# An object with a mass of  16 kg is lying still on a surface and is compressing a horizontal spring by 5/3 m. If the spring's constant is  4 (kg)/s^2, what is the minimum value of the surface's coefficient of static friction?

Sep 3, 2016

$\mu = 0.0425$

#### Explanation:

Looking at the problem we can write the equilibrium force equation in horizontal direction:
$\text{Friction force = Spring force}$
So, $\text{Friction Coefficient"(mu) * "Reaction force" (R) = "Spring constant" (k) * "Displacement} \left(x\right)$
$\mu \cdot R = k \cdot x$ ;or
$\mu \cdot m g = k \cdot x$ ;or
$\mu \cdot 16 \cdot 9.81 = 4 \cdot \frac{5}{3}$ ;or
$\mu = 0.0425$
Thus the Friction coefficient is $\mu = 0.0425$