Help a HS teacher understand uniform motion?

[William Ray]

Here is another suggestion. Present your teacher with the following hypothetical situation.

Suppose the two of us are driving on a straight highway at 60 mph. If I asked you "Am I in uniform motion, what would you answer?"

I see three answers, to which there are three responses from you depending on what the teacher says.
1. Teacher says "yes".
Then you say, "Nonsense. Do you see me move? Wouldn't you say that my velocity is zero? By your reasoning I should not be uniform motion."
2. Teacher says "no".
Then you say, "Nonsense. Look at the speedometer. It reads 60 mph. If that's not uniform motion, what is?"
3. Teacher is savvy enough to say, "With respect to what?"
Then you say, "Why does that matter? Can I simultaneously be and not be in uniform motion?".

If, after this, your teacher remains unconvinced, give up.

I like this - it's simple and sufficiently inescapable that it might actually work to sway the discussion on pure logic, rather than requiring an outside arbiter.

Thanks!

 

[William Ray]

...The only explanation that one can give her is that a physicist does not think that way and then explain her how and why physicists think differntly.

And that would work perfectly, if only I could find some "light reading" physics authority who laid that discussion out in relatively simple terms. Galileo comes so close.

She's not stupid, but she's not a physicist. She's a high-school teacher, and she probably had what, a whole 2 science classes in her college career? Physics for poets probably, at that? As a result, arguments appropriate for physicists are lost on her, as she just doesn't have the tools to weigh and work through the consequences of her rationalizations about the subject, versus someone else's.

That doesn't mean it's not worth trying to help her improve her understanding, and it doesn't mean she's a write-off for being irrational, it just means that she needs to be presented with the "how a physicist would think about this" information in a fashion that she can absorb, and from some venue that she'd buy into as "they probably know more about this than I do, so I should probably listen to them". If Feynman ever gave a lecture on this for the general public, that would probably be perfect...

 

[newjerseyrunner]

We can still do classical mechanics without constantly qualifying each result in relativistic terms. You would go crazy if you tried. She may still be an Aristotelian in her thinking, but that may not even be entering her mind.

But if you're supposed to be teaching Newtonian physics, you absolutely must understand relativity. It just doesn't work without it.

Forget the word relativity. That invokes thoughts of Einstein and more advanced stuff. Refer the teacher to Galilean invariance.

 

[Buckethead]

Fun discussion. Here is my take:

1) You could try and explain that speed (motion) is like distance. Something can't just have a distance of 0 or of 5 feet. It must have a distance relative to something. Ask her what is the distance to the moon. She will say 256,000 miles. Then say to her, "I wasnt't asking you what the distance of the moon from the Earth, just what is the distance."

2) Ask her if an object in motion can have a negative velocity. If she says yes, ask her if she can point out an object that has negative velocity and why. If she says no, go on to the next argument.

3) Ask her if she can come up with any measurable difference between an object in motion and an object in rest. Clearly she cannot in which case you can point out that if two things have exactly the same properties, then they are one in the same.

4) Ask her if she can't think of anything in the universe that has a zero velocity. If she can't, ask her why and she may see from this that velocity, like distance is not an absolute value.

 

[laymanB]

But if you're supposed to be teaching Newtonian physics, you absolutely must understand relativity. It just doesn't work without it.

Good point.

Forget the word relativity. That invokes thoughts of Einstein and more advanced stuff. Refer the teacher to Galilean invariance.

But can't you do examples and sensibly talk about the results without asking what they look like from a different reference frame?

 

[Metmann]

But can't you do examples and sensibly talk about the results without asking what they look like from a different reference frame?

I agree, the notion of Galilean relativity is sometimes criminally neglected when teaching classical mechanics. I like to think about Newtonian Mechanics as being based on the Galilean relativity principle in analogy with the usual way of teaching SR. Maybe one could say: Physics is the mathematics of frames.

 

[Dadface]

I assume that most of the high school students referred to in this thread will be about thirteen to fourteen years old and novices when it comes to Newton and his laws. If so, if some of the points made in this thread are conveyed to the students without proper care it may make a conceptually difficult subject even more difficult. This can be avoided with careful planning and a careful choice of words. As part of a summing up of a lesson the first law can be expressed in traditional formal ways such as the following :

In the absence of blah blah blah... an object will remain at rest or move with a constant velocity.

If taught properly many students are likely to understand that and most will know that there is a difference between being at rest and moving. And being at rest is a sort of special case in that it represents an extreme minimum case the maximum extreme being defined by the speed of light.

 

[jbriggs444]

most will know that there is a difference between being at rest and moving

It's not what you don't know that gets you. It's what you know for sure that just ain't so.

 

[Herman Trivilino]

Physics accepts two conditions for an object - in uniform motion, or in non-uniform motion.

And since the first of those is equivalent to a state of rest, you can just as correctly label the two conditions as a state of rest and a state of non-uniform motion. That's the part that's a matter of semantics.

Again, I don't believe this is semantics. It is a core, and quite important fundamental principle in physics, that you can't tell _anything_ about whether the object is moving, or not, with the radar gun. Only that you can tell whether the object is moving relative to the radar gun.

I agree. That's the physics part.

What I don't understand is what difference this makes. All I see is that she's got the semantics part wrong. I don't see where she's got the physics part wrong. She needs to teach students how to solve physics problems, and to do that they need to understand things like the fact that the velocity is zero at the turning points in one-dimensional motion, and that it's not zero otherwise. She can't articulate her position, but what it boils down to is that once a reference frame is chosen, there is something unique about a state of rest in that frame of reference. And it's equally unique to have any other value of velocity you can think of, such as -2.5 m/s.

I understand your point. My point is that your point makes no sense to her because she doesn't have the experience with physics to appreciate it, and she won't until she does!

Perhaps when she encounters her students having the misconception that a net force of zero implies a state of rest, not a state of uniform motion, she'll start to understand what you're telling her.

 

[Spinnor]

"blanket of snow"

I do believe she is right, a blanket of snow can keep the ground warm if the outside air temp is low. Snow on the ground can help spring arrive earlier.

"Working like an insulating blanket, snow cover holds heat in the ground beneath it and prevents ground moisture from evaporating into the atmosphere ..."

From, https://nsidc.org/cryosphere/frozenground/what_affects_fg.html

From, https://www.google.com/search?safe=...3i22i29i30k1j33i21k1j33i160k1.134.FAL6JBAEG3U

 

[Chestermiller]

I do believe she is right, a blanket of snow can keep the ground warm if the outside air temp is low. Snow on the ground can help spring arrive earlier.

"Working like an insulating blanket, snow cover holds heat in the ground beneath it and prevents ground moisture from evaporating into the atmosphere ..."

From, https://nsidc.org/cryosphere/frozenground/what_affects_fg.html

From, https://www.google.com/search?safe=...3i22i29i30k1j33i21k1j33i160k1.134.FAL6JBAEG3U

The maximum temperature of snow or water in contact with melting snow is 0C. That doesn’t seem very warm to me.

 

[Herman Trivilino]

The maximum temperature of snow or water in contact with melting snow is 0C. That doesn’t seem very warm to me.

It would if the air temperature is -20 °C.

 

[Chestermiller]

It would if the air temperature is -20 °C.

If the air temperature is minus 20C, the snow temperature will cool down to -20 too.

 

[William Ray]

"Physics accepts two conditions for an object - in uniform motion, or in non-uniform motion."

And since the first of those is equivalent to a state of rest, you can just as correctly label the two conditions as a state of rest and a state of non-uniform motion. That's the part that's a matter of semantics.

Ah, I believe I understand where you're coming from now. And I agree, it would be purely a matter of semantics if she was simply re-naming things "a state of rest" and "non-uniform motion". I might raise my eyebrows at that, but I wouldn't be putting much effort into attempting to help her improve her understanding in that case. I probably also wouldn't be particularly concerned if she was teaching that there was an "at rest" state with properties that were indistinguishable from the properties of uniform motion.

The issue that I have is that she's teaching the students that this "rest" state has different properties from uniform motion. She's not articulating anything about the differences (no big surprise there!), but is grading things as incorrect, if the students give "uniform motion" answers to "at rest" problems. In her world, "zero velocity", and "the velocity is not changing" are not true statements with respect to an object "at rest". In my opinion, this is going to break students' understandings at a fairly fundamental level, and I'd like to help her back on the right path before things get too confused.

 

[William Ray]

If the air temperature is minus 20C, the snow temperature will cool down to -20 too.

Heh - I wasn't going to get into this, but... Snow is mostly trapped air, and makes a fairly good insulator. Also, in most areas, there's quite a lot of stored heat energy available in the earth. A decent layer of snow can make a quite dramatic difference in the surface-soil temperature, by decreasing the losses to significantly colder air, and thereby shifting the thermal gradient up in the soil.

 

[Buckethead]

I don't see where she's got the physics part wrong. She needs to teach students how to solve physics problems, and to do that they need to understand things like the fact that the velocity is zero at the turning points in one-dimensional motion, and that it's not zero otherwise.

This is not correct. If you throw a ball into the air so that it slows, stops, and reverses, the entire time it is an inertial frame in a gravitational field. At no time is it experiencing proper acceleration from the time it is released until the time it is stopped by the ground. You also cannot say that it is in motion unless you specify a point of reference. It is possible to say the ball is at rest when it is released and in motion the entire remainder of its journey if the point of reference is an observer moving with the same velocity as the ball when it is released.

 

[Chestermiller]

Heh - I wasn't going to get into this, but... Snow is mostly trapped air, and makes a fairly good insulator. Also, in most areas, there's quite a lot of stored heat energy available in the earth. A decent layer of snow can make a quite dramatic difference in the surface-soil temperature, by decreasing the losses to significantly colder air, and thereby shifting the thermal gradient up in the soil.

So, are you saying that a blanket of snow causes the crocuses to come up early, and, in years when we don't have any snow whatsoever, the crocuses come up late?

 

[jbriggs444]

If the air temperature is minus 20C, the snow temperature will cool down to -20 too.

No, It will not.

 

[Spinnor]

It would if the air temperature is -20 °C.

If the air temperature is minus 20C, the snow temperature will cool down to -20 too.

Snow can be up to 90 percent air which is a good insulator so it slows the transfer of heat. the top layer of snow may approach -20 but the snow will slow the slow the release of heat from the earth.

 

[Chestermiller]

No, It will not.

Snow can be up to 90 percent air which is a good insulator so it slows the transfer of heat. the top layer of snow may approach -20 but the snow will slow the slow the release of heat from the earth.

With a blanket of snow, would it at least be correct to say that the temperature at the ground surface would never get above 0C (since, if the snow at the surface were melting, ice water would be produced at the surface at 0 C)?

 

[Spinnor]

With a blanket of snow, would it at least be correct to say that the temperature at the ground surface would never get above 0C (since, if the snow at the surface were melting, ice water would be produced at the surface at 0 C)?

Interesting and complicated thermo problem. Bottom line, I think your mother in laws observation can be backed up with solid physics but not here.

 

[Chestermiller]

Interesting and complicated thermo problem. Bottom line, I think your mother in laws observation can be backed up with solid physics but not here.

It doesn’t seem very complicated to me. My background is in thermodynamics and heat transfer. Would you like me to show you how to analyze it?

Are you saying that my mother-in-law is correct about the blanket of snow helping the crocuses emerge earlier (even, as we know, the surface temperature can't be more than 0 C with snow present on the surface)?

 

[Spinnor]

It doesn’t seem very complicated to me. My background is in thermodynamics and heat transfer.

I am on someone's clock. My hunch is you are wrong on this.

 

[Chestermiller]

I am on someone's clock. My hunch is you are wrong on this.

There is a big difference between a hunch and actual physical analysis. So I offer again: would you like me to show you how to analyze this (with proper heat transfer equations)?

And you haven't answered my question about the crocuses.

 

[jbriggs444]

With a blanket of snow, would it at least be correct to say that the temperature at the ground surface would never get above 0C (since, if the snow at the surface were melting, ice water would be produced at the surface at 0 C)?

Yes, that statement I can agree with.

 

[William Ray]

So, are you saying that a blanket of snow causes the crocuses to come up early, and, in years when we don't have any snow whatsoever, the crocuses come up late?

I am saying that a blanket of snow eliminates most radiative heat loss from the soil, and slows (assuming an air temperature below 0C) conductive heat loss. As a result, the soil under the snow will often be warmer than it would be without the snow. What effect that has on crocuses I cannot say.

Fundamentally, the layer of snow on the ground is no different than a layer of fiberglass insulation on the ground, with the exception of the fact that the snow melts at a lower temperature than the fiberglass. So long as the temperatures involved are such that the "insulating stuff", whatever it is, doesn't melt, it functions as an insulator and decreases thermal flux across it. Given that the Earth beneath the snow provides a practically infinite reservoir of heat energy, during periods when that thermal flux would generally be "out of the soil", putting an insulator in the way results in the soil being warmer than in the absence of the insulator.

 

[Spinnor]

I am saying that a blanket of snow eliminates most radiative heat loss from the soil, and slows (assuming an air temperature below 0C) conductive heat loss. As a result, the soil under the snow will often be warmer than it would be without the snow. What effect that has on crocuses I cannot say.

Fundamentally, the layer of snow on the ground is no different than a layer of fiberglass insulation on the ground, with the exception of the fact that the snow melts at a lower temperature than the fiberglass. So long as the temperatures involved are such that the "insulating stuff", whatever it is, doesn't melt, it functions as an insulator and decreases thermal flux across it. Given that the Earth beneath the snow provides a practically infinite reservoir of heat energy, during periods when that thermal flux would generally be "out of the soil", putting an insulator in the way results in the soil being warmer than in the absence of the insulator.

In addition a clear cool night sky radiates less heat towards the ground then snow at zero. ? The snow actually radiates more heat towards the ground then a clear cool sky. ?

I remember in a post to sci.physics that an infrared thermometer I pointed towards a clear summer sky show a temp well below freezing.

 

[Chestermiller]

I am saying that a blanket of snow eliminates most radiative heat loss from the soil, and slows (assuming an air temperature below 0C) conductive heat loss. As a result, the soil under the snow will often be warmer than it would be without the snow. What effect that has on crocuses I cannot say.

Fundamentally, the layer of snow on the ground is no different than a layer of fiberglass insulation on the ground, with the exception of the fact that the snow melts at a lower temperature than the fiberglass. So long as the temperatures involved are such that the "insulating stuff", whatever it is, doesn't melt, it functions as an insulator and decreases thermal flux across it. Given that the Earth beneath the snow provides a practically infinite reservoir of heat energy, during periods when that thermal flux would generally be "out of the soil", putting an insulator in the way results in the soil being warmer than in the absence of the insulator.

When water melts at 0C, the water formed is also at 0C. This would happen at the ground surface. The water formed would seep into the pores of the snow above. As long as there is any snow left at the ground surface, the water and snow would have to be at thermal equilibrium at 0 C. So, with snow on the ground, the temperature at the ground surface could never get higher than 0 C. I stand by this, and @jbriggs444 seems to agree with me.

Here is a heat balance at the surface of the ground that captures the mechanisms you discussed above. Let q(t) be the upward heat flux from the ground surface and let $\lambda$ be the heat of melting (334 J/gm) of snow. The heat balance is:
$$-\rho \lambda \frac{d\delta}{dt}=q(t)-k\frac{(0-T_{air})}{\delta}$$where k is the thermal conductivity of the snow layer (typically, 0.045W/m.C for dry snow), $\rho$ is the bulk density of the snow (typically 100 kg/m^3 for dry snow). The second term on the right hand side represents the rate at which heat is conducted away from the interface through the snow layer to the surrounding air above. The overall right hand side represents the net upward flux of heat into the interface. It is equal to the rate at which ice melts to form water at the surface times the heat of melting (the left hand side). The melting causes the snow layer to decrease in thickness (from below), as captured by the minus sign on the left hand side..

Even if the heat conduction through the snow layer were zero (k = 0), the above equation would reduce to $$-\rho \lambda \frac{d\delta}{dt}=q(t)$$ Under these circumstances, the temperature at the surface would remain at 0 C while the snow is melting (from below), and the melting rate would be given by: $$\frac{d\delta}{dt}=-\frac{q}{\rho \lambda}$$ Back to the original equation, if the air temperature above the layer were below 0C, the melting rate would slow down.

Melting would stop all together if the air temperature were low enough. The air temperature for this to happen would be
$$T_{air}=-\frac{q\delta}{k}$$ If the air temperature dropped below this value, the temperature at the surface would actually drop below 0C, and would be given by
$$T_{surface}=T_{air}+\frac{q\delta}{k}<0$$

 

[Herman Trivilino]

If the air temperature is minus 20C, the snow temperature will cool down to -20 too.

Given enough time, yes. But suppose it goes to -20 °C for just a few hours at night, and warms back up each day. Any form of insulation will moderate the temperature of whatever's underneath the insulation. And just a few feet below the surface the ground stays above 0 °C all winter long. The frost layer (layer of frozen earth) may not be as thick because of the snow, bringing the Spring (soil) thaw earlier in the year than it otherwise would have.

So, with snow on the ground, the temperature at the ground surface could never get higher than 0 C.

Not an issue. The ground is already frozen solid anyway, and will stay that way as long as the air temperature stays below water's freezing point. What happens, though, when the air gets even colder? The ground will get colder and freeze deeper. A blanket of snow will hinder this process. Call a local funeral home and ask them why burials are more expensive in the winter. To save money many if not most families will wait until after the Spring thaw for the burial service.

 

[Chestermiller]

Given enough time, yes. But suppose it goes to -20 °C for just a few hours at night, and warms back up each day. Any form of insulation will moderate the temperature of whatever's underneath the insulation. And just a few feet below the surface the ground stays above 0 °C all winter long. The frost layer (layer of frozen earth) may not be as thick because of the snow, bringing the Spring (soil) thaw earlier in the year than it otherwise would have.
Not an issue. The ground is already frozen solid anyway, and will stay that way as long as the air temperature stays below water's freezing point. What happens, though, when the air gets even colder? The ground will get colder and freeze deeper. A blanket of snow will hinder this process. Call a local funeral home and ask them why burials are more expensive in the winter. To save money many if not most families will wait until after the Spring thaw for the burial service.

Thanks. I agree. Apparently William Ray and Spinnor don't get the idea that, if you put a thermometer in a bucket of ice water, the temperature you measure will be 0C.