# An object with a mass of 4 kg is on a ramp at an incline of pi/8 . If the object is being pushed up the ramp with a force of  2 N, what is the minimum coefficient of static friction needed for the object to remain put?

Feb 3, 2018

$0.36$

#### Explanation:

Component of weight of the object acting downward along the inclined plane is $m g \sin \theta = 4 \cdot 10 \cdot \sin \left(\frac{\pi}{8}\right) = 15.30 N$

So,unbalanced force acting downwards along the inclined plane is $\left(15.30 - 2\right) N = 13.30 N$

So,this amount of force must be supplied by the frictional force upwards.

So,frictional force acting here is $\mu \cdot N = \mu \cdot m g \cos \left(\frac{\pi}{8}\right)$ ($\mu$ is the desired coefficient of friction)

So, $\mu m g \cos \left(\frac{\pi}{8}\right) = 13.50$

or, $\mu = 0.36$