An object with a mass of #14 kg# is on a plane with an incline of # -(5 pi)/12 #. If it takes #12 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?

1 Answer

Answer:

#4.07, 3.93#

Explanation:

The force #F# required to push an object of mass #m=9# kg downward on an inclined plane at an angle #theta=-{5\pi}/12=-75^\circ# & coefficient of static friction #\mu_s# is given as

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

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

#\mu_s=\frac{12+14\times9.81\sin75^\circ}{15\times9.81\cos75^\circ}#
#=4.07#

Similarly, when the motion starts, then the force (F) required to keep the object moving on the plane is given as

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

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

#\mu_k=\frac{7+14\times9.81\sin75^\circ}{15\times9.81\cos75^\circ}#
#=3.93#