# An object with a mass of 6 kg is on a plane with an incline of  - pi/6 . If it takes 18 N to start pushing the object down the plane and 1 N to keep pushing it, what are the coefficients of static and kinetic friction?

Feb 16, 2016

${\mu}_{s} = \frac{3 \sqrt{3}}{10}$
${\mu}_{k} = \frac{1}{20 \sqrt{6}}$

#### Explanation:

$f = \mu N$

$N = m g \cos \theta = m g \frac{\sqrt{3}}{2}$

Now that we have our prerequisites
Lets consider the static case first

$18 = \mu m g \frac{\sqrt{3}}{2}$
$18 = \mu 4 \cdot 10 \frac{\sqrt{3}}{2}$

Solving we get

${\mu}_{s} = \frac{3 \sqrt{3}}{10}$

Lets consider the kinetic case

$1 = {\mu}_{k} \cdot 4 \cdot 10 \cdot \frac{\sqrt{3}}{2}$

Solving we get

${\mu}_{k} = \frac{1}{20 \sqrt{6}}$