Question

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?

Answer 1

The static coefficient must equal 0.048

Explanation:

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

`F = (3(kg)/s^2)(5/4m)` = `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=muF_N = mumg`

`15/4N = mu (8kg)(9.8m/s^2)`

`3.75 N = muxx78.4N`

`mu=3.75/78.4 = 0.048`