The free body diagram of the object can be shown as,
The net force which acts along the horizontal axis can be expressed as,
[tex]F=mg\sin \theta-\mu N[/tex]According to free body diagram,
[tex]N=mg\cos \theta[/tex]Plug in the known value in the above equation.
[tex]\begin{gathered} F=mg\sin \theta-\mu mg\cos \theta \\ \mu mg\cos \theta=F-mg\sin \theta \\ \mu=\frac{F}{mg\cos\theta}-\frac{mg\sin \theta}{mg\cos \theta} \\ =\frac{F}{mg\cos\theta}-\tan \theta \end{gathered}[/tex]Substitute the known values,
[tex]\begin{gathered} \mu=\frac{-13.89\text{ N}}{(51.40kg)(9.8m/s^2)\cos32.88^{\circ}}(\frac{1kgm/s^2}{1\text{ N}})-\tan 32.88^{\circ} \\ =-\frac{0.028}{0.84}-0.646 \\ =-0.033-0.646 \\ =-0.679 \end{gathered}[/tex]Thus, the coefficient of kinetic friction is 0.679 and negative sign indicates that the frictional force is in opposite direction of motion of object.
