex]
Horizontal:
[tex]\begin{gathered} F_h-F=ma \\ F=\mu N \\ \text{ Therefore:} \\ F=\mu\cdot(F_v-mg) \\ \text{ replacing:} \\ F_h-\mu\cdot(F_v-mg)=ma \end{gathered}[/tex]
We plug in each value and solve for the coefficient of friction, like this:
[tex]\begin{gathered} 86\cdot\cos 57-\mu\cdot(86\cdot\sin 57-3.63\cdot9.8)=3.63\cdot6.23 \\ \mu=\frac{86\cdot\cos 57-3.63\cdot6.23}{86\cdot\sin 57-3.63\cdot9.8} \\ \mu=0.66 \end{gathered}[/tex]
The coefficient of friction is equal to 0.66
