Work done by a normal force (or rather, work NOT done)

[jbriggs444]

When you guys are talking about "relative motion", do you mean relative motion between the point of application of the force that's acting and the point on the material that's being acted upon, or do you mean the motion of the contact point (as a whole) in the chosen reference frame?

I believe that I used the phrase "relative motion" in one of my posts. I meant the velocity of the one surface in the rest frame of the other surface. How fast is one object rubbing across the other.

You could call it a "slip rate". In the case of kinetic friction, the slip rate multiplied by the parallel force will tell you how rapidly mechanical energy is being dissipated into heat at the interface.

This rate does not depend on what reference frame you are using to analyze the problem. It is invariant.

 

[erobz]

It seems like the author of that text would deny the center of mass work argument.

Rather, Newton’s Second Law…good for everything…but cars with tires. If you want to examine cars you have to take the wheels off.

 

[hutchphd]

It seems like the author of that text would deny the center of mass work argument.

Rather, Newton’s Second Law…good for everything…but cars with tires. If you want to examine cars you have to take the wheels off.

This is ridiculous. You need to understand what you are quoting
Newtons Second Law is good for everything. One must define the "motion of the body" with some care if we allow deformation of structure of the body by defining the center of mass as the invariant
Energy conservation is also good for everything but the book-keeping is far more complicated. Hence the proliferation of "kinds" of forces. These are artisanal for various disciplines. Small wonder the student is often left bewildered. Better we should teach caloric and aether.

 

[erobz]

This is ridiculous. You need to understand what you are quoting
Newtons Second Law is good for everything. One must define the "motion of the body" with some care if we allow deformation of structure of the body by defining the center of mass as the invariant
Energy conservation is also good for everything but the book-keeping is far more complicated. Hence the proliferation of "kinds" of forces. These are artisanal for various disciplines. Small wonder the student is often left bewildered. Better we should teach caloric and aether.

All I want is for someone to show me how it works. If the car were a black box...everything is fine. Draw some wheels on it...Suddenly everyone has to do so serious mental gymnastics to avoid the reality that while nothing changed between scenarios, everything changed.

I'm sorry (for you and everyone else annoyed by this line of inquiry) I'm the only one dumb enough to bothered by this.

 

[sophiecentaur]

And? If one has a theory, It must contend with the "Yebbuts"... if its easily punctured, it's probably not good. I don't see why this should be an issue.

The thing about this "theory" is that it's tried and tested; we're way past the stage where an Einstein can come along and find the need to extend it. The problem that you seem to be trying to introduce is not the theory itself but its interpretation. In fact it's more of a method than an actual theory. It works but it doesn't take into account the human desire to identify intent and agency in a simple physical relationship.

It's important to be able to look at these things without requiring them to 'want' or 'try' to make things happen. Work is an aspect of Energy and, just like Money, it doesn't matter what units of currency are used or how it's used in transactions. If a 'yebbut' asks a question about a 'special circumstance' then they have to include all the variables involved; very often there will be unknowns and this basic method can't operate with unknowns (or unidentified factors). Thus, there is nothing to 'puncture' but the inadequate model that's been introduced. You can't blame arithmetic when you've spent too much this month.

 

[sophiecentaur]

Suddenly everyone has to do so serious mental gymnastics to avoid the reality

No gymnastics needed here, once you accept that Momentum and Work are different things (and adhere to the strict definitions). Momentum can be transferred without any Energy being transferred at the point of interest. You're bringing in an illegal yebbut, here.

I think PF has input quite enough into this thread; imo, it's up to you to do some serious reconciliation exercises between your two opposing pictures of what's happening in this mechanical situation.

The wonderful Mr Worthington, my A Level Maths master used to say "Know the rule, keep to the law and you can't do wrong". Every brilliant Scientist was sticking to that maxim, even when he/she came up with a revolutionary theory.

 

[sophiecentaur]

I'm the only one dumb enough to bothered by this.

Not necessarily 'dumb' - just not prepared to work at it. I read the word "discipline" higher up and that's what you should be after.

 

[erobz]

Not necessarily 'dumb' - just not prepared to work at it. I read the word "discipline" higher up and that's what you should be after.

I'm not lazy. "Dumb", but not lazy.

 

[Ebby]

If you look at the trajectory of a point on the periphery of a rolling disc, it follows a cycloid. As it approaches the ground, its motion approaches vertical. At the instant it touches ground, it has no forward velocity. What is critical here is that the forward motion approaches zero faster than its distance from the ground does.

Ah! Now I'm beginning to understand the wheel-related problem.

Actually, I came up with a way for me to understand this by imagining that the car isn't a car but a half-track (a vehicle with the front wheels of a car but a set of tracks instead of the rear wheels). I then imagined one of the links in the tracks as it touches the ground. Providing the track isn't slipping, it is easy to see that this link does not move relative to the ground (though the vehicle is making progress), and is therefore at rest in the Earth frame.

Now just shrink the length of the tracks until you have a wheel, and you have the cycloidal path haruspex mentions, with the point of contact being instantaneously at rest.

 

[hutchphd]

Suddenly everyone has to do so serious mental gymnastics

Nobody needs to do any gymnastics and they should cease (that was my point!). The car with wheels is in fact a different system than the car without but the fundamental rules change not at all. If you wish to make special rules for each special case then feel free but don't complain about the complication. Learn the fundamentals (once!): that is where the discipline is required. I do not think it is taught well in many books

 

[erobz]

Nobody needs to do any gymnastics and they should cease (that was my point!). The car with wheels is in fact a different system than the car without but the fundamental rules change not at all. If you wish to make special rules for each special case then feel free but don't complain about the complication. Learn the fundamentals (once!): that is where the discipline is required. I do not think it is taught well in many books

Do I need to remind you that you and I have been through this problem before? You agreed with me that "static friction" needed an overhaul then in context of the very same problem. What have you realized since?

https://www.physicsforums.com/threa...cceleration-of-a-vehicle.1045808/post-6804186

In the canon of introductory physics we should ban "static friction" and revise the whole notion of "dissipative forces"

 

[hutchphd]

Am I not speaking your native tongue???? I am (trying to) say the exact same thing again...

 

[erobz]

Am I not speaking your native tongue???? I am (trying to) say the exact same thing again...

No...I don't understand. I don't wish to make special rules for each case. The complication seems to be there, it is not of my making.

 

[jbriggs444]

No...I don't understand. I don't wish to make special rules for each case. The complication seems to be there, it is not of my making.

"Everything should be as simple as it can be but not simpler"

The complexity is there in nature. We try to summarize it as best we can.

 

[hutchphd]

The complication is there. A car with wheels is more complicated than one without. Sliding surfaces containing 10²³ atoms that can jiggle are necessarilly more complicated than monolithic "frictionless" ones. But making up a bunch of different names does not aid understanding.
ERRATUM I'm late to the party......

 

[sophiecentaur]

No...I don't understand. I don't wish to make special rules for each case. The complication seems to be there, it is not of my making.

I have read many threads similar to this one and they all go the same way and cease to be fun. It's quite depressing when someone who clearly is having a problem with a topic, tries to dictate the way the technical argument goes and insists on seeing things his way, in the face of a lot of well informed comments from people who clearly know their subject.

The complication that the OP sees is totally of his own making. Instead of looking for the common message, he's desperately trying to find inconsistencies from the slight variations in wording in various sources (posters and books). He has mis-interpreted a question in Ohanian and uses that to cast doubt on the whole way a wheel acts.

I imagine the car at a time t, and then I imagine the car at a time a fraction of a second later, and this point (to me at least) seems to have moved...

He has dismissed the basic maths of the situation and come to his own (wrong) conclusions. A bit of humility for the subject could help him a lot. The basics of the theory of limits agrees with Ohanian's statement.

 

[sophiecentaur]

If you look at the trajectory of a point on the periphery of a rolling disc, it follows a cycloid. As it approaches the ground, its motion approaches vertical. At the instant it touches ground, it has no forward velocity. What is critical here is that the forward motion approaches zero faster than its distance from the ground does.

It's also interesting to note that a beetle on the sidewall of the tyre will experience a constant acceleration, throughout the cycle of rotation v²/r when the car is not actually accelerating, despite the apparent 'leaping' motion when viewed from the frame of the road. Things are not always what they seem.

 

[jbriggs444]

It's also interesting to note that a beetle on the sidewall of the tyre will experience a constant acceleration

Constant magnitude of acceleration. But the poor beetle's little legs will need to provide a force that varies in magnitude and direction over time: $F_\text{legs}=mg\hat{j} - \frac{mv^2\hat{r}}{|r|}$ where $\vec{r}$ is the directed displacement from axle to beetle and $\hat{j}$ is a unit vector directed skyward.

 

[Ebby]

The complication that the OP sees is totally of his own making. Instead of looking for the common message, he's desperately trying to find inconsistencies from the slight variations in wording in various sources (posters and books). He has mis-interpreted a question in Ohanian and uses that to cast doubt on the whole way a wheel acts.

He has dismissed the basic maths of the situation and come to his own (wrong) conclusions. A bit of humility for the subject could help him a lot. The basics of the theory of limits agrees with Ohanian's statement.

No I'm very happy that you have all helped me and I can now see how the wheel problem works (see #44). I think you may be confusing me with someone else in the thread. I have learned a great deal.

Thank you all.

Btw, the Ohanian book is excellent. It is by far the best physics textbook I've come across as it asks great questions.

 

[sophiecentaur]

Constant magnitude of acceleration. But the poor beetle's little legs will need to provide a force that varies in magnitude and direction over time: $F_\text{legs}=mg\hat{j} - \frac{mv^2\hat{r}}{|r|}$ where $\vec{r}$ is the directed displacement from axle to beetle and $\hat{j}$ is a unit vector directed skyward.

I'm not sure about this. My actual word was 'experience'. That implies the beetle's (rotating but he doesn't know it) frame. You can ignore the constant horizontal velocity component and you are left with a centripetal component which is constant and in the same direction for the beetle (i.e. UP and towards the centre). This holds until the insect tries to move, of course. This is the same as for the crew on a Space Wheel. Equivalence says that they will not be able to tell the difference when sitting still.

 

[sophiecentaur]

No I'm very happy that you have all helped me and I can now see how the wheel problem works (see #44). I think you may be confusing me with someone else in the thread. I have learned a great deal.

Thank you all.

That's great.

 

[jbriggs444]

I'm not sure about this. My actual word was 'experience'. That implies the beetle's (rotating but he doesn't know it) frame. You can ignore the constant horizontal velocity component and you are left with a centripetal component which is constant and in the same direction for the beetle (i.e. UP and towards the centre). This holds until the insect tries to move, of course. This is the same as for the crew on a Space Wheel. Equivalence says that they will not be able to tell the difference when sitting still.

Yes, on a Space Wheel, there would be no periodic deviations. Just a constant apparent centrifugal force. On a rotating tire there is the Earth's gravity to worry about. From the point of view of the rotating frame, this is a force that continually rotates, always pointing in the direction of the rotating road.

 

[sophiecentaur]

On a rotating tire there is the Earth's gravity to worry about

Oh. I forgot about that. But g is a small fraction of the centripetal acceleration at normal / even low car speeds. At 10m/s and a 0.3m radius, the acceleration is around 300m/s². So my mistake has little effect on the beetle's experience. Either way, the view from the roadside is a lot more dramatic and it's the sort of thing that constitutes cognitive conflict - nice!!!

PS Human balance sense is very sensitive to these things so a human in the beetle's shoes would feel pretty bad. Fairground rides are so mild in terms of g but can seriously upset the passengers. I think the cognitive conflict could be the other way round??