# An object with a mass of 5 kg is on a ramp at an incline of pi/12 . If the object is being pushed up the ramp with a force of  8 N, what is the minimum coefficient of static friction needed for the object to remain put?

Dec 29, 2015

The minimum coefficient of static friction needed is $0.07$.
Assuming the sistem with $x$ on the surface of ramp and $y$ on the normal of surface.
There is the orizontal component that is F(x)=|8N-(mgsin15°)|=4.7N
F(f)=CF(y)=C(mgcos15°)=4.7N
and $C = \frac{4.7}{66.33} = 0.07$.