# An object with a mass of  4 kg is lying on a surface and is compressing a horizontal spring by 8 cm. If the spring's constant is  2 (kg)/s^2, what is the minimum value of the surface's coefficient of static friction?

Feb 2, 2016

$\mu = 2 \times \frac{.08}{4 \times 9.81} = \frac{.04}{9.81} \approx .004$

#### Explanation:

Take FBD:
1) y-direction $N = m g$
2) x-direction ${F}_{m s} = \mu N$
Insert 1) into 2)
$k x = \mu m g$
$\mu = \frac{k x}{m g}$
$\mu = 2 \times \frac{.08}{4 \times 9.81} = \frac{.04}{9.81} \approx .004$