Slipping rolling cylinder friction

[xzibition8612]

Homework Statement

The cylinder is released from rest on the inclined plane. The coefficient of friction between cylinder and plane is μ. Determine the motion of the cylinder, assuming that μ is large enough to prevent slipping.

Homework Equations

The Attempt at a Solution

ok don't determine the motion. I have the solution in the textbook.

My question is about the friction. In my book it says "We are to assume the cylinder rolls. In this case the friction force f is an unknown and has a value satisfying 0≤f≤f_max where f_max=μN. After solving for f, we shall then impose the condition that it be less than μN, since we know the cylinder is not slipping"

Please note the friction vector is pointing to the right on the bottom of the cylinder.

I'm confused here about this friction. Why is f≤f_max? My intuition tells me if friction force is very big then the cylinder wouldn't roll. So if f≥f_max wouldn't the cylinder just not move? Why would it slip if f≥f_max? Thanks for explaining

 

[Doc Al]

The amount of friction force you need to prevent slipping is f. As long as f turns out to be less than the max possible, which is μN, then things are good. But if the f needed is more than the surfaces can deliver, meaning if f > μN, then you'll begin to slip. Not enough friction is available.

 

[xzibition8612]

so the maximum amount of friction available on this natural surface is uN. Meaning its not possible for f to be greater than this amount. So if it turns out f>uN, it means the cylinder will slip since not enough friction is present. Am I getting this correctly? Thanks.

 

[Doc Al]

so the maximum amount of friction available on this natural surface is uN. Meaning its not possible for f to be greater than this amount. So if it turns out f>uN, it means the cylinder will slip since not enough friction is present. Am I getting this correctly?

Yes. Exactly right.

 

[Nickie]

.I would like to clarify a few things about the concept of slipping and rolling friction in this scenario.

Firstly, the concept of friction is related to the resistance between two surfaces in contact. In this case, the friction force is acting between the cylinder and the inclined plane. The coefficient of friction, μ, is a measure of the roughness of the surfaces in contact and determines the strength of the friction force.

Secondly, there are two types of friction that can occur in this scenario: static and kinetic friction. Static friction occurs when two surfaces are not moving relative to each other, and kinetic friction occurs when there is relative motion between the two surfaces.

Now, in this scenario, we are assuming that the cylinder is rolling without slipping. This means that there is no relative motion between the cylinder and the inclined plane, and hence, the kinetic friction is zero. The friction force acting on the cylinder is solely due to static friction.

The maximum value of static friction, fmax, is given by μN, where N is the normal force between the cylinder and the inclined plane. This means that the friction force can have a maximum value of μN, but it can also have any value between 0 and μN, depending on the conditions.

So, when the book says that f≤fmax, it means that the friction force must be less than or equal to the maximum value of static friction. This condition is necessary for the cylinder to roll without slipping, as any value of friction force greater than fmax would result in slipping and the cylinder would not roll.

To summarize, the condition f≤fmax is imposed to ensure that the cylinder rolls without slipping, and it does not mean that the cylinder cannot move at all if f≥fmax. I hope this clarifies your confusion about the friction in this scenario.