Rolling resistance when speed is zero

[haushofer]

Dear all,

I have a very simple question. The rolling resistance (rr) of, say, a car, is defined as being proportional to the normal force/weight of an object. That seems reasonable:

$F_{rr} = C_{rr} \times F_N$

The coefficient $C_{rr}$ is a constant, depending on the materials. But now a simple yet confused question: what's $F_{rr}$ for a car standing still on a road? According to the formula, the car is subject to a $F_{rr}$ due to the normal force/weight. On the one hand, this seems not so silly, because the tires are deformed, but on the other hand: which force is then opposing this $F_{rr}$ such that the car doesn't move? And how does this rolling resistance develop when the car starts to move? I guess the direction here is important; the definition above is not a vector equation (), so maybe I'm confused about the directions. Also, forces like the normal force are "reactive forces", which adjust themselves to the situation, but in this case the movement is perpendicular to the normal force.

I'm asking this as a physics teacher :)

 

[256bits]

If you had a box on a table, not moving, and not being subjected to an external horizontal force, would you be saying that there is a static friction force ( when speed is zero ) acting upon the box?

 

[etotheipi]

As a very simple model, you can imagine a rigid wheel rolling along a deformable surface that exhibits hysteresis. When the wheel is moving, the material just in front of the wheel is being compressed whilst the material just behind the wheel is relaxing. The magnitude of the work done by normal forces at the front of the wheel during the compression is then slightly greater than the magnitude of the work done by normal forces at the back of the wheel during the relaxation, and the result is that the normal forces at the front are loosely greater in magnitude. You will end up with a resultant normal force with a resistive component.

(Source: https://lockhaven.edu/~dsimanek/scenario/rolling.htm)

But if the wheel is stationary and subject to no other external forces, then the situation is symmetric and there doesn't seem like any reason why the normal forces would be greater on one side than the other, so no rolling resistance. That of course changes if you try to push the wheel out of the divot!

 

[haushofer]

If you had a box on a table, not moving, and not being subjected to an external horizontal force, would you be saying that there is a static friction force ( when speed is zero ) acting upon the box?

Well, no, because otherwise there would be a resultant force letting the box move in the direction of the resistance force.

But as I said, maybe I'm confused about its direction.

 

[haushofer]

As a very simple model, you can imagine a rigid wheel rolling along a deformable surface that exhibits hysteresis. When the wheel is moving, the material just in front of the wheel is being compressed whilst the material just behind the wheel is relaxing. The magnitude of the work done by normal forces at the front of the wheel during the compression is then slightly greater than the magnitude of the work done by normal forces at the back of the wheel during the relaxation, and the result is that the normal forces at the front are loosely greater in magnitude. You will end up with a resultant normal force with a resistive component.

But if the wheel is stationary and subject to no other external forces, then the situation is symmetric and there doesn't seem like any reason why the normal forces would be greater on one side than the other. That of course changes if you try to push the wheel out of the divot!

That sounds reasonable, thanks! But then the rolling resistance would depend on velocity, right? Being described by some step function, implicitly assumed in my formula for the rolling resistance force?

 

[etotheipi]

That sounds reasonable, thanks! But then the rolling resistance would depend on velocity, right? Being described by some step function, implicitly assumed in my formula for the rolling resistance force?

I think in reality rolling resistance depends on lots of different factors, e.g. bearing friction, the aforementioned asymmetric pressure distribution on the wheel, deformation of the wheel itself, etc., so there probably will be some dependence on speed if you look close enough. In the idealised case, I presume it's often approximated that there is little/no variation with speed.

But I don't know much more about the subject than this, so I think I will also wait for someone more knowledgeable to come along

 

[haushofer]

The same question is posed her,

https://physics.stackexchange.com/questions/524481/rolling-resistance-and-net-force-on-a-vehicle

stating that indeed the rolling resistance force is simply zero for v=0, implying some sort of step function in its definition.

 

[256bits]

Well, no, because otherwise there would be a resultant force letting the box move in the direction of the resistance force.

But as I said, maybe I'm confused about its direction.

There might be/or could some hysteresis regarding rolling resistance - you have noticed that when a wheel rolls and then comes to a stop it will briefly and slightly roll backwards - at least some do and others do not depending upon the wheel and surface materials - all forces in the horizontal direction will be balanced when the wheel completely ceases motion. As @etotheipi has mentioned.

I don't think that is what you are asking, but it could be.
Assuming thought that you asking about a wheel at rest and with all forces horizontally being zero, one has to overcome the "rolling resistance" to initiate motion. A force less than that and the wheel does not move. What you are doing is akin to lifting the wheel up an over a bump, and an endless series of bumps, if you want to look at it that way, and at nearly the same time but with an incremental time delay, the wheel is falling down from a bump at the rear, and an endless series of bumps there also - if you can imagine both processes occurring concurrently leaving the wheel axis at a steady vertical height when in motion at steady velocity. It ends up being as described above.
Perhaps the analogy helps, maybe not.

 

[256bits]

The same question is posed her,

https://physics.stackexchange.com/questions/524481/rolling-resistance-and-net-force-on-a-vehicle

stating that indeed the rolling resistance force is simply zero for v=0, implying some sort of step function in its definition.

It would be zero, or at least the sum of forces zero.
As I mentioned with static friction, or implied, as you apply a force horizontally, the static friction increases from zero to the point where the external force overcomes the static friction maximum, and the box will move ( disregarding stiction ).

I think I would agree with the reference given.

 

[Lnewqban]

Dear all,

I have a very simple question. The rolling resistance (rr) of, say, a car, is defined as being proportional to the normal force/weight of an object. That seems reasonable:

$F_{rr} = C_{rr} \times F_N$

The coefficient $C_{rr}$ is a constant, depending on the materials.

That coeficient also depends on velocity of the vehicle and torque applied to the wheel.
Please, see:
https://en.m.wikipedia.org/wiki/Rolling_resistance

You can consider that resistive force to be zero when there is no movement.

 

[jbriggs444]

The same question is posed her,

https://physics.stackexchange.com/questions/524481/rolling-resistance-and-net-force-on-a-vehicle

stating that indeed the rolling resistance force is simply zero for v=0, implying some sort of step function in its definition.

Clearly such an assertion is dead wrong.

I can stop at a traffic signal with my brakes not applied on roads with a variety of near-level grades.

 

[hutchphd]

I'm asking this as a physics teacher :)

There are an abundance of vector forces at the the interface. Always.

Absent any external force in a particular direction they (Canonically ) sum to zero in that direction.

Why do we insist upon confusing the situation so badly by defining the "Force of Friction" as some fundamental law?

 

[haushofer]

Thanks everyone, I think I got it.

My conclusion: the rolling resistance is a reactive force as long as the applied force is smaller than the $F_{rr}$ as given by the formula. As such the resultant force stays zero. As soon as the applied force becomes bigger than $F_{rr}$ as given by the formula, the $F_{rr}$ remains constant and motion starts.

The size of the force $F_{rr}$ as given by the formula thus only applies when the applied force exceeds $F_{rr}$. I believe this idea is also applied in one of the phet-simulations online,

https://phet.colorado.edu/sims/cheerpj/the-ramp/latest/the-ramp.html?simulation=the-ramp&locale=nl

 

[sophiecentaur]

implying some sort of step function in its definition.

I'm asking this as a physics teacher :)

I think you need to learn to avoid getting into the naming game when its not strictly necessary. I know that students like to hang onto names rather than ideas and this is not helped by the fashion for 'multiple choice answers' exam questions.

A vicious circle gets created when a test question has an option (a least worst) which involves a term that some examiner introduced into a question. Once a student learns the 'correct answer' for the question, the term in the question then becomes the 'official' word and they want to hang on to it forever. 'As a teacher', I think you should try to avoid that sort of situation with students and learn suitable ways of avoiding being nailed down in this way. It can lead to Physics by Numbers and is why a teacher of a (any) specialist subject should have qualifications (formal or informal) that are at least two stages up on the level that's being taught.

IMO "Rolling Resistance" is, and always was, a very loose term and it's used in merely practical application. "Static Resistance" is a bit better defined and can be measured properly.

Frr remains constant and motion starts

By no means. The resistance cannot be relied on as being constant. It will usually depend greatly on speed and is often dependent on time too.

 

[haushofer]

I think you need to learn to avoid getting into the naming game when its not strictly necessary. I know that students like to hang onto names rather than ideas and this is not helped by the fashion for 'multiple choice answers' exam questions.

I'm not sure what you mean, but I just wanted to understand the whole notion of rolling resistance a bit better for myself. I don't do multiple choice answers anyway :P The "step function" was just for my own understanding.

By no means. The resistance cannot be relied on as being constant. It will usually depend greatly on speed and is often dependent on time too.

Well, that's clear, but the question is: on which scales?

 

[sophiecentaur]

I just wanted to understand the whole notion of rolling resistance a bit better for myself

Fair enough but you were asking as a Physics Teacher and my comments stand. Merely giving something a name can give trouble and this is a good example because it would really depend on context. You are lucky not to have to deal with multiple choice questions but the problem still arises with students who are more invested in categorising than acknowledging the fact that many terms are very vague. I would say RR is pretty vague and not worth losing too much sleep over. It's pretty rare that things actually roll without sliding (that even goes for gears).

You ask about "scales" but the values involved are totally case dependent.