What is the alternate formula for finding friction coefficient on a ramp?

[jerz211]

I understand the equation to find the coefficient of friction.

fr = a/b

a -> height of the ramp
b -> length of the base of the ramp.

But i understand that it's also possible to find friction coefficient using angle of elevation of the ramp.

So if i know the angle of elevation and the height of the ramp, is it possible to still find the friction coefficient?

In other words, is there an alternate formula (other than fr = a/b) ??

 

[_Mayday_]

I have never used that equation myself, and I can't really see how it works? To find the coefficient of friction surely you would need some other forces, and not just the dimensions of the ramp. I have always used $F=\mu R$ where F is friction, $\mu$ is the coefficient of friction and R is the normal reaction. If you are interested there is a good little tutorial I used a few weeks ago for an exam that had this type of thing in it.

http://www.mathsrevision.net/alevel/pages.php?page=79"

I hope this helps somewhat jerz211, if not just say and I will see if i can find a more informative tutorial.

_Mayday_

 

[tiny-tim]

Hi jerz211!

But i understand that it's also possible to find friction coefficient using angle of elevation of the ramp.

So if i know the angle of elevation and the height of the ramp, is it possible to still find the friction coefficient?

In other words, is there an alternate formula (other than fr = a/b) ??

I have never used that equation myself, and I can't really see how it works? To find the coefficient of friction surely you would need some other forces, and not just the dimensions of the ramp.

Yes, it does work, if the block is not moving:

If W is the weight, N is the normal reaction, F is the friction force, and θ is the angle of elevation,

then applying good ol' Newton's second law in the normal direction, and along the slope, respectively, gives:

N = Wcosθ, and F = W sinθ.

So the coefficient of static friction is F/N, which is simply tanθ.

And tanθ = opp/adj = height/base = a/b.

 

[_Mayday_]

A right, yeah thanks for that Tim. I'm just used to working with moving objects and inclined plains.

 

[Doc Al]

I have never used that equation myself, and I can't really see how it works? To find the coefficient of friction surely you would need some other forces, and not just the dimensions of the ramp.

It's not just any old dimensions of the ramp, but dimensions at a particular point: When the ramp is raised to an angle such that the object just begins to start slipping--that's when it's true that the coefficient of static friction equals tanθ. (It's not true in general for any angle.)