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?

1 Answer
Mar 31, 2016

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#