# An object with a mass of # 5 kg# is lying still on a surface and is compressing a horizontal spring by #2 m#. If the spring's constant is # 6 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?

##### 1 Answer

#### Explanation:

This problem works easier if the spring constant is in units of

Multiply both sides of

Now we see that the expression is

These are the units of Newton's 2nd Law. So truly,

Since the spring has been compressed by 2 m, the force it is exerting on the object is

Since the object remains "still", the static friction,

And

Going back to the formula for

Solving for

That is the minimum coefficient of static friction that will allow the object to remain still. A larger

I hope this helps,

Steve