An object with a mass of #9# #kg# is on a plane with an incline of #- pi/4 #. If it takes #15# #N# to start pushing the object down the plane and #7# #N# to keep pushing it, what are the coefficients of static and kinetic friction?
The coefficient of static friction is
The negative sign on the angle is not relevant in this case: the angle of the inclined plane is
The force perpendicular to the plane, the normal force, will be given by:
Based on this, the frictional force will be:
We will find two different values, the static friction,
The force parallel to the plane due to gravity will be given by:
Overcoming the force of static friction requires this parallel force plus
Once it is moving, keeping it moving only requires
Coefficients of friction do not have units.