How can the coefficient of friction change? Does it?

[Ameer Bux]

Homework Statement

The coefficient of static and kinetic friction is constant for a specific surface. On an incline plane s and k are both equal to tan of the inclined angle. If the angle increases then tan changes which means the coefficient of friction changes. How is this so?

Homework Equations

Fs = s x Fn
s = tan

The Attempt at a Solution

Attached picture

 

[TSny]

The coefficients are considered to be constants, independent of the angle of incline. However, you could have a particular situation where the angle of the incline happens to be such that the tangent of the angle equals the coefficient of friction. If you changed the angle, then the tangent of the angle would no longer equal the coefficient.

 

[mastrofoffi]

No it does not change as the angle changes: the friction coefficient only depends on the nature of the materials in contact.
When you say μ=tanθ you have to remind that θ is the maximun angle for which the body is still at rest.
So if α is your actual angle, you have no motion until α<θ: if the relation you used was correct it would mean that μ=tanα is increasing as α is increasing from 0 to π/2 and you would have infinite friction as α approaches π/2, and I'm sure you agree that would make no sense

 

[CWatters]

+1

The coefficient of static friction allows you to calculate the max force that is needed to overcome friction. If the applied force is lower then the friction force will also be lower.

 

[haruspex]

constant for a specific surface.

No, it is constant for a specific combination of two surfaces in contact.

s and k are both equal to tan of the inclined angle.

Others have answered this in various ways. Here's another.
It is merely that you are used to questions in which either the object is about to slip (μ_s=tan θ) or is slipping at constant speed (μ_k=tan θ). I.e., the angle is just that angle which achieves the relevant condition, given the coefficient.

 

[deepblue29]

Homework Statement

The coefficient of static and kinetic friction is constant for a specific surface. On an incline plane s and k are both equal to tan of the inclined angle. If the angle increases then tan changes which means the coefficient of friction changes. How is this so?

Homework Equations

Fs = s x Fn
s = tan

The Attempt at a Solution

Attached picture

Coefficient of friction, aka mu, cannot change because Force of friction and Force of normal change proportionally to the inclined angle theta.

 

[Steve4Physics]

Hi @deepblue2 and welcome to PF.

Q1. You are replying to a 7 year old thread; is that deliberate?

Coefficient of friction, aka mu, cannot change because Force of friction and Force of normal change proportionally to the inclined angle theta.

Consider an object resting on an inclined plane. You appear to be saying that if the angle changes from (say) 44.5º to 89º, the normal force will double and the frictional force will double.

Q2. Is that what you mean?

It will help if you can answer both questions.

 

[deepblue29]

Hi @deepblue2 and welcome to PF.

Q1. You are replying to a 7 year old thread; is that deliberate?Consider an object resting on an inclined plane. You appear to be saying that if the angle changes from (say) 44.5º to 89º, the normal force will double and the frictional force will double.

Q2. Is that what you mean?

It will help if you can answer both questions.

I don't understand what you mean by deliberate. I am just responding to a question with my knowledge that I have of physics, regardless of the date. What I mean is that as Θ theta gets bigger, the Force of normal gets smaller and same for the Force of friction. They get proportionally changed, which means that the mu is constant.

 

[Steve4Physics]

I don't understand what you mean by deliberate. I am just responding to a question with my knowledge that I have of physics, regardless of the date.

Some replies are posted by accident because the poster didn't realise that the thread was many years old. I was checking to help you avoid accidentally wasting your time!

What I mean is that as Θ theta gets bigger, the Force of normal gets smaller and same for the Force of friction. They get proportionally changed, which means that the mu is constant

Beware of oversimplification. For the simple case of a block resting on an inclined plane, as the angle increases, the frictional force will change from:

i) non-limiting static friction (no sliding when angle is small);

ii) limiting static frction (sliding about to start at some unique angle);

iii) kinetic friction (sliding occurs for large enough angle).

The 3 cases are handled differently.