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?

Answer 1

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

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}#

Putting the matching value in the equation above, we obtain

#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}#

Putting the matching value in the equation above, we obtain

#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
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Answer 2

The coefficient of static friction is μs = 0.174 and the coefficient of kinetic friction is μk = 0.071.

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