# An object with a mass of 10 kg is on a plane with an incline of  - pi/4 . 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?

Mar 9, 2018

#### Answer:

${\mu}_{s} = 0.173$
${\mu}_{k} = 0.101$

#### Explanation:

$\frac{\pi}{4}$ is $\frac{180}{4} \mathrm{de} g = 45 \mathrm{de} g r e e s$

The mass of 10Kg on the incliine resolves to a 98N force vertically.
The component along the plane will be :

$98 N \cdot \sin 45 = 98 \cdot .707 = 69.29 N$

Let the static friction be ${\mu}_{s}$

Static Friction force =${\mu}_{s} \cdot 98 \cdot \cos 45 = 12$

${\mu}_{s} = \frac{12}{98 \cdot 0.707} = 0.173$

Let kinetic friction be ${\mu}_{k}$

Kinetic Friction force =${\mu}_{k} \cdot 98 \cdot \cos 45 = 7$

${\mu}_{k} = \frac{7}{98 \cdot 0.707} = 0.101$