An object with a mass of  25 kg is lying still on a surface and is compressing a horizontal spring by 5/2 m. If the spring's constant is  4 (kg)/s^2, what is the minimum value of the surface's coefficient of static friction?

Jan 21, 2016

I found $0.04$

Explanation:

Have a look:

Jan 21, 2016

$\mu = \frac{k x}{m g}$
$\mu = \frac{2}{49}$
$\mu \approx .04$

Explanation:

Take a look at the figure ignore d(t) we will not need it
Now put free body diagram we will have the following equations

1. $W = N$
2. ${F}_{k} = k x = {F}_{f}$
Where,
$W = m g$
N = Normal force;
${F}_{k}$ = spring force
${F}_{f}$ = frictional force
now ${F}_{f} = \mu N$
But $N = m g$
So, $\mu m g = k x$ substitute and get
$\mu = \frac{k x}{m g}$
$\mu = \frac{2}{49}$