Question

An object with a mass of `18 kg` is lying on a surface and is compressing a horizontal spring by `60 cm`. If the spring's constant is `4 (kg)/s^2`, what is the minimum value of the surface's coefficient of static friction?

Answer 1

Force F required to compress a spring by x unit is
`F=k*x`,where k = force constant.
Here x =0.6m
`k=4kgs^-2`
hence Force exerted on the object of mass 1 kg is `F=4(kg)/s^2*0.6m=2.4(kg*m)/s^2=2.4N`
This force is balanced by the then static frictional force as it is self adjusting one,

So the minimum value of the coefficient of static frictions
`mu_s=F/N`,where N is the normal reaction exerted on the body by the floor. Here `N =mg=18*9.8N`
So
`mu_s=F/N=2.4/(9.8xx18)=0.013`