Question

An object with a mass of `6 kg` is on a ramp at an incline of `pi/12`. If the object is being pushed up the ramp with a force of `3 N`, what is the minimum coefficient of static friction needed for the object to remain put?

Answer 1

The coefficient of static friction is `=-0.55`

Explanation:

Taking the direction up and parallel to the plane as positive `↗^+`

The coefficient of static friction is `mu_s=F_r/N`

Then the net force on the object is

`F=F_r+Wsintheta`

`=F_r+mgsintheta`

`=mu_sN+mgsintheta`

`=mmu_sgcostheta+mgsintheta`

`=mg(mu_scostheta+sintheta)`

So,

`F/(mg)=(mu_scostheta+sintheta)`

`mu_scostheta=F/(mg)-sintheta`

`mu_s=1/costheta*(F/(mg)-sintheta)`

`=1/cos(pi/12)*(3/(6*9.8)-sin(pi/12))`

`=-0.55`