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

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