Applications of Newton's laws - coefficient of friction

[Jujubee37]

Homework Statement

A skier traveling 12.9-m/s reaches the slope of a steady upward 14.9-degree incline and glides up 13.4-m up this slope before coming to rest. What was the average coefficient of friction between the skies and the slope?

Relevant Equations

fr = Fr/N is an equation to use but im not sure how that equation would work in this case. The answer should be a value between 0-1 but I keep getting something over that.

https://www.physicsforums.com/attachments/277763

 

[kuruman]

Please show us the answer you got and the math that produced it. Then we will be able to diagnose if and where you went wrong.

 

[Jujubee37]

0=12.9^2+2(a)(13.4) which got me -6.2 m/s/s

 

[kuruman]

0=12.9^2+2(a)(13.4) which got me -6.2 m/s/s

That would be the acceleration if the skier were on a horizontal surface. Here the skier is going up a hill and gravity also has something to say about the acceleration. Draw a free body diagram of the skier.

 

[Jujubee37]

okay so I did the diagram and worked out the equation. 9.8sin(14.9)+u(9.8)cos(14.9)=6.2 which got me 0.388 which is the correct answer. thank you

 

[kuruman]

okay so I did the diagram and worked out the equation. 9.8sin(14.9)+u(9.8)cos(14.9)=6.2 which got me 0.388 which is the correct answer. thank you

You are welcome and also welcome to PF.

 

[haruspex]

The answer should be a value between 0-1

There's no upper limit to coefficients of friction, certainly nothing special about a value of 1.
But for a skier on snow, you would expect it to be rather lower.

 

[kuruman]

There's no upper limit to coefficients of friction, certainly nothing special about a value of 1.
But for a skier on snow, you would expect it to be rather lower.

That is my understanding too. Nevertheless, out of curiosity I visited several sites looking for coefficients of kinetic friction greater than 1. The only one I could find was aluminum on aluminum with μ_s = 1.05-1.35 and μ_k = 1.4. This is not a typographical error on my part. See e.g. here. I encountered the same numbers elsewhere which makes me wonder whether they copy from each other trusting that the initial report of these numbers is correct.

The question of why the coefficient of static friction is (generally) greater than the coefficient of kinetic friction has appeared on many PF threads of which I list only the first four:
https://www.physicsforums.com/threa...ways-smaller-than-the-static-friction.140426/
https://www.physicsforums.com/threads/kinetic-vs-static-friction-question.93180/
https://www.physicsforums.com/threads/static-friction-vs-dynamic-kinetic-friction.39630/
https://www.physicsforums.com/threads/kinetic-static-friction.102818/

Is aluminum a friction anomaly? I do not know. However, I do know that although aluminum skis exist, aluminum ski slopes do not.

 

[haruspex]

That is my understanding too. Nevertheless, out of curiosity I visited several sites looking for coefficients of kinetic friction greater than 1. The only one I could find was aluminum on aluminum with μ_s = 1.05-1.35 and μ_k = 1.4. This is not a typographical error on my part. See e.g. here. I encountered the same numbers elsewhere which makes me wonder whether they copy from each other trusting that the initial report of these numbers is correct.

The question of why the coefficient of static friction is (generally) greater than the coefficient of kinetic friction has appeared on many PF threads of which I list only the first four:
https://www.physicsforums.com/threa...ways-smaller-than-the-static-friction.140426/
https://www.physicsforums.com/threads/kinetic-vs-static-friction-question.93180/
https://www.physicsforums.com/threads/static-friction-vs-dynamic-kinetic-friction.39630/
https://www.physicsforums.com/threads/kinetic-static-friction.102818/

Is aluminum a friction anomaly? I do not know. However, I do know that although aluminum skis exist, aluminum ski slopes do not.

I see tables giving slightly different values, but still with that anomaly, e.g. https://engineeringlibrary.org/reference/coefficient-of-friction.
I cannot find any discussion of this, which in itself is strange.
I struggle to understand how such a result could be obtained. If $N\mu_s$ is just exceeded then it starts to slide, whereupon the frictional force becomes $N\mu_k$ and instantly stops it again. So did it slide or didn't it?
Maybe it creeps at a constant speed, with the frictional force rising from $N\mu_s$ to $N\mu_k$, just matching the applied force?