Question

An object with a mass of `4 kg` is on a ramp at an incline of `pi/8`. 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

`0.36`

Explanation:

Component of weight of the object acting downward along the inclined plane is `mg sin theta=4*10*sin (pi/8)=15.30 N`

So,unbalanced force acting downwards along the inclined plane is `(15.30-2)N = 13.30N`

So,this amount of force must be supplied by the frictional force upwards.

So,frictional force acting here is `mu*N=mu*mg cos (pi/8)` (`mu` is the desired coefficient of friction)

So, `mu mg cos (pi/8) = 13.50`

or, `mu=0.36`