Question

An object with a mass of `7 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

`mu = (6/(mgcos(pi/12)) - tan (pi/12))`

Explanation:

From FBD:
`F_i = F_f + F_(|\|) = mu F_N + mgsinalpha`
`F_i = mumgcosalpha + mgsinalpha`
`6 = mumgcos(pi/12) + mgsin(pi/12)`
Solve for `mu`
`mu = (6-mgsin(pi/12))/(mgcos(pi/12))`
`mu = (6/(mgcos(pi/12)) - tan (pi/12))`
Now pull out your calculator and voila!