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?

1 Answer
Jul 13, 2016

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.