I Is Mechanical Energy Conservation Free of Ambiguity - follow up

[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:

 

[kuruman]

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 ?

Try answering the questions in the following problem, originally post #40 here, that features a driven wheel. I hope that it will show you how static friction works in the context of rolling without slipping. If you wish us to check your answers, please post them on a separate thread and let us know.

Problem
A yo-yo of radii $R_1=R$ and $R_2=\frac{7}{5}R$ is acted upon by forces $F$ and $\kappa F~~~(0<\kappa<\infty)$ as shown in the figure on the right. The yo-yo rolls without slipping on the horizontal surface. The mass of the yo-yo is $M$ and its moment of inertia about its center of mass is $I=qMR_2^2.$
Given quantities are $R$, $F$, $\kappa$, $M$ and $q$.

(a) Find the linear acceleration of the center of mass of the yo-yo in terms of the given quantities.
(b) Find the force of static friction acting on the yo-yo in terms of the given quantities..
(c) Find the value of $\kappa$ such that the yo-yo rolls at constant velocity.
(d) Find the value of $\kappa$ such that the force of static friction is zero.
(The ratio $R_2/R_1$ is given a numerical value to match the drawing to scale.)

 

[jbriggs444]

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 ?

In my view, we need not chase down a point by point analogy. It is more basic than that.

Whether we have an unbalanced linear force that tends to cause the rate of translation of the object not to match its rate of rotation or an unbalanced rotational torque that tends to cause the rate of rotation of the object not to match its translation rate does not matter greatly. Either way, static friction acts to preserve the state of rolling without slipping.

 

[erobz]

In case anyone has though on the "static friction" more. I hope this explains myself better than I have. Take a box on an incline, zoom in:

The circles are all microscopic "points of contact". Lets say we have a static equilibrium in the classical sense We sum over all points of contact the micro Normals $N_i^\mu$. I used $\mu$ to make clear they are micro.

What we now call the "static friction" is just the component of the summation parallel to the incline. And the Normal is the perpendicular component of the summation.

I put "$f_s$" in quotes for a reason. It seems to me that if we adopt the microscopic view this concept of "friction" doesn't even exist there. If we start pushing on the box they all shift to the opposite "micro hills" and start working against you. When you push hard enough you smash pulverize the some of micro hills, the thing we call "kinetic friction" is really just the sum of these micro Normals parallel to the slope at some instant.

Why are we using all these different "friction" concepts that are actually just type of force in the microscopic world? Students ( like myself) are always confused about all these different "frictions" but when you take a bit to sketch out the fine detail...it becomes apparent. What is going on and these conceptually difficult to pin down concepts of friction is becoming trivial?

I guess I'm kind of just miffed that know one took the time to draw out these scenarios in some "microscopic detail" we inevitably cover before they tell you about the god forsaken force models $f_k = m_k N$, $f_s \leq \mu_s N$ etc... The microscopic description covered in a few sentences, then its on to "lets solve these problem no one in the class really thought about...

The best part, those three sentences agree with this! Now everyone will say, "oh yeah I knew that - what a fool!"

How about next time someone ask why "static friction" can't do work we just retort with "well, what is "static friction" and when they inevitably give us the equation, we say "not the equation", what is it...on a microscopic scale... Because this force that we divide up clearly can do work in almost all manifestations of its existence.

 

[jbriggs444]

How about next time someone ask why "static friction" can't do work we just retort with "well, what is "static friction"

You say lump it in with "static friction". I say call it "rolling resistance". As long as the retarding force is predicted accurately, the name matters little.

The character of the interaction (micro-sliding, the crushing of hills into valleys and plastic deformation) does not fit my intuition of how static friction should work (the locking together of micro-hills with micro-valleys). Which is why I prefer not to apply that name.

 

[erobz]

You say lump it in with "static friction". I say call it "rolling resistance". As long as the retarding force is predicted accurately, the name matters little.

The character of the interaction (micro-sliding, the crushing of hills into valleys and plastic deformation) does not fit my intuition of how static friction should work (the locking together of micro-hills with micro-valleys). Which is why I prefer not to apply that name.

Rolling resistance incorporates macroscopic deformations that we can usually see in the body. I think its intuitively explained by a nonrigid macroscopic body. We never really "see" the micro Normals in this way. That would be my objection to marrying those things under one name.

These various ideas being lumped under this outwardly mysterious "friction" force that is defined piecewise by what values it currently has based on how hard you are pushing, versus just accepting that the same force responsible for locking the hills and valleys together is the same force ( varying magnitudes and numbers) that which destroys these hills and valleys as the materials are pulverized/rearranged and the body is accelerated seems far more intuitive to me. I say marry static and kinetic friction under the thing by which they manifest (on a classical level), the micro Normals.

"Static friction", "kinetic friction" - are effectively treated as "different forces", when they should be treated as different outcomes of the same force, the inability of one object to occupy the same space at the same time force that we all know and love (classically), normal forces.

 

[A.T.]

How about next time someone ask why "static friction" can't do work we just retort with ... [ microscopic stuff ]

You can do you. I will just give simple examples, where basic macroscopic static friction is doing work. There is no need for all that microscopic complexity to disprove this claim.

You say lump it in with "static friction". I say call it "rolling resistance". As long as the retarding force is predicted accurately, the name matters little.

True, but using naming that creates inconsistencies across scales is hardly useful. The macroscopic static friction doesn't dissipate mechanical energy, in contrast to rolling resistance which used to account for dissipative effects. Therefore lumping dissipative microscopic kinetic friction under macroscopic static friction makes little sense.

 

[erobz]

True, but using naming that creates inconsistencies across scales is hardly useful. The macroscopic static friction doesn't dissipate mechanical energy, in contrast to rolling resistance which used to account for dissipative effects. Therefore lumping dissipative microscopic kinetic friction under macroscopic static friction makes little sense.

They are the same force, different outcomes. The force that pushes while it gives becomes impact force, its still a normal force. It pushes until the material gives way, and normal forces keep on pushing when they find new stuff in their way. I cant see why we should create things that don't need to be created like "static friction force" and "kinetic friction force" in a theory, when something more simple and fundamental explains it?

Its consistent across scales. If we push on something with $F$ and it doesn't move ( does no work) we don't say $F$ isn't $F$, we just say $F$ is now doing work?

"Static friction" is the parallel components of micro normal summation not doing work, and "kinetic friction" is.

 

[A.T.]

I cant see why we should create things that don't need to be created like "static friction force" and "kinetic friction force" in a theory, when something more simple and fundamental explains it?

If there was no need for these concepts, they would not have been created. They are very useful for solving practical problems. They are not there to explain anything on a fundamental level.

How many pages of missing this point do you intend to write?

 

[erobz]

If there was no need for these concepts, they would not have been created. ... They are not there to explain anything on a fundamental level.

How many pages of missing this point do you intend to write?

At least one more post.

In other words "We never thought of it, but ..." I would say the reason why you guys never thought of it is because you probably weren't stay at home dads. You all had jobs to do, and advanced physics to study and publish...cutting edge stuff. Or...you were teachers and loaded to the hilt. Too busy to correct it on the fly while living your lives. Many have said on here friction could use revisit as we continuously torment each other and the students trying to explain it... It seems better to me, and I am much closer to a student in classical mechanics than yourselves.

There are very useful for solving practical problems.

Yeah, I made through some physics courses too without actually understanding it...is that the ideal?

 

[jbriggs444]

At least one more post.

In other words "We never thought of it, but ..."

It is hard not to respond to things like this. I do not appreciate words being thrust in my mouth.

My previous intent to self-stifle was wise. I will now do so.

 

[erobz]

Anyhow, I give up...call me a crank and give me the boot.

 

[erobz]

I did computer programming, system management and network engineering. I had a life.

I know, I'm saying that! This is reading like you think I'm saying the opposite.

 

[erobz]

What is absurd to me is the idea that we should discard the concept of static friction, the concept of normal force

Let me stop you there, my whole argument is the normal force, where did you see that it is to be discarded. I said it is the truly fundamental thing that should be explicitly kept. In post 63 its in the vector summation with fat arrows. It is the sum over all micro Normals perpendicular to our "flat" theoretical incline.

 

[kuruman]

I would say the reason why you guys never thought of it is because . . .

Never thought of what? It seems to me that you are overthinking the contact force exerted by a surface. A block resting on a flat surface near the surface of the Earth is subject to two, equal in magnitude and opposite in direction, forces. Each of these forces is the vector sum of myriads of interactions, gravitational and electrostatic in nature. For the purposes of drawing FBDs, not writing research articles, it suffices to draw one and only one arrow representing the net force that is exerted by each entity. See figure (A) below. The blue down arrow $\mathbf{F_g}$ represents the net force exerted by the Earth and the red up arrow $\mathbf{F_c}$ represents the net contact force exerted by the surface.

Question: How should this FBD change if the plane on which the block rests is angled at $\theta$?
Answer: Not at all, see figure (B) below. The force that the Earth exerts on the block has not changed, the block is still at rest, therefore the contact force must have the same magnitude and opposite direction as the force of gravity.

The term "friction" denotes the component of the electrostatic force between an atom in the block (system) and an atom in the surface (external) in the specific direction parallel to the surface. Likewise "normal" denotes the component of the same force between the same two atoms perpendicular to the surface. Add all relevant external forces vectorially to get the net normal component and the net friction component of the external force. In figure (A) the red arrow has zero net "friction" component. In figure (B) the red arrow has net "friction" component up the incline and equal to $F_c\sin\theta.$

When a surface is said to be "smooth", this is another way of saying that the contact force can only have a normal component. When a surface is said to be "rough" and you are given $\mu_k$, this is another way of giving you the tangent of the angle between the contact force and the normal direction. "Friction" is just a direction of a component of the net contact force just like "normal", "centripetal", "radial", "tangential", etc. It is not a force in and of itself. The net contact force with the surface is.

 

[A.T.]

In other words "We never thought of it, but ..."

" ... thankfully we met a true genius, who for the first time ever realized that friction is not one of the fundamental forces of nature."

 

[erobz]

" ... thankfully we met a true genius, who for the first time ever realized that friction is not one of the fundamental forces of nature."

Finally…someone gets it! Do I get my “Doctor of Thinkology” now too?

 

[cianfa72]

I posted my solution attempt to the problem in post #61 on PF's homework help.
May I kindly ask you to take a look at it ?

Thanks.

 

[hutchphd]

At least one more post.

In other words "We never thought of it, but ..." I would say the reason why you guys never thought of it is because you probably weren't stay at home dads. You all had jobs to do, and advanced physics to study and publish...cutting edge stuff. Or...you were teachers and loaded to the hilt. Too busy to correct it on the fly while living your lives. Many have said on here friction could use revisit as we continuously torment each other and the students trying to explain it... It seems better to me, and I am much closer to a student in classical mechanics than yourselves.


Yeah, I made through some physics courses too without actually understanding it...is that the ideal?

May I suggest a look at the "Fluctuation-dissipation Theorem which puts some theoretical meat on these purportedly rigidly practical bones. This is exactly the Nexus of your incredulity about a false dichotomy IMHO. Perhaps I misunderstand, but I think maybe you do.