Question

An object with a mass of `8 kg` is on a plane with an incline of `- pi/12`. If it takes `12 N` to start pushing the object down the plane and `9 N` to keep pushing it, what are the coefficients of static and kinetic friction?

Answer 1

I assume that the angle of inclination is `pi/12` instead provided ,
we know for that

from the FBD diagram we can conclude that

`f_("static")=mgmucostheta`

`f_("dynamic")=mgmusintheta`

substituting the values you can get your answer (here a in the image is the angle you provided)

`mu_("static")=f_("static")/(mgcostheta)`

`mu_("dynamic")=f_("dynamic")/(mgsintheta)`