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

May 6, 2017

The coefficient of static friction is $= 0.05$

#### Explanation:

The coefficient of static friction is

${\mu}_{s} = {F}_{r} / N$

${F}_{r} = k \cdot x$

The spring constant is $k = 4 k g {s}^{-} 2$

The compression is $x = \frac{5}{2} m$

Therefore,

${F}_{r} = 4 \cdot \frac{5}{2} = 10 N$

The normal force is

$N = m g = 5 g N$

The coefficient of static friction is

${F}_{r} = \frac{10}{5 g} = 0.05$