Question

An object with a mass of `5 kg` is on a ramp at an incline of `pi/8`. If the object is being pushed up the ramp with a force of `4 N`, what is the minimum coefficient of static friction needed for the object to remain put?

Answer 1

`0.326`

Explanation:

The force `F` causing the object of mass `5`kg to slide down parallel to the ramp, having coefficient of friction `\mu` & inclined with the horizontal at an angle `\theta=\pi/8`, is given by the condition of minimum force applied to keep the object at rest

`F=mg\sin\theta-\mumg\cos\theta`

But a force of `4\ N` is applied up to keep the object stationary then in equilibrium we have

`mg\sin\theta-\mumg\cos\theta=4`

`5\cdot 9.81\sin(\pi/8)-\mu(5\cdot 9.81) \cos(\pi/8)=4`

`\mu=\frac{5\cdot 9.81\sin(\pi/8)-4}{5\cdot 9.81\cos(\pi/8)}`

`=0.326`