Question

An object with a mass of `15 kg` is lying on a surface and is compressing a horizontal spring by `10 cm`. If the spring's constant is `8 (kg)/s^2`, what is the minimum value of the surface's coefficient of static friction?

Answer 1

The minimum coefficient of static friction is `mu = 5.4 * 10^-3`.

Explanation:

We know that the frictional force due to static friction will be the normal force of the object on the surface times the coefficient of static friction, `mu`. The normal force, in turn, is simply the block's mass times the force of gravity:

`F = -mu N`
`F = -g m mu`

And Hooke's law tells us that the force due to the spring is...

`F = -kx`

These two values will be equal when `mu` is at the minimum to keep the block stationary, so we can set the equations equal and plug in given values.

`-kx = -g m mu`
`kx = g m mu`
`8*.1 = 9.8*15*mu`
`.8 = 147mu`
`0.0054 = mu`

And using scientific notation to simplify we get:

`mu = 5.4 * 10^-3`