# An object with a mass of 12 kg is on a plane with an incline of  -(3 pi)/8 . If it takes 25 N to start pushing the object down the plane and 15 N to keep pushing it, what are the coefficients of static and kinetic friction?

May 2, 2016

${\mu}_{s} = 2.97$ and ${\mu}_{k} = 2.75$

#### Explanation:

Here, $\theta = \frac{3 \pi}{8}$

As we can observe, for both the cases (static and kinetic), the force applied is given as:

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

so, putting $m = 12 k g$, $\theta = \frac{3 \pi}{8}$, and $g = 9.8 m {s}^{-} 2$

${F}_{s , k} = 45 {\mu}_{s , k} - 108.65$ ($F$ is expressed in Newtons)

${F}_{s} = 25$ gives:

${\mu}_{s} = 2.97$

and, ${F}_{k} = 15$ gives:

${\mu}_{k} = 2.75$