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

Answer:

#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.