Question

An object with a mass of `25 kg` is lying still on a surface and is compressing a horizontal spring by `5/2 m`. If the spring's constant is `4 (kg)/s^2`, what is the minimum value of the surface's coefficient of static friction?

Answer 1

I found `0.04`

Explanation:

Have a look:

Answer 2

`mu = (kx)/(mg)`
`mu = 2/49`
`mu ~~ .04`

Explanation:

Take a look at the figure ignore d(t) we will not need it
Now put free body diagram we will have the following equations

1. `W = N`
2. `F_k =kx = F_f`
   Where,
   `W = mg`
   N = Normal force;
   `F_k` = spring force
   `F_f` = frictional force
   now `F_f = muN`
   But `N = mg`
   So, `mumg = kx` substitute and get
   `mu = (kx)/(mg)`
   `mu = 2/49`