Question

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?

Answer 1

`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`