An object with a mass of #5 kg# is on a plane with an incline of # -(5 pi)/12 #. If it takes #12 N# to start pushing the object down the plane and #2 N# to keep pushing it, what are the coefficients of static and kinetic friction?
If angle of inclination is
(see explanation regarding angle)
We're asked to find the coefficient of static friction
We'll call the positive
There is no net vertical force, so we'll look at the horizontal forces (we WILL use the normal force magnitude
We're given that the object's mass is
Since the angle is
Which is much more realistic considering the object remains stationary (due to static friction) unless a force acts on it.
The formula for the coefficient of static friction
Since the object in this problem "breaks loose" and the static friction eventually gives way, this equation is simply
Since the two vertical quantities
The coefficient of static friction is thus
The coefficient of kinetic friction
The coefficient of kinetic friction is thus