Re: [IAEP] Gravity for Beginners...
And, as Edward knows, it is almost beyond belief that Newton did take into account all of these factors the very first time out of the chute in the Principia. Cheers, Alan From: Edward Cherlin echer...@gmail.com To: Yamandu Ploskonka yamap...@gmail.com Cc: iaep iaep@lists.sugarlabs.org Sent: Sat, March 27, 2010 8:48:26 PM Subject: Re: [IAEP] Gravity for Beginners... On Sat, Mar 27, 2010 at 23:11, Yamandu Ploskonka yamap...@gmail.com wrote: How much lighter is a person in La Paz, Bolivia, than at sea level? This actually was asked by a kid when I was there last time. For practical purposes let's assume La Paz is 3.800 m over sea level Fascinating question. The simplest answer is that weight is inversely proportional to distance from the center, which we can approximate as 40,000 km/pi, or 12,742 km on average. This would give us a difference of roughly one part in 5,000 in weight for a difference of 4 parts in 10,000 in height. However, the distance between surface and center is actually 43 km greater at the equator than at the pole, so we have to do some much finer calculations to locate sea level at he latitude of La Paz. Then we have to decide whether to ask what the weights would be on a stationary Earth, or whether we will take rotation into account, resulting in apparent decreases in centripetal forces. If we wanted to be really finicky, we could take relativity into account also. ^_^ On 03/27/2010 10:03 PM, Edward Cherlin wrote: If the kids could really measure accurately, which can be done with a high quality pendulum, they would find that the acceleration is not actually constant, but differs by about one part in a million from 14 feet above the ground and at the ground level (due the more accurate inverse square Newton Law). And if they had access to atomic clocks, they could observe the difference in the rate of passage of time at higher and lower altitudes, which are of practical importance in the clocks on GPS satellites. Measuring the deviations from Newton's Law in a falling object near the surface of the Earth requires greater precision than is available. It is observable with great difficulty in the precession of the orbit of Mercury around the Sun, and more clearly in binary pulsar systems. Please don't hesitate to ask questions. Cheers, Alan From: Walter Benderwalter.ben...@gmail.com To: Jeff Elknerj...@elkner.net Cc: iaep@lists.sugarlabs.org Sent: Sat, March 20, 2010 12:41:01 PM Subject: Re: [IAEP] Gravity for Beginners... kino will let you export your movie as a series of stills... I am sure there are many Free multimedia programs with a similar capability. regards. -walter On Sat, Mar 20, 2010 at 3:17 PM, Jeff Elknerj...@elkner.net wrote: Hi All, I'm working on a derivative version of Gravity for 10 Year Olds to use with my high school age students, which I'm calling Gravity for Beginners: https://docs.google.com/Doc?docid=0ARq50A7-FeDXZGd2MnN0ODJfMjAwNmc0NHF4ZHIhl=en Day 2 has the following: Show the students how to overlay frames from their videos to get this effect: Can anyone point me to easy instructions on how to do this? I can't really use the lesson without it. Thanks! jeff elkner ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep -- Walter Bender Sugar Labs http://www.sugarlabs.org ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep -- Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin Silent Thunder is my name, and Children are my nation. The Cosmos is my dwelling place, the Truth my destination. http://www.earthtreasury.org/ ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep
Re: [IAEP] Gravity for Beginners...
On 28.03.2010, at 06:48, Edward Cherlin wrote: On Sat, Mar 27, 2010 at 23:11, Yamandu Ploskonka yamap...@gmail.com wrote: How much lighter is a person in La Paz, Bolivia, than at sea level? This actually was asked by a kid when I was there last time. For practical purposes let's assume La Paz is 3.800 m over sea level Fascinating question. The simplest answer is that weight is inversely proportional to distance from the center, which we can approximate as 40,000 km/pi, or 12,742 km on average. This would give us a difference of roughly one part in 5,000 in weight for a difference of 4 parts in 10,000 in height. However, the distance between surface and center is actually 43 km greater at the equator than at the pole, so we have to do some much finer calculations to locate sea level at he latitude of La Paz. Then we have to decide whether to ask what the weights would be on a stationary Earth, or whether we will take rotation into account, resulting in apparent decreases in centripetal forces. If we wanted to be really finicky, we could take relativity into account also. ^_^ Indeed. My 10 year old son came home recently with the claim that people on mountains live longer. We had some fun introducing relativity, but didn't actually bother to calculate what fraction of a second this would amount to over a lifetime ;) - Bert - ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep
Re: [IAEP] Gravity for Beginners...
On Sun, Mar 28, 2010 at 07:03, Alan Kay alan.n...@yahoo.com wrote: And, as Edward knows, it is almost beyond belief that Newton did take into account all of these factors the very first time out of the chute in the Principia. Yes, it's all in Book III of the Principia, under the title The System of the World. Orbits of planets, moons, and comets; water tides (but not rock tides); rotational bulges and the variation of gravity from equator to poles; precession of equinoxes; the effect of the Sun on the Moon's orbit; and so on, plus generally good philosophy and bad theology. There are a few other such minds known, able to create multiple branches of math or physics. Archimedes, Leonardo da Vinci (who couldn't publish), Euler, Gauss, Einstein...Those who can create even one are the great men and women of their fields. Coming up with even one significant new idea, and then working out its consequences for a lifetime, makes one a leader. The most amazing thing about the Principia to me is that Newton translated all of the calculus that he used to work out these discoveries into Euclidean geometry for publication, solely in order to avoid controversy over the foundations of the calculus. Since then, Abraham Robinson and John Horton Conway have demonstrated how actual infinitesimals can be incorporated into arithmetic and calculus. Cheers, Alan From: Edward Cherlin echer...@gmail.com To: Yamandu Ploskonka yamap...@gmail.com Cc: iaep iaep@lists.sugarlabs.org Sent: Sat, March 27, 2010 8:48:26 PM Subject: Re: [IAEP] Gravity for Beginners... On Sat, Mar 27, 2010 at 23:11, Yamandu Ploskonka yamap...@gmail.com wrote: How much lighter is a person in La Paz, Bolivia, than at sea level? This actually was asked by a kid when I was there last time. For practical purposes let's assume La Paz is 3.800 m over sea level Fascinating question. The simplest answer is that weight is inversely proportional to distance from the center, which we can approximate as 40,000 km/pi, or 12,742 km on average. This would give us a difference of roughly one part in 5,000 in weight for a difference of 4 parts in 10,000 in height. However, the distance between surface and center is actually 43 km greater at the equator than at the pole, so we have to do some much finer calculations to locate sea level at he latitude of La Paz. Then we have to decide whether to ask what the weights would be on a stationary Earth, or whether we will take rotation into account, resulting in apparent decreases in centripetal forces. If we wanted to be really finicky, we could take relativity into account also. ^_^ On 03/27/2010 10:03 PM, Edward Cherlin wrote: If the kids could really measure accurately, which can be done with a high quality pendulum, they would find that the acceleration is not actually constant, but differs by about one part in a million from 14 feet above the ground and at the ground level (due the more accurate inverse square Newton Law). And if they had access to atomic clocks, they could observe the difference in the rate of passage of time at higher and lower altitudes, which are of practical importance in the clocks on GPS satellites. Measuring the deviations from Newton's Law in a falling object near the surface of the Earth requires greater precision than is available. It is observable with great difficulty in the precession of the orbit of Mercury around the Sun, and more clearly in binary pulsar systems. Please don't hesitate to ask questions. Cheers, Alan From: Walter Benderwalter.ben...@gmail.com To: Jeff Elknerj...@elkner.net Cc: iaep@lists.sugarlabs.org Sent: Sat, March 20, 2010 12:41:01 PM Subject: Re: [IAEP] Gravity for Beginners... kino will let you export your movie as a series of stills... I am sure there are many Free multimedia programs with a similar capability. regards. -walter On Sat, Mar 20, 2010 at 3:17 PM, Jeff Elknerj...@elkner.net wrote: Hi All, I'm working on a derivative version of Gravity for 10 Year Olds to use with my high school age students, which I'm calling Gravity for Beginners: https://docs.google.com/Doc?docid=0ARq50A7-FeDXZGd2MnN0ODJfMjAwNmc0NHF4ZHIhl=en Day 2 has the following: Show the students how to overlay frames from their videos to get this effect: Can anyone point me to easy instructions on how to do this? I can't really use the lesson without it. Thanks! jeff elkner ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep -- Walter Bender Sugar Labs http://www.sugarlabs.org ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep
Re: [IAEP] Gravity for Beginners...
If the kids could really measure accurately, which can be done with a high quality pendulum, they would find that the acceleration is not actually constant, but differs by about one part in a million from 14 feet above the ground and at the ground level (due the more accurate inverse square Newton Law). And if they had access to atomic clocks, they could observe the difference in the rate of passage of time at higher and lower altitudes, which are of practical importance in the clocks on GPS satellites. Measuring the deviations from Newton's Law in a falling object near the surface of the Earth requires greater precision than is available. It is observable with great difficulty in the precession of the orbit of Mercury around the Sun, and more clearly in binary pulsar systems. Please don't hesitate to ask questions. Cheers, Alan From: Walter Bender walter.ben...@gmail.com To: Jeff Elkner j...@elkner.net Cc: iaep@lists.sugarlabs.org Sent: Sat, March 20, 2010 12:41:01 PM Subject: Re: [IAEP] Gravity for Beginners... kino will let you export your movie as a series of stills... I am sure there are many Free multimedia programs with a similar capability. regards. -walter On Sat, Mar 20, 2010 at 3:17 PM, Jeff Elkner j...@elkner.net wrote: Hi All, I'm working on a derivative version of Gravity for 10 Year Olds to use with my high school age students, which I'm calling Gravity for Beginners: https://docs.google.com/Doc?docid=0ARq50A7-FeDXZGd2MnN0ODJfMjAwNmc0NHF4ZHIhl=en Day 2 has the following: Show the students how to overlay frames from their videos to get this effect: Can anyone point me to easy instructions on how to do this? I can't really use the lesson without it. Thanks! jeff elkner ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep -- Walter Bender Sugar Labs http://www.sugarlabs.org ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep -- Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin Silent Thunder is my name, and Children are my nation. The Cosmos is my dwelling place, the Truth my destination. http://www.earthtreasury.org/ ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep
Re: [IAEP] Gravity for Beginners...
On Sat, Mar 27, 2010 at 23:11, Yamandu Ploskonka yamap...@gmail.com wrote: How much lighter is a person in La Paz, Bolivia, than at sea level? This actually was asked by a kid when I was there last time. For practical purposes let's assume La Paz is 3.800 m over sea level Fascinating question. The simplest answer is that weight is inversely proportional to distance from the center, which we can approximate as 40,000 km/pi, or 12,742 km on average. This would give us a difference of roughly one part in 5,000 in weight for a difference of 4 parts in 10,000 in height. However, the distance between surface and center is actually 43 km greater at the equator than at the pole, so we have to do some much finer calculations to locate sea level at he latitude of La Paz. Then we have to decide whether to ask what the weights would be on a stationary Earth, or whether we will take rotation into account, resulting in apparent decreases in centripetal forces. If we wanted to be really finicky, we could take relativity into account also. ^_^ On 03/27/2010 10:03 PM, Edward Cherlin wrote: If the kids could really measure accurately, which can be done with a high quality pendulum, they would find that the acceleration is not actually constant, but differs by about one part in a million from 14 feet above the ground and at the ground level (due the more accurate inverse square Newton Law). And if they had access to atomic clocks, they could observe the difference in the rate of passage of time at higher and lower altitudes, which are of practical importance in the clocks on GPS satellites. Measuring the deviations from Newton's Law in a falling object near the surface of the Earth requires greater precision than is available. It is observable with great difficulty in the precession of the orbit of Mercury around the Sun, and more clearly in binary pulsar systems. Please don't hesitate to ask questions. Cheers, Alan From: Walter Benderwalter.ben...@gmail.com To: Jeff Elknerj...@elkner.net Cc: iaep@lists.sugarlabs.org Sent: Sat, March 20, 2010 12:41:01 PM Subject: Re: [IAEP] Gravity for Beginners... kino will let you export your movie as a series of stills... I am sure there are many Free multimedia programs with a similar capability. regards. -walter On Sat, Mar 20, 2010 at 3:17 PM, Jeff Elknerj...@elkner.net wrote: Hi All, I'm working on a derivative version of Gravity for 10 Year Olds to use with my high school age students, which I'm calling Gravity for Beginners: https://docs.google.com/Doc?docid=0ARq50A7-FeDXZGd2MnN0ODJfMjAwNmc0NHF4ZHIhl=en Day 2 has the following: Show the students how to overlay frames from their videos to get this effect: Can anyone point me to easy instructions on how to do this? I can't really use the lesson without it. Thanks! jeff elkner ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep -- Walter Bender Sugar Labs http://www.sugarlabs.org ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep -- Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin Silent Thunder is my name, and Children are my nation. The Cosmos is my dwelling place, the Truth my destination. http://www.earthtreasury.org/ ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep
Re: [IAEP] Gravity for Beginners...
Thanks! I'll let you know how it goes. On Sat, Mar 20, 2010 at 6:05 PM, Alan Kay alan.n...@yahoo.com wrote: You can do the overlays in Etoys by using its paint tool to paint out (using transparent paint) the middle of the frames so the others will show through. Also take a look at http://www.vpri.org/pdf/rn2005001_learning.pdf which shows this, and another way to do the measuring by putting frames side by side and using the height of translucent rectangles to do the measuring. There are several key techniques here to keep in mind, even with high school students. One is the 7 + or - 2 principle of not trying to jam too many ideas at once into the For the 5th graders we did fun and games with speed and acceleration several months before dropping objects off the roof of the school. The kids used the translucent rectangles here to get some visual memories of these ideas. (Both Newton and Einstein like to do math first -- to provide concepts and vocabulary -- before looking at the physical world. The translucent rectangles also help a lot with measuring errors (and the fact that you only have pixels, and there is some motion blur in the videos). What you want is for the differences that are clearly shown when the translucent rectangles are overlaid should look to be of constant size (pretty nearly as Newton would say). This gives rise to the hypothesis of constant acceleration, which is then tested by making a simulation with constant acceleration and finding some way to see if the video and the simulation match up. The 10 year olds found some good ways to do this. If the kids could really measure accurately, they would find that the acceleration is not actually constant, but differs by about one part in a million from 14 feet above the ground and at the ground level (due the more accurate inverse square Newton Law). Please don't hesitate to ask questions. Cheers, Alan From: Walter Bender walter.ben...@gmail.com To: Jeff Elkner j...@elkner.net Cc: iaep@lists.sugarlabs.org Sent: Sat, March 20, 2010 12:41:01 PM Subject: Re: [IAEP] Gravity for Beginners... kino will let you export your movie as a series of stills... I am sure there are many Free multimedia programs with a similar capability. regards. -walter On Sat, Mar 20, 2010 at 3:17 PM, Jeff Elkner j...@elkner.net wrote: Hi All, I'm working on a derivative version of Gravity for 10 Year Olds to use with my high school age students, which I'm calling Gravity for Beginners: https://docs.google.com/Doc?docid=0ARq50A7-FeDXZGd2MnN0ODJfMjAwNmc0NHF4ZHIhl=en Day 2 has the following: Show the students how to overlay frames from their videos to get this effect: Can anyone point me to easy instructions on how to do this? I can't really use the lesson without it. Thanks! jeff elkner ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep -- Walter Bender Sugar Labs http://www.sugarlabs.org ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep
