# An object with a mass of 8 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 20, 2016

The static coefficient must equal 0.048

#### Explanation:

We are looking at a case of balanced forces here. The force of the spring $F = k x$ will push on the mass with a force of

$F = \left(3 \frac{k g}{s} ^ 2\right) \left(\frac{5}{4} m\right)$ = $\frac{15}{4}$ N

Static friction will be equal in magnitude to this, as there is no motion.

Writing the force of friction as ${F}_{f} = \mu {F}_{N} = \mu m g$

$\frac{15}{4} N = \mu \left(8 k g\right) \left(9.8 \frac{m}{s} ^ 2\right)$

$3.75 N = \mu \times 78.4 N$

$\mu = \frac{3.75}{78.4} = 0.048$