An object with a mass of #2 kg# is on a plane with an incline of # - pi/3 #. If it takes #12 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:

coefficients of static & kinetic friction are #2.955# & #2.242# respectively

Explanation:

Let #mu_s# & #mu_k# be the coefficients of static & kinetic friction on a plane inclined at an angle #\theta=\pi/3#

When the object of mass #m=2\ kg# is just to start sliding down the incline under the application of a force #F=12\ N#, balancing the force along the incline

#F+mg\sin\theta=mu_smg\cos\theta#

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

setting the corresponding value in above equation, we get

#mu_s=\frac{12+2\cdot 9.81\sin(\pi/3)}{2\cdot 9.81\cos(\pi/3)}#

#=2.955#

Similarly, when the object of mass #m=2\ kg# is sliding down the incline under the application of a force #F=5\ N#, balancing the force along the incline

#F+mg\sin\theta=mu_kmg\cos\theta#

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

setting the corresponding value in above equation, we get

#mu_k=\frac{5+2\cdot 9.81\sin(\pi/3)}{2\cdot 9.81\cos(\pi/3)}#

#=2.242#

hence coefficients of static & kinetic friction are #2.955# & #2.242# respectively