An object with a mass of 7 kg is lying still on a surface and is compressing a horizontal spring by 5/4 m. If the spring's constant is 3 (kg)/s^2, what is the minimum value of the surface's coefficient of static friction?

Dec 17, 2017

The coefficient of static friction is $= 0.055$

Explanation:

The mass is $m = 7 k g$

The compression of the spring is $x = \frac{5}{4} m$

The spring constant is $k = 3 k g {s}^{-} 2$

The reaction of the spring is $R = k x = 3 \cdot \frac{5}{4} = \frac{15}{4} = 3.75 N$

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

The normal reaction of the object is $N = m g = 7 \cdot 9.8 = 68.6 N$

The coefficient of static friction is

${\mu}_{s} = \frac{R}{N} = \frac{3.75}{68.6} = 0.055$