Question

An object with a mass of `5 kg` is on a ramp at an incline of `pi/12`. If the object is being pushed up the ramp with a force of `2 N`, what is the minimum coefficient of static friction needed for the object to remain put?

Answer 1

Lets consider the total force on the object:

1. `2N` up the slant.
2. `mgsin(pi/12) ~~ 12.68 N` downwards.

Hence the total force is `10.68N` downwards.

Now the force of friction is given as `mumgcostheta` which in this case simplifies to `~47.33mu N`

so `mu = 10.68/47.33 ~~ 0.23`

Note, had there not been the extra force, `mu = tantheta`