Question

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

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