# An object with a mass of #4 kg# is lying still on a surface and is compressing a horizontal spring by #7/8 m#. If the spring's constant is #12 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?

##### 2 Answers

#### Answer:

The coefficient of static friction must be at least 0.268

#### Explanation:

If the object is motionless, then Newton's first law assures us that the (two) horizontal forces acting on it must be is balance.

These forces are the elastic force of the spring, which is described by Hooke's law:

and the force of friction:

where

Putting it together, we get

and, solving for

#### Answer:

The coefficient of static friction is

#### Explanation:

The mass is

The compression of the spring is

The spring constant is

The reaction of the spring is

THe acceleration due to gravity is

The normal reaction of the object is

The coefficient of static friction is