Question

An object with a mass of `12 kg` is lying on a surface and is compressing a horizontal spring by `50 cm`. If the spring's constant is `6 (kg)/s^2`, what is the minimum value of the surface's coefficient of static friction?

Answer 1

`mu_s>=0.025`

Explanation:

The situation here is that the spring is already compressed by `0.5m` and the object is at rest as the surface is with friction.

That means force of friction and spring force are balancing each other out.

`F_s=F_f`

Spring forces is `F_s=kx` Given `k=6kg/s^2` and `x=0.5m`
`F_s=6*0.5=3N`

Now, frictional force depends on the normal force of the body. Since the surface is horizontal, the entire weight of the body is the normal force. So, `F_f=\mu_s*N=\mu_s*m*g=\mu_s*12*10`

Equating the two, `cancel3^1=\mu_s*cancel120^40`

So, that's how the minimum static constant is so small.