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

[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??