Question

An object with a mass of `4 kg` is on a plane with an incline of `- pi/4`. If it takes `7 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

`\mu_s=1.252` & `\mu_k=1.18`

Explanation:

The force `F` required to push an object of mass `m=4` kg downward on an inclined plane at an angle `theta=-{\pi}/4=-45^\circ` & coefficient of static friction `\mu_s`

`F=\mu_s mg\cos\theta-mg\sin\theta`

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

`\mu_s=\frac{7+4\times9.81\sin45^\circ}{4\times9.81\cos45^\circ}`
`=1.252`

Similarly, when the motion starts, then the force (F) required to keep the object moving

`F=\mu_k mg\cos\theta-mg\sin\theta`

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

`\mu_k=\frac{7+4\times9.81\sin45^\circ}{4\times9.81\cos45^\circ}`
`=1.18`