Help a HS teacher understand uniform motion?

[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.

 

[Mister T]

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.

 

[Mister T]

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
$$T_{surface}=T_{air}+\frac{q\delta}{k}<0$$

 

[Mister T]

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.

 

[William Ray]

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.

[edited]
I'm not sure where you get the impression that I don't get that idea. I don't believe anyone's disagreeing with you that the surface of the ground will not exceed 0C. I also don't see why you think this is relevant to the question you asked. You are aware that the temperature of the air, (as well as the black-body temperature of the night sky, though it seems we're mostly ignoring radiation here), are significantly below 0C for much of the winter, in many parts of the world?

If you can find anything in what I've said that suggests that there is not an upper limit to the temperature that the sub-snow ground can attain, I'll eat my shorts. Otherwise I believe you're off base here.

 

[Chestermiller]

[edited]
I'm not sure where you get the impression that I don't get that idea. I don't believe anyone's disagreeing with you that the surface of the ground will not exceed 0C. I also don't see why you think this is relevant to the question you asked. You are aware that the temperature of the air, (as well as the black-body temperature of the night sky, though it seems we're mostly ignoring radiation here), are significantly below 0C for much of the winter, in many parts of the world?

If you can find anything in what I've said that suggests that there is not an upper limit to the temperature that the sub-snow ground can attain, I'll eat my shorts. Otherwise I believe you're off base here.

I'm very sorry. Please forgive me. This is all my misinterpretation of what you were saying.

Chet

 

[William Ray]

I'm very sorry. Please forgive me. This is all my misinterpretation of what you were saying.

Chet

Delighted to hear it! I'd hate to think that one or the other of us had gone insane :-)

 

[nitsuj]

lol what of the blanket of snow keeping the ground cold,

Given "mother in laws" reasoning a thicker blanket would maintain the delta in temps better. I'm sure Canadian golf courses have plenty to say about snow blankets.

I would also imagine the average ground temp has a huge influence on this. I think it might be called "frost depth". The ground where I live is probably only frozen a couple of meters down at it's peak...now does the blanket maintain the frost or protect it from going deeper?

 

[laymanB]

I’m confused. Is the snow blanket at rest, uniform motion, or non-uniform motion?