Coefficient of Friction? How does this make any sense?

[hellocubed]

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I am confused about a "coefficent of friction on an Incline" problem in BR. The problem asked if a woman is sliding down a hill, does her mass have any affect on her acceleration? The math shows that Mass and gravity have no effect on an object's acceleration down the slope.

u (mgcosQ)=(mgsinQ)
u (cosQ)= (sinQ)

And then they take it even further with

u= (sinQ)/(cosQ)

Whatttt?
I am absolutely confused here.
1.) why did they make uN equal to the (mgsinQ) force down a hill? They did NoT set a precedent saying that she was Not experiencing acceleration.
2.) so.... when an object slides down a hill without acceleration change, does this mean that the u ALWAYS equals (sinQ)/(cosQ)?

 

[MedPR]

I am confused about a "coefficent of friction on an Incline" problem in BR. The problem asked if a woman is sliding down a hill, does her mass have any affect on her acceleration? The math shows that Mass and gravity have no effect on an object's acceleration down the slope.



And then they take it even further with



Whatttt?
I am absolutely confused here.
1.) why did they make uN equal to the (mgsinQ) force down a hill? They did NoT set a precedent saying that she was Not experiencing acceleration.
2.) so.... when an object slides down a hill without acceleration change, does this mean that the u ALWAYS equals (sinQ)/(cosQ)?

which problem is this?

 

[hellocubed]

Sorry, I am at work right now and don't have the book with me.
But it was in the second chapter Physics


It went along the lines of:
A skier falls off his skis and begins sliding down the slope. Which of these variables will affect his acceleration/velocity?

One of the choices was Mass. I thought that's what it was because of the whole MgsinQ. But apparently mass cancels out and has no effect on her acceleration.

My concern #1 was part of the problem.
My concern #2 was not, but it was an illustrated part of the math that doesn't seem to make conceptual sense to me.

 

[MedPR]

I see. Well here's what I came up with.

Let's assume there is an acceleration (it doesn't really matter if all you want to do is rule out mass as a factor here). We'll call "down the ramp" the positive direction. So you have ma=mgsinQ-umgcosQ. You should be familiar with the a=gsinQ being the acceleration up/down an incline and mgcosQ being the normal force. Obviously frictional force = uNormal.

So from ma=mgsinQ-umgcosQ, you can factor out m (and g, but let's keep it as simple as possible here) to get:

ma=m(gsinQ-ugcosQ)

Divide both sides by m, and voila, mass is gone.

I'm not sure about problem 2, but it does seem that in cases of 0 acceleration, that the coefficient of friction = sinQ/cosQ.

 

[MT Headed]

Ironically that is the original definition of the coefficient of friction... the tangent of the angle at which an object breaks free and starts sliding (u-static), or the tangent of the angle at which an object slides across a tilted surface at a constant speed (u-kinetic).

http://en.wikipedia.org/wiki/Coefficient_of_friction#Angle_of_friction

This is also quite cool, and explains how a part of the world works:

http://en.wikipedia.org/wiki/Angle_of_repose