Question

An object with a mass of `19 kg` is on a ramp at an incline of `pi/12`. If the object is being pushed up the ramp with a force of `6 N`, what is the minimum coefficient of static friction needed for the object to remain put?

Answer 1

Given that

• the angle of inclination of the ramp `theta=pi/12`.

• the mass of the object kept on the ramp `m=19kg`.

• the object being pushed up by a force `F=6N`

Now

• the component of gravitational force acting on the object against applied force along the ramp `=mgsintheta`

• normal reaction acting on the object `mgcostheta`

• upward static frictional force acting on the object `f=mumgcostheta`, where `mu` is the coefficient of static friction.

Cinsidering the equilibrium of forces we get following relation

`mgsintheta-f=F`

`=>mgsintheta-mumgcostheta=F`

`=>mu=(mgsintheta-F)/(mgcostheta)`

`=>mu=(19xx9.8xxsin(pi/12)-6)/(19xx9.8xxcos(pi/12))`

`=>mu=tan(pi/12)-6/(19xx9.8xxcos(pi/12))`

`=>mu~~0.23`