# Newton's Laws: Friction: Inclined Plane

Yes. so as long as the object is not sliding... $$\Sigma$$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 $$\mu*Fnormal$$

The block won't slip as long as Ff< $$\mu*Fnormal$$

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

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

if slipping happens at 17, then tan(17) = $$\mu$$

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

learningphysics
Homework Helper
It does... but when it slides $$\Sigma$$Fx is not 0 and the frictional force changes... it depends on the coefficient of kinetic friction.

We assume the object is not sliding and found the "required" static frictional force to keep it from sliding... the required static frictional force is mgsin(theta).

But we aren't sure yet if this static frictional force is possible... we need to check that it is less than $$\mu_s*F_{normal}$$...

if it isn't... then it is impossible for the block to be prevented from sliding...

When the block slides frictional force changes to $$\mu_k*Fnormal$$.

You may in the future have a problem where you need to determine if the block will slide or not... the way to do it is to see what the "required frictional force is" to prevent sliding... then to see if it is less than $$\mu_s*Fnormal$$... if it isn't, then the block slides... then you may be asked to calculate the acceleration of the sliding block... so then you'd use frictional force = $$\mu_k*Fnormal$$...

It does... but when it slides $$\Sigma$$Fx is not 0 and the frictional force changes... it depends on the coefficient of kinetic friction.

We assume the object is not sliding and found the "required" static frictional force to keep it from sliding... the required static frictional force is mgsin(theta).

But we aren't sure yet if this static frictional force is possible... we need to check that it is less than $$\mu_s*F_{normal}$$...

if it isn't... then it is impossible for the block to be prevented from sliding...

When the block slides frictional force changes to $$\mu_k*Fnormal$$.

You may in the future have a problem where you need to determine if the block will slide or not... the way to do it is to see what the "required frictional force is" to prevent sliding... then to see if it is less than $$\mu_s*Fnormal$$... if it isn't, then the block slides... then you may be asked to calculate the acceleration of the sliding block... so then you'd use frictional force = $$\mu_k*Fnormal$$...

Ohhh alright that makes sense. Well thanks again for all your help!