- #26

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Yes. so as long as the object is not sliding... [tex]\Sigma[/tex]Fx = Ff-Fgparallel = 0

let's do this for an arbitrary angle where it is not slipping...

Hence Ff- mgsin(theta) = 0

Ff = mgsin(theta).

and in the y-direction:

Fnormal - mgcos(theta) = 0

Fnormal = mgcos(theta)

Now the maximum possible static frictional force is [tex]\mu*Fnormal[/tex]

The block won't slip as long as Ff< [tex]\mu*Fnormal[/tex]

in other words the block won't slip as long as [tex]mgsin(\theta)<\mu*mgcos(\theta)[/tex]

from that we get [tex]tan(\theta)<\mu[/tex] for no slipping... or in other words [tex]tan(\theta)>=\mu[/tex] when slipping happens.

if slipping happens at 17, then tan(17) = [tex]\mu[/tex]

Oh but I have a question, what happens if it IS sliding? Doesn't Fx still = Ff-Fgparallel?