# 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?

Apr 21, 2016

Lets consider the total force on the object:

1. $2 N$ up the slant.
2. $m g \sin \left(\frac{\pi}{12}\right) \approx 12.68 N$ downwards.

Hence the total force is $10.68 N$ downwards.

Now the force of friction is given as $\mu m g \cos \theta$ which in this case simplifies to ~47.33mu N

so $\mu = \frac{10.68}{47.33} \approx 0.23$

Note, had there not been the extra force, $\mu = \tan \theta$