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The Academics Thread


Pariah

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Hm, I did something I hope I didn't swear several decades back that I'd never do, and that's invoke some obscure trig identities in a homework problem.  Namely and to wit,

 

cos( arctan(x) ) = 1 / sqrt(1 + x^2)

sin( arctan(x) ) = x / sqrt(1 + x^2)

 

Ah well, I'll just put "Only the north end of a southbound horse would expect students to find these and use them" on the solutions key.

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I learned several years ago that they no longer mention polar coordinates in the freshman calculus series, let alone do calculus in such coordinates.  I have never understood why that change was made to the curriculum.  There are lots of things that are flat-out painful in Cartesian coordinates that are trivially easy in polar coordinates.  Fantastic labor-saver, IMO.  But Nooooooooooooo, can't add anything to the toolkit or their poor little brains will explode!

 

Grr.

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Gov DeSantis is well on his way to destroying education in Florida. He already attacked the free speech ability of professors at UF, is working on re-writing history (i.e. you can say there were slaves but not why), and now teachers can be sued for discussing gender identity. 

 

Florida Gov. Ron DeSantis signals support for 'Don't Say Gay' bill

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Another round of parent-teacher conferences successfully completed. Or at least survived.

 

In a related story: I was talking with one of my fellow teachers yesterday, and she told me that her daughter had had my chemistry class a few years ago. Now she's in college studying biomedical engineering.

 

This teacher told me that whenever her daughter gets stuck on something in chemistry, she pulls out the notebook she kept from my class and looks it up. And that helps her to figure it out. She said her daughter told her, "Every time I have a problem, I get out Mr P's notebook and I can find the answer."

 

For everybody who wonders how or why teachers continue to do what they do in an increasingly hostile cultural environment, this is how and this is why.

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6. Two equal masses hang on a cord from opposite sides of an ideal, frictionless pulley. The two masses are not at the same height: mass U is higher than mass L. Assuming the two masses start at rest, how will they move once they are released, if they move at all? Explain in terms of Newton's Laws of Motion.

 

This seems to have overthrown a rather large portion of the class.

ex2q3.png

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1 hour ago, Cancer said:

 

This seems to have overthrown a rather large portion of the class.

ex2q3.png

 

Assuming that the mass of the cord is negligible, then I'd say that Newton's Third Law would be the relevant case. The downward force on U by gravity would be countered by the downward force on L by gravity. Since the two masses are equal, start at rest, and are both experiencing the same acceleration, there wouldn't be any movement in the two masses, because the forces on the two masses oppose each other equally.

 

Mind you, it's been about 30 years since my last college Physics course, so I may be a bit rusty.

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