An object with a mass of #6 kg# is on a plane with an incline of # - pi/4 #. If it takes #24 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?
u(static) = 0.58, u(kinetic) = 0.22
To start motion, Force down = Opposing Frictional Force
Opposing Frictional Force = u(static) Normal Force.
Weight down = mg = 6 (9.8 m/s^2) = 58.8 N
Normal Force is found with trigonometry = 58.8 cos pi/4 =
58.8 [sqrt 2] / 2 = 41.6 N
So .... 24 = u(static) 41.6 => u(static) = 0.58
Similarly 9 = u(kinetic) 41.6 => u(kinetic) = 0.22