Question

An object with a mass of `3` `kg` is lying on a surface and is compressing a horizontal spring by `10` `cm`. If the spring's constant is `9` `kgs^-2`, what is the minimum value of the surface's coefficient of static friction?

Answer 1

The frictional coefficient `mu=0.03`.

Explanation:

(convert the distance to SI units: `10` `cm` = `0.1` `m`)

The force exerted by the spring is given by:

`F=kx=9xx0.1=0.9` `N`

Since the object is stationary, this force applied by the spring must be being balanced by the frictional force.

The frictional force is given by:

`F_"frict"=muF_"normal"`

And the normal force is the gravitational force:

`F_"normal"=mg=3xx9.8=29.4` `N`

Rearranging:

`mu=F_"frict"/F_"normal"=0.9/29.4=0.03`

(frictional coefficients do not have units)

(side note: I keep saying that `kgs^-2` is an odd unit for spring constant. It is correct, but so is `Nm^-1`, and the latter makes is easier to understand what is going on in most contexts.)