Applications of Newton's laws - coefficient of friction

• Jujubee37
In summary: That is a difficult question to answer. I think it would depend on the specifics of the situation. If the coefficient of static friction is greater than the coefficient of kinetic friction, then it probably slid. If the coefficient of static friction is less than the coefficient of kinetic friction, then it probably doesn't slide.
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

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.

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

Jujubee37 said:
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
Jujubee37 said:
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.

Jujubee37
Jujubee37 said:
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.

haruspex said:
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 μs = 1.05-1.35 and μk = 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/

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

kuruman said:
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 μs = 1.05-1.35 and μk = 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/

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?

PeroK

1. What is the coefficient of friction?

The coefficient of friction is a dimensionless number that represents the amount of resistance or friction between two surfaces in contact. It is a measure of how difficult it is to slide one surface over another.

2. How is the coefficient of friction calculated?

The coefficient of friction is calculated by dividing the force of friction between two surfaces by the normal force, or the force perpendicular to the surfaces in contact. This calculation can be done using Newton's second law, which states that force is equal to mass times acceleration.

3. What are some real-life applications of Newton's laws and the coefficient of friction?

The coefficient of friction is used in many practical applications, such as designing car brakes, determining the grip of tires on different road surfaces, and creating non-slip surfaces for floors and shoes. It is also used in engineering to design machines and structures that can withstand the forces of friction.

4. How does the coefficient of friction affect the motion of objects?

The coefficient of friction affects the motion of objects by creating a force that opposes their motion. This force, known as friction, can either increase or decrease an object's speed depending on its direction and magnitude. The higher the coefficient of friction, the greater the force of friction and the more it will slow down an object's motion.

5. How does the coefficient of friction differ between different surfaces?

The coefficient of friction can vary greatly between different surfaces depending on their texture, material, and other factors. For example, the coefficient of friction between rubber and concrete is much higher than that between ice and metal. The type of motion, such as sliding or rolling, can also affect the coefficient of friction between two surfaces.

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