I Is Mechanical Energy Conservation Free of Ambiguity - follow up

[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.