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?

1 Answer
Feb 17, 2017

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