# An object with a mass of  2 kg is lying still on a surface and is compressing a horizontal spring by 80 c m. If the spring's constant is  9 (kg)/s^2, what is the minimum value of the surface's coefficient of static friction?

Jun 10, 2016

$\mu = \frac{3.6}{g}$

#### Explanation:

The force due to the static friction is $\mu \times m g$ and the force exerted by the spring is $K \times \Delta x$ The equilibrium is mantained as log as

$\mu \times m g \ge K \times \Delta x$

then the minimum value for $\mu$ is

$\mu = \frac{K \times \Delta x}{m g} = \frac{9 \times 0.80}{2 \times g} = \frac{3.6}{g}$