# Does coefficient of static friction change with angle

Hi all, I am very confused by this concept. As I searched online, all respondents say that friction decreases as angle increases because normal force decreases. BUT, they don't explain this phenomenon:

A block on a ramp is static at certain angle, and after the ramp is raised by a certain degree, the block is still static. Obviously, in both cases static friction is equal to the component of weight horizontal to the incline. And this component force is INCREASING, which means the friction is also INCREASING. As the angle increases, the normal force decreases, so wouldn't the combination of these two changes indicate that the coefficient is increasing?

I am confused.

Chestermiller
Mentor
Hi all, I am very confused by this concept. As I searched online, all respondents say that friction decreases as angle increases because normal force decreases. BUT, they don't explain this phenomenon:

A block on a ramp is static at certain angle, and after the ramp is raised by a certain degree, the block is still static. Obviously, in both cases static friction is equal to the component of weight horizontal to the incline. And this component force is INCREASING, which means the friction is also INCREASING. As the angle increases, the normal force decreases, so wouldn't the combination of these two changes indicate that the coefficient is increasing?

I am confused.
This is how you go about measuring the coefficient of friction. The coefficient of friction itself does not depend on the angle. You raise the angle until block starts to slip. At that point, the coefficient of static friction is determined to be the tangent of that angle, which is equal to the component of the block's weight parallel to the ramp divided by the component of block's weight perpendicular to the surface. You are not measuring the coefficient of static friction until the block just starts to slip.

A.T.
wouldn't the combination of these two changes indicate that the coefficient is increasing?
Have you looked at the definition of the static friction coefficient?

Merlin3189
Homework Helper
Gold Member
I'm not sure if this is what Chester and AT have already said in their more mathematical way, but the thing you seem to be missing here is that the coefficient of friction tells you the maximum frictional force before something slips (or as it slips, re. ChesterM)
When the block lies on a flat horizontal surface, there is no frictional force, because their is no sideways force to oppose. But if you try to pull it sideways, then you will feel the friction opposing whatever force you apply, up to the limit of Nμ.
With your inclined plane, you see smaller frictional force when the plane is near horizontal, simply because there is less gravitational force to oppose. The friction force is less than Nμ and the block does not slip. At a certain angle the gravitational force down the slope reaches Nμ and if you increase the slope any further, the block slips, because now the gravitational force down the slope is greater than friction Nμ. (And N is also decreasing with increasing slope. But μ is constant.)

• CWatters
CWatters
Homework Helper
Gold Member
A block on a ramp is static at certain angle, and after the ramp is raised by a certain degree, the block is still static. Obviously, in both cases static friction is equal to the component of weight horizontal parallel to the incline. And this component force is INCREASING, which means the friction is also INCREASING. As the angle increases, the normal force decreases, so wouldn't the combination of these two changes indicate that the coefficient is increasing?

No the coefficient of friction μ is a property of the materials and surfaces in contact and is nominally considered to be a constant.

It's as Merlin said. The equation F = μN gives you the maximum force that friction can provide before slipping occurs. The actual friction force will vary depending on the situation, in this case it depends on the angle of the incline.

As I searched online, all respondents say that friction decreases as angle increases because normal force decreases. BUT, they don't explain this phenomenon

As the angle increases TWO things happen at the same time...

1) The component of gravity acting parallel/down the slope increases bringing it closer and closer to the point where it will slide. However, thanks to Newton's third law the actual friction force acting up the slope increases to match. These forces must be equal because the object isn't accelerating.

2) The maximum allowed force before sliding occurs reduces. That's because the component of gravity acting at 90 degrees to the slope, and therefore the normal force N, reduces.

So you have the actual friction force increasing (1) and the maximum friction force reducing (2).