An object with a mass of 14 kg is on a plane with an incline of  -(5 pi)/12 . If it takes 12 N to start pushing the object down the plane and 7 N to keep pushing it, what are the coefficients of static and kinetic friction?

$4.07 , 3.93$

Explanation:

The force $F$ required to push an object of mass $m = 9$ kg downward on an inclined plane at an angle $\theta = - \frac{5 \setminus \pi}{12} = - {75}^{\setminus} \circ$ & coefficient of static friction $\setminus {\mu}_{s}$ is given as

$F = \setminus {\mu}_{s} m g \setminus \cos \setminus \theta - m g \setminus \sin \setminus \theta$

$\setminus {\mu}_{s} = \setminus \frac{F + m g \setminus \sin \setminus \theta}{m g \setminus \cos \setminus \theta}$

$\setminus {\mu}_{s} = \setminus \frac{12 + 14 \setminus \times 9.81 \setminus \sin {75}^{\setminus} \circ}{15 \setminus \times 9.81 \setminus \cos {75}^{\setminus} \circ}$
$= 4.07$

Similarly, when the motion starts, then the force (F) required to keep the object moving on the plane is given as

$F = \setminus {\mu}_{k} m g \setminus \cos \setminus \theta - m g \setminus \sin \setminus \theta$

$\setminus {\mu}_{k} = \setminus \frac{F + m g \setminus \sin \setminus \theta}{m g \setminus \cos \setminus \theta}$

$\setminus {\mu}_{k} = \setminus \frac{7 + 14 \setminus \times 9.81 \setminus \sin {75}^{\setminus} \circ}{15 \setminus \times 9.81 \setminus \cos {75}^{\setminus} \circ}$
$= 3.93$