An object with a mass of #12 kg# is on a plane with an incline of # - pi/6 #. If it takes #6 N# to start pushing the object down the plane and #4 N# to keep pushing it, what are the coefficients of static and kinetic friction?

Question

An object with a mass of #12 kg# is on a plane with an incline of # - pi/6  #.  If it takes #6   N# to start pushing the object down the plane and #4   N# to keep pushing it, what are the coefficients of static and kinetic friction?

Emily Abbate · Accepted Answer

coefficient of static friction #mu s = 0.366 .sqrt(3)#
coefficient of kinetic friction #mu k = 0.355 .sqrt(3)# the incline is making an angle of #-pi/6# = -30 degrees from the horizontal. The weight mass applied vertically is the force acting on the body. down = #12 kg . 10 m/s^2# = 120 N the typical response of a plane operating perpendicular to its own plane, say R distributing the weight across the plane in component parts and angled at a 30 degree angle with respect to the plane #mg.cos 30# = #120 . sqrt(3) /2 # = R and mg. sin30 will behave in a plane-like manner. since the motion must be initiated with a force of 6 N. Frictional force, therefore, is equal to 6 N + mg sin 30 = 6 N + 120/2 = 66 N. #fs = mu s . R # = 66N so, #mus = {66 / (60. sqrt (3))}# #mu s# = #0.366 sqrt(3)# However, a force of 4 N is enough to keep the body moving once it begins to move, so #f k = mu k .R # = 64N so, #mu k = {64 / (60. sqrt (3))}# #mu k = 0.355. sqrt(3)#

Layla Ahmed · Answer

undefined Coefficient of static friction: 0.5
Coefficient of kinetic friction: 0.33