# An object with a mass of #5 kg# is on a plane with an incline of # - pi/8 #. If it takes #8 N# to start pushing the object down the plane and #3 N# to keep pushing it, what are the coefficients of static and kinetic friction?

##### 1 Answer

#### 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=5gcos(pi/8) \ \ N#

Initially it takes

# D+mgsin theta -F = 0 #

# :. F = 8+5gsin (pi/8) \ \ N#

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

# F = mu R => 8+5gsin (pi/8) = mu (5gcos(pi/8)) #

# :. mu = (8+5gsin (pi/8))/(5gcos(pi/8)) #

# :. mu = 0.5909306 ... #

Once the object is moving the driving force is reduced from

# D+mgsin theta -F = 0 #

# :. F = 3+5gsin (pi/8) \ \ N#

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

# F = mu R => 3+5gsin (pi/8) = mu (5gcos(pi/8)) #

# :. mu = (3+5gsin (pi/8))/(5gcos(pi/8)) #

# :. mu = 0.4804482 ... #

So the static coefficient of friction is

the kinetic coefficient of friction is