# An object with a mass of 12 kg is on a plane with an incline of  - pi/6 . If it takes 6 N to start pushing the object down the plane and 3 N to keep pushing it, what are the coefficients of static and kinetic friction?

Coefficient of Static Friction ${\mu}_{s} = 0.05891329277$
Coefficient of Kinetic Friction ${\mu}_{k} = 0.02945664639$

#### Explanation:

The given data:

$\theta = \frac{- \pi}{6} = - {30}^{\circ}$
mass $m = 12 \text{ }$kg

Force needed to move the object down ${F}_{s} = 6 \text{ }$N
Force needed to continue moving the object down ${F}_{k} = 3 \text{ }$N

Compute the normal force ${F}_{n}$

${F}_{n} = m \cdot g \cdot \cos \left(\frac{\pi}{6}\right) = 12 \cdot \left(9.8\right) \cdot \cos \left(\frac{\pi}{6}\right) = 101.8445875 \text{ }$N

Compute for the Coefficient of Static Friction ${\mu}_{s}$

${F}_{s} = {\mu}_{s} \cdot {F}_{n}$
$6 = {\mu}_{s} \left(101.8445875\right)$

${\mu}_{s} = \frac{6}{101.8445875}$
${\mu}_{s} = 0.05891329277$

Compute for the Coefficient of Kinetic Friction ${\mu}_{k}$

${F}_{k} = {\mu}_{k} \cdot {F}_{n}$
$3 = {\mu}_{k} \left(101.8445875\right)$

${\mu}_{k} = \frac{3}{101.8445875}$

${\mu}_{k} = 0.02945664639$

God bless....I hope the explanation is useful.