I Is Mechanical Energy Conservation Free of Ambiguity - follow up

[jbriggs444]

I'm in the frame of the bricks, I can see the stuff in the ground frame passing by me and I cannot conclude that I am moving. So I can turn reality upside down and its perfectly valid, and also suddenly useless? So basically, the problem of the truck bed "dragging me and the bricks along for a ride" suddenly becomes the truck is on a world sized treadmill...the entire question becomes pointless there if I don't know about the wheels on the truck.

What are you trying to calculate? Yes, it is all useless if you are not trying to calculate anything.

You adopt a frame of reference which lets you concentrate on a particular interaction without needing to worry about anything else. If you are trying to model a box in the bed of an accelerating pickup truck, it might be easier to shift to a frame in which the truck is stationary and the bed is tilted. It is the same situation either way.

 

[erobz]

...there seems to be no relative motion, there is energy loss

I'm not following, there seems to be relative motion at all but one of those micro normal/kinetic friction interfaces. So I don't think I'm talking about "creep" in a rolling wheel.

 

[erobz]

What are you trying to calculate? Yes, it is all useless if you are not trying to calculate anything.

You adopt a frame of reference which lets you concentrate on a particular interaction without needing to worry about anything else. If you are trying to model a box in the bed of an accelerating pickup truck, it might be easier to shift to a frame in which the truck is stationary and the bed is tilted. It is the same situation either way.

A fantasy flat box and a flat bed. It doesn't stay on the bed as the truck accelerates. Period. In the perfect world that we often do physics in static friction is nonsense.

 

[jbriggs444]

I'm not following, there seems to be relative motion at all but one of those micro normal/kinetic friction interfaces. So I don't think I'm talking about "creep" in a rolling wheel.

In a free rolling wheel, the dominant form of energy loss is rolling resistance.

 

[erobz]

You say yourself that static friction is just an engineering approximation, but when confronted with the reality that what it would do as a combined effect generates heat as a "wheel" rolls you appear not to "actually" believe yourself. I can't see why everyone is so conflicted on this.

Can someone tell me why it's a such a deal to say out loud the phrase "static friction - the sum of a bunch of tiny (dare I say quantum?) interactions consumes mechanical energy"? Am I a heretic, or not?

The funny thing is that people think A.I. would be better if it just admitted to us when it doesn't know something instead of trying to make something up.

 

[A.T.]

static friction - the sum of a bunch of tiny (dare I say quantum?) interactions consumes mechanical energy

A book on a incline can be held in place by static friction indefinitely. Where is the energy coming from to sustain that static friction, if it consumes mechanical energy?

 

[jbriggs444]

You say yourself that static friction is just an engineering approximation, but when confronted with the reality that what it would do as a combined effect generates heat as a "wheel" rolls you appear not to "actually" believe yourself. I can't see why everyone is so conflicted on this.

Can someone tell me why it's a such a deal to say out loud the phrase "static friction - the sum of a bunch of tiny (dare I say quantum?) interactions consumes mechanical energy"? Am I a heretic, or not?

You may be confusing the map with the territory.

A contact interaction can be regarded as the vector sum of a multitude of micro-interactions. Yes.

A contact interaction where there is negligible relative movement between the mating objects can also be regarded as the vector sum of a normal force and a force of static friction.

If there actually is some relative movement between the mating objects then the model of static friction alone will fail to capture the energy lost to that relative movement. Yes. In that case you do not have purely static friction. At best you have static friction plus something else. In which case, static friction is not the thing consuming mechanical energy. The something else is.

If the relative movement is negligible then you have static friction. But then the lost mechanical energy is negligible. And should be neglected.

 

[erobz]

A book on a incline can be held in place by static friction indefinitely. Where is the energy coming from to sustain that static friction, if it consumes mechanical energy?

You are missing the point. What we define is static friction...is not really always static friction. In static equilibrium the micro Normals are supporting it. This is distinctly different from a rolling wheel. In the case of the rolling wheel what we call "static friction" is actually a summation over all contact points the parallel components of micro normals and micro kinetic friction. One of those is the instantaneous center of rotation for a rigid body, the rest of them kinetic friction is consuming mechanical energy.

 

[jbriggs444]

You are missing the point. What we define is static friction...is not really always static friction. In static equilibrium the micro Normals are supporting it. This is distinctly different from a rolling wheel.

I define "static friction" as the tangential component of the contact force when there is negligible movement between the mating objects.

I do not define "static friction" as the vector sum of some set of hypothetical micro-normals that make up the contact force when there is non-negligible relative movement between the surfaces.

If you want to make the point that the model of static friction plus normal force is not exactly accurate for a rolling wheel, I grant your point. So what? Static friction is a feature of a good enough model, not necessarily an exact feature of the underlying reality. If you want a more accurate model, factor in rolling resistance.

Yes, in the real world, the dividing line between kinetic and static friction is not as sharp as in the model.

 

[erobz]

I do not define "static friction" as the vector sum of some set of hypothetical micro-normals that make up the contact force when there is non-negligible relative movement between the surfaces.

But there is motion, and maybe trillions of electrostatic interactions at the thing we so brazenly refer to as the IC in a perfectly shaped wheel on a perfectly smooth line. I don't care how you define it, because you didn't separate out the effects. There are components of Normals heading every which way in a rolling wheel, and there are trillions of friction generating contact points too! Explain how did you isolated these effects to arrive at your definition?

We give up and say "this is static friction" but there we are some how "butt hurt" when its apparent there is work done when you zoom in!

 

[jbriggs444]

But there is motion, and maybe trillions of electrostatic interactions at the thing we so brazenly refer to as the IC in a perfectly shaped wheel on a perfectly smooth line. I don't care how you define it, because you didn't separate out the effects. There are components of Normals heading every which way in a rolling wheel, and there are trillions of friction generating contact points too! Explain how did you isolated these effects to arrive at your definition?

Measurement. The normal force is measurable. The frictional force is measurable. The velocities of the mating surfaces are measurable. The torques and rotation rates of a tire and dynamometer are measurable.

For that matter, the force of a book on a sloping table is measurable.

 

[erobz]

Measurement. The normal force is measurable. The frictional force is measurable. The velocities of the mating surfaces are measurable. The torques and rotation rates of a tire and dynamometer are measurable.

For that matter, the force of a book on a sloping table is measurable.

Are you saying the micro frictions do no mechanical work (as in zero) work? They are kinetic frictions, they are moving, and there are an unholy amount of them in that tiny little thing we call a "point of contact".

 

[jbriggs444]

Are you saying the micro frictions do no mechanical work (as in zero) work? They are kinetic frictions, they are moving, and there are an unholy amount of them in that tiny little thing we call a "point of contact".

In the case of a book on a table, you are saying that the micro frictions do non-negligible mechanical work?

And that this is something that we must surely model at the risk of committing Grave Error?

Or are you simply trying to say that any real wheel will eventually roll to a stop, even though our idealized models say that it won't? So our idealized models are Gravely Wrong?


It is a feature of practical physics that we use models that are good enough to produce adequately accurate results for the task at hand with acceptable reliability in a feasible time frame.

 

[erobz]

If you want to make the point that the model of static friction plus normal force is not exactly accurate for a rolling wheel, I grant your point. So what? Static friction is a feature of a good enough model, not necessarily an exact feature of the underlying reality. If you want a more accurate model, factor in rolling resistance.

Yes, in the real world, the dividing line between kinetic and static friction is not as sharp as in the model.

Yes, I'm trying to make that point.

But you say "so what", add "rolling resistance" leads to the fact that by what measure "rolling resistance" isn't really properly isolated either and seems partially contributable to the truth.

 

[erobz]

In the case of a book on a table, you are saying that the micro frictions do non-negligible mechanical work?

And that this is something that we must surely model at the risk of committing Grave Error?

Or are you simply trying to say that any real wheel will eventually roll to a stop, even though our idealized models say that it won't? So our idealized models are Gravely Wrong?

I'm saying if you want to make a physicist lose their mind in the bedroom, grab onto them and whisper "static friction does work on a rolling wheel" in their ear and hold on - they don't know why they are thrashing about wildly - but they sure are!

 

[jbriggs444]

Yes, I'm trying to make that point.

Consider it made. The map is not the territory. The map only needs to be good enough to get the job done. The perfect is the enemy of the good.

But you say "so what", add "rolling resistance" leads to the fact that by what measure "rolling resistance" isn't really properly isolated either and seems partially contributable to the truth.

Well yes, rolling resistance is an engineering approximation as well. So what? It's models all the way down.

 

[jbriggs444]

I'm saying if you want to make a physicist lose their mind in the bedroom, grab onto them and whisper "static friction does work on a rolling wheel" in their ear and hold on - they don't know why they are thrashing about wildly - but they sure are!

Pot. Kettle. Black.

I've been trying to find common ground. But it seems that there is none. So I will try to manfully stifle myself and bow out.

 

[A.T.]

In static equilibrium the micro Normals are supporting it.

On sufficiently microscopic levels, there is no static equilibrium, no well defined normals, and no clear distinction between mechanical and thermal energy. Just fuzzy atoms jiggling and bouncing around. Macroscopic concepts are not meaningful on microscopic scales.

In the case of the rolling wheel what we call "static friction" is actually a summation over all contact points the parallel components of micro normals and micro kinetic friction.

Anything that dissipates energy as heat is expressed as rolling resistance or kinetic friction.

 

[A.T.]

they don't know why they are thrashing about wildly - but they sure are!

I see a lot of projection here ...

 

[erobz]

Pot. Kettle. Black.

I've been trying to find common ground. But it seems that there is none. So I will try to manfully stifle myself and bow out.

There is no reason to feel that way. I think we've found all kinds of common ground. I was just making a joke that I found funny. Yeah, I'm thrashing around too! no doubt.

But I feel my position is the defensive one...say static friction - the way we handle it- does work on the rolling wheel and people lose it (not just you - its every time its encountered - which is often), and I honestly can't see why that is so controversial. I want to get down to brass tacks on "the big deal".

Mulled the car example where the road "gives work" here before and there was palpable outrage at the notion that we have to accept it as we taught it. You even said, that's an ok way to look at it, kind of. There is something you still don't like about it obviously, but I feel like everyone is spitting it into their napkin when I'm not looking instead of adding something (maybe the exact spice isn't known be we agree it need something) to the meal.

 

[erobz]

On sufficiently microscopic levels, there is no static equilibrium, no well defined normals, and no clear distinction between mechanical and thermal energy. Just fuzzy atoms jiggling and bouncing around. Macroscopic concepts are not meaningful on microscopic scales.

See, you said to me "none of this is on really the level ...quantum mechanics" I only ask for something in between, and that is only because I'm sternly scolded for saying "static friction " does some work.

The truth as I see it is when nothing is moving "static friction" is really just the sum of micro Normals components parallel...to the direction it "would like to move" from the applied force. However, when a "wheel" is rolling, there is sliding going on. It might be rotation about a point, but could be millions of micro peaks and valleys sliding against each other on either side of the "IC"...where there is sliding, there is work. What we call static friction is the aggregate of these micro forces (and some lattice energy breaking).

Quantum mechanics...I think there is still some middle ground so that it can be taught to noobs like me.

 

[A.T.]

I'm sternly scolded for saying "static friction " does some work.

@jbriggs444 described cases where static friction is doing work.

... there is sliding going on.

If the sliding is not negligible and you want to take it into account, then you can model it as sliding friction, or lump it with other dissipative effects in rolling resistance. But static friction is what can hold a book in place indefinitely, because it doesn't dissipate mechanical energy.

 

[jbriggs444]

There is no reason to feel that way.

All right. With some trepidation, I will unstifle.

What we call static friction is the aggregate of these micro forces (and some lattice energy breaking).

The aggregate of the micro forces is the total contact force. And the total contact torque. It is not just friction. We are free to separate out components and call one component the "normal force" and another component the "frictional force".

If there is negligible relative movement between the surfaces, we can call the frictional force "static".

If there is non-negligible relative movement, we will need to account for that. Maybe as an adjustment on top of "static friction" or maybe by calling it "kinetic friction" instead.

If there is negligible relative movement then there is negligible net mechanical work done across the interface by static friction.

If there is negligible frictional force across the interface, there is negligible work (both flavors) done across the interface.

In the case of an unslipping driven wheel (perhaps driven by rolling resistance) there can be non-negligible center of mass work done by static friction even though the net mechanical work done across the interface is zero. This should not be controversial.

Now let us get to rolling resistance. Part of rolling resistance can be modelled as the net torque resulting from a forward shift of the line of action of the normal force and from all of your micro-sliding. That torque absorbs work. Part can be modelled as the wheel rolling up in its self-generated divot resulting in a backward tilt of the normal force. That effect also absorbs work. I do not choose to regard either effect as "static friction", even though both effects act to retard the motion of the rolling wheel.

 

[erobz]

The aggregate of the micro forces is the total contact force. And the total contact torque. It is not just friction. We are free to separate out components and call one component the "normal force" and another component the "frictional force".

If there is negligible relative movement between the surfaces, we can call the frictional force "static".

I'm not sure I get the torque aspect just yet, but anyhow... So we can say that the normal force in "smooth world" is the summation of the vertical components of the contact force. So for a box on a rough surface we apply a horizontal force the summation of the vertical components must sum to the weight of the box. If it's not moving as we apply $F$ the summation of the horizontal components of the contact force must equal $F$.

Can we call this horizontal micro summation of the contacts "static friction"? Is there some particular worry that drives you to specifically "frictional force"?

Something like this: (excuse the reuse of the "wheel curves" for the “box”)

I think well have more contacts (micro Normals) on the left side of hills but...

I'm thinking they either shear off some of these hills (breaking material bonds) and/or “slide/launch” up an over, making kinetic friction the actor. Or am I blind to some nasty combination that needs to happen... I imagine that as the box starts to move forward the contact force components in the horizontal direction could drop.

Could kinetic friction just be the shearing of material from the softer, sending micro chunks flying, and maybe just deforming the harder of the two materials. I'm just thinking that on average the lower horizontal component than "static friction" we observe was the thing begins to accelerate, higher spikes in force-material destruction, but overall far less points of contact because the body is now microscopically bouncing upward overall removing points of contact from the interaction?

Is a separate kinetic friction that is "normal" to the micro Normals even actually there...do we need it in this microscopic view of intermittent material destruction? This is occurring to me after I realize that the jagged and fractal nature of the mating surfaces is far more convoluted/intricate than I give them credit for in my simple illustration.

 

[cianfa72]

We are not moving forward. If you are going to adopt a frame, adopt the frame!

If you want to ask what is holding the box in place against the gravity-like rearward pseudo-force, that would be the static friction of stationary pickup truck bed on stationary box.

Ok, here gravity-like rearward pseudo-force is inertial force that exists in the rest frame of the accelerating pickup truck's bed.

I believe the term "gravity-like" refers to the very deep feature that pseudo/inertial forces acting on bodies are the same regardless of bodies' masses (let me say it is just the point of GR's weak equivalence principle).

 

[cianfa72]

What are you trying to calculate? Yes, it is all useless if you are not trying to calculate anything.

You adopt a frame of reference which lets you concentrate on a particular interaction without needing to worry about anything else. If you are trying to model a box in the bed of an accelerating pickup truck, it might be easier to shift to a frame in which the truck is stationary and the bed is tilted. It is the same situation either way.

Ah ok, basically your proposal here is to use gravity as substitute for pseudo/inertial forces appearing in the accelerating reference frame.

This way, in the inertial rest frame $\mathcal A$ of truck's bed there are, by definition, no pseudo/inertial forces. The bed is tilted hence the force of gravity acting on the box can be broken along the component normal to the bed and parallel to it. The former is balanced from bed's normal force at the contact point. The box w.r.t $\mathcal A$ doesn't move at all hence the static friction $f_s$ from the bed on the box adjusts itself to balance out the force of gravity's parallel component to the bed.

 

[cianfa72]

Consider now a billiard ball on an incline (let's take the billiard ball as system). It rolls without slipping while its CoM accelerates w.r.t. the incline's rest frame. Acting on the ball parallel to the incline are the parallel's component of force of gravity and the static friction $f_s$ (since the ball rolls without slipping the kinetic friction $f_k$ vanishes).

Now, as you pointed out, static friction $f_s$ adjusts itself to give the observed ball's CoM acceleration. I believe it actually points in the direction opposite to the parallel's component of force of gravity acting on the ball.

From a logical viewpoint, is it actually the same as a "driven wheel", i.e. a wheel driven by the attached drive shaft ?

 

[jbriggs444]

From a logical viewpoint, is it actually the same as a "driven wheel", i.e. a wheel driven by the attached drive shaft ?

In my view, yes.

For purposes of a discussion of static friction and rolling without slipping, I would count this as a "driven wheel".

 

[cianfa72]

For purposes of a discussion of static friction and rolling without slipping, I would count this as a "driven wheel".

In case of a real "driven wheel" which is the analogous of the incline parallel's component of the force of gravity acting on the ball. Is it the force applied on the (driven) wheel by the attached drive shaft ?

 

[erobz]

In case of a real "driven wheel" which is the analogous of the incline parallel's component of the force of gravity acting on the ball. Is it the force applied on the (driven) wheel by the attached drive shaft ?

There will be an external force and torque on the drive shaft once the driveshaft/wheel system is separated from the rest of the car as a free body. They are third law pairs to the forces/torques on the free body of the remainder of the car. With w.r.t. the driving forces and torques: