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

Answer:

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#