# An object with a mass of  3 kg is lying still on a surface and is compressing a horizontal spring by 60 c m. If the spring's constant is  2 (kg)/s^2, what is the minimum value of the surface's coefficient of static friction?

Mar 20, 2018

The coefficient of static friction is $= 0.04$

#### Explanation:

The mass is $m = 3 k g$

The compression of the spring is $x = 0.6 m$

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

The reaction of the spring is $R = k x = 2 \cdot 0.6 = 1.2 N$

The acceleration due to gravity is $g = 9.8 m {s}^{-} 2$

The normal reaction of the object is

$N = m g = 3 \cdot 9.8 = 29.4 N$

The coefficient of static friction is

${\mu}_{s} = \frac{R}{N} = \frac{1.2}{29.4} = 0.04$