An object with a mass of #4 kg# is on a plane with an incline of # - pi/4 #. If it takes #7 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?

1 Answer

Answer:

#\mu_s=1.252# & #\mu_k=1.18#

Explanation:

The force #F# required to push an object of mass #m=4# kg downward on an inclined plane at an angle #theta=-{\pi}/4=-45^\circ# & coefficient of static friction #\mu_s#

#F=\mu_s mg\cos\theta-mg\sin\theta#

#\mu_s=\frac{F+mg\sin\theta}{mg\cos\theta}#

#\mu_s=\frac{7+4\times9.81\sin45^\circ}{4\times9.81\cos45^\circ}#
#=1.252#

Similarly, when the motion starts, then the force (F) required to keep the object moving

#F=\mu_k mg\cos\theta-mg\sin\theta#

#\mu_k=\frac{F+mg\sin\theta}{mg\cos\theta}#

#\mu_k=\frac{7+4\times9.81\sin45^\circ}{4\times9.81\cos45^\circ}#
#=1.18#