# An object with a mass of 1 kg is lying still on a surface and is compressing a horizontal spring by 1/4 m. If the spring's constant is 3 kgs^-2, what is the minimum value of the surface's coefficient of static friction?

The force exerted by the spring is $F = k x = 3 \times \frac{1}{4} = \frac{3}{4}$ $N$.
The frictional force is given by ${F}_{\text{frict"=muF_"norm}} = \mu m g = \mu \times 1 \times 9.8$ $N$
$9.8 \mu = \frac{3}{4}$, and rearranging, $\mu = 0.076$ (no units).