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non plug-and-chug



Greetings,
I emailed the following challenge to my grade 11 and 12 physics students and to the graduates who chose to remain on the list. This type of problem does a good job of identifying the formal operational thinkers, but doesn't necessarily teach thinking skills to the others. I had one gifted student last year who would tune out until I posed such a problem. Then he would light up and work feverishly.
Here's the problem;
"Don't miss the August issue of Scientific American featuring a cover article by Mordechai Milgrom, the Israeli physicst who proposes a controvertial solution to the galactic rotation problem by modifying Newton's F = ma as an alternative to the dark matter hypothesis!
The problem has been that stars in galaxies are all rotating way too fast to be held in their orbit by the central galactic mass that is calculated from the brightness of the galctic core. So, astrophysicists have proposed invisible "dark matter" to make up the missing mass. Problem is, there would have to be many times more dark matter than visible matter, and invisible matter is hard to detect.

So Milgrom says, maybe F=m a is more like F= m a^2 when the acceleratrion is very small, like around a = 10^ -10 m/s^2., (Milgrom's constant) , If so

then dark matter is not needed to explain galactic rotation.

The orbital speeds he predicts using this Modification Of Newtonian Dynamics (MOND) match the observed speeds (for all but one type of galaxy) very closely whereas Newton's unmodified law makes velocity predictions that are as low as 1/3 of the observed values.

Milgrom's formula for the modification of Newton's second law is not included in the article.See if you can use Milgrom's constant to modify F= ma to act linearly for larger accelerations, and like F=ma squared for small accelerations to get a graph like on page 44 of the magazine. Check your formula by graphing it on your calculator. Remember, Milgrom did not derive his formula from frist principles - he just designed an exponent to fudge Newton's second law to give the curve on page 44 . "

-Barry Gragg,

The Dwight School,

NY, NY,

Proud Home of the 2002 NYC Science Olympiad Cowabungee and Physics Lab Champs.













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