An object with a mass of  3 kg is lying on a surface and is compressing a horizontal spring by 25 cm. If the spring's constant is  9 (kg)/s^2, what is the minimum value of the surface's coefficient of static friction?

Jul 22, 2017

The coefficient of friction is $= 0.077$

Explanation:

The coefficient of static friction is

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

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

The spring constant is $k = 9 k g {s}^{-} 2$

The compression is $x = 0.25 m$

Therefore,

${F}_{r} = 9 \cdot 0.25 = 2.25 N$

The normal force is

$N = m g = 3 g N$

The coefficient of static friction is

${\mu}_{s} = \frac{2.25}{3 g} = 0.077$