[tex]\mu = 0.177[/tex]
Explanation:
Let's look at the forces on the two axes:
[tex]x:\:\:\:F - f_n = F - \mu N = 0\:\:\:\:\:\;(1)[/tex]
[tex]y:\:\:\:N - mg = 0\:\:\:\:\:\:\:\:\:(2)[/tex]
Substituting (2) into (1) and solving for [tex]\mu[/tex], we get
[tex]F = \mu mg[/tex]
[tex]\mu = \dfrac{F}{mg} = \dfrac{12.0\:\text{N}}{(6.9\:\text{kg})(9.8\:\text{m/s}^2)} = 0.177[/tex]
