# An object with a mass of 1 kg is lying still on a surface and is compressing a horizontal spring by 1/3 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 2, 2017

The coefficient of static friction is $= 0.1$

#### Explanation:

The force of friction is

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

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

The compression of the spring is $\Delta x = \frac{1}{3} m$

Therefore,

${F}_{r} = 3 \cdot \frac{1}{3} = 1 N$

The coefficient of static friction is

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

The normal force is $N = m g = \left(1 g\right) N$

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

So,

The coefficient of static friction is

${\mu}_{s} = \frac{1}{1 g} = 0.1$