Insights Corrections to MIT Open Courseware: Systems of Varying Mass

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The discussion highlights significant concerns regarding the solutions provided in the MIT Open Courseware for the 8-01sc Classical Mechanics course, specifically in the section on applying Newton's Laws to systems of varying mass. The primary issue identified is that while the answers may be correct, the algebraic methods used are flawed, leading to potential confusion for students. A critical flaw noted is the incorrect representation of a system's momentum as a function of time while simultaneously treating it as a function of two variables, which results in contradictory equations. This confusion appears to stem from an improper application of the fundamental equations of motion, particularly the relationship between force, momentum, and mass variation. The reliability of MIT's material is questioned due to these inaccuracies.
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Corrections to
MIT Open Courseware 8-01sc classical mechanics,
fall 2016
Applying Newton’s Laws to systems of Varying Mass
PDF Course Link
My concerns with the solutions provided on the cited MIT Open Courseware web page are, mostly:


Despite arriving at the correct answers, the algebraic methods are invalid. As a result, they can be utterly confusing to the student.
The main flaw, repeated throughout, is writing a system state (momentum) as a function of time only, but effectively defining it as a function of two variables. In some places, this leads to contradictory equations.


This mangled treatment likely results from an attempt to use ##F=\frac {dp}{dt}## in conjunction with ##\frac{dp}{dt}=m\frac{dv}{dt}+\frac{dm}{dt}v##, instead of the...

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That's a bit concerning. I usually take material from MIT as being pretty much 'gospel' !
 
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