# An object with a mass of #8 kg# is on a plane with an incline of # - pi/6 #. If it takes #9 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?

##### 1 Answer

The static coefficient of friction is

The kinetic coefficient of friction is

#### Explanation:

For our diagram,

If we apply Newton's Second Law up perpendicular to the plane we get:

#R-mgcostheta=0#

#:. R=8gcos(pi/6) \ \ N#

Initially it takes

# D+mgsin theta -F = 0 #

# :. F = 9+8gsin (pi/6) \ \ N#

And the friction is related to the Reaction (Normal) Force by

# F = mu R => 9+8gsin (pi/6) = mu (8gcos(pi/6)) #

# :. mu = (9+8gsin (pi/6))/(8gcos(pi/6)) #

# :. mu = 0.7099051 ... #

Once the object is moving the driving force is reduced from

# D+mgsin theta -F = 0 #

# :. F = 2+8gsin (pi/6) \ \ N#

And the friction is related to the Reaction (Normal) Force by

# F = mu R => 2+8gsin (pi/6) = mu (8gcos(pi/6)) #

# :. mu = (2+8gsin (pi/6))/(8gcos(pi/6)) #

# :. mu = 0.6068069 ... #

So the static coefficient of friction is

the kinetic coefficient of friction is