# An object with a mass of 7 kg is lying still on a surface and is compressing a horizontal spring by 5 /8 m. If the spring's constant is 16 (kg)/s^2, what is the minimum value of the surface's coefficient of static friction?

Apr 26, 2017

The coefficient of static friction is $= 0.15$

#### Explanation:

The force of friction is

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

The spring constant is $k = 16 k g {s}^{-} 2$

The distance is $\Delta x = \frac{5}{8} m$

Therefore,

${F}_{r} = 16 \cdot \frac{5}{8} = 10 N$

The coefficient of static friction is

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

The normal force is $N = m g = \left(7 g\right) N$

So,

${\mu}_{s} = \frac{10}{7 g} = 0.15$