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 #6 N# to keep pushing it, what are the coefficients of static and kinetic friction?
1 Answer
Answer:
Explanation:
We're asked to find the coefficients of static friction
NOTE: Since the given angle is negative (
I will use this angle for the problem's work.
The coefficient of static friction
where

#f_s# is the magnitude of the static friction force (the maximum allowed force before the object begins to move) 
#n# is the magnitude of the normal force exerted by the incline plane (equal to#mgcostheta# )
We realize that the object starts to move when the static friction force is equal in magnitude to the other forces acting on the object (gravitational and applied force).
Thus,
We're given the mass is
The magntide of the normal force
Thus,
The coefficient of static friction
where
The magnitude of the kinetic friction force will be equal to the applied pushing force (
Therefore, we have