# 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 #5 N# to keep pushing it, what are the coefficients of static and kinetic friction?

Consider a coordinate system with its X-axis parallel to the plane downward and Y-axis perpendicular to the plane upward.

Resolve the weight into components that are parallel and perpendicular to the inclined plane

Static Equilibrium: In this case the frictional force is due to static friction.

Dynamic Equilibrium: In this case the frictional force is due to kinetic friction.

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The coefficient of static friction is μs = 0.50 and the coefficient of kinetic friction is μk = 0.17.

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