# 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  18 (kg)/s^2, what is the minimum value of the surface's coefficient of static friction?

May 19, 2017

The coefficient of static friction is $= 0.061$

#### Explanation:

The coefficient of static friction is

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

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

The spring constant is $k = 18 k g {s}^{-} 2$

The compression is $x = 0.6 m$

Therefore,

${F}_{r} = 18 \cdot 0.6 = 10.8 N$

The normal force is

$N = m g = 18 g N$

The coefficient of static friction is

${F}_{r} = \frac{10.8}{18 g} = 0.061$