Question

Can I know the answer first then we go with the steps so I can compare?

Answer 1

0.66

Explanation:

Free body diagram:

Therefore:

`\begin{gathered} F_v=86\cdot\sin 57 \\ F_h=86\cdot\cos 57 \end{gathered}`

Vertical:

`\begin{gathered} F_v=mg+N \\ N=F_v-mg \end{gathered}`

Horizontal:

`\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}`

We plug in each value and solve for the coefficient of friction, like this:

`\begin{gathered} 86\cdot\cos 57-\mu\cdot(86\cdot\sin 57-3.63\cdot9.8)=3.63\cdot6.23 \\ \mu=(86\cdot\cos 57-3.63\cdot6.23)/(86\cdot\sin 57-3.63\cdot9.8) \\ \mu=0.66 \end{gathered}`

The coefficient of friction is equal to 0.66