An object with a mass of #5 kg# is on a plane with an incline of # - pi/8 #. If it takes #18 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?
Coefficient of static friction :
Coefficient of kinetic friction :
Step1 : Draw a free body diagram showing all these forces.
(1) Gravitational force (weight) :
(3) Frictional force :
Step 2 : Pick a 2D cartesian system with its X axis parallel to the incline and directed downward and its Y axis perpendicular to the plane.
Step 3: Resolve these forces into their X and Y components carefully assigning the signs:
Step 4: Equilibrium condition is that the net force acting on the object must be zero. Apply this condition by adding the vectors component-wise and set each component separately to zero.
Net Force :
Static Equilibrium: When the vector sum of these forces is zero and the object is at rest, the object is in static-equilibrium and the friction in that cases is the static friction. The coefficient of friction is the static friction coefficient (
Dynamics Equilibrium: When the vector sum of these forces is zero and the object slides with a constant velocity, the object is in dynamic equilibrium and the friction in that case is kinetic friction.The coefficient of friction is the coefficient of kinetic friction,