Pedagogical Machine: Solving Homework Equations

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In summary, the conversation discusses the solution to a problem involving three masses (m1, m2, and m3) and their respective accelerations. The goal is for m2 to be at rest relative to m1, which implies that m3 must also be at rest in the vertical direction. By boosting to a frame co-moving with m1, it is found that F = (m1 + m2 + m3)(m3/m2)g. The limiting cases of m3 = 0 and m2 = 0 are also discussed. One person prefers analyzing the problem from the stationary frame, while the other dislikes working with pseudo forces.
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Homework Statement


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Homework Equations


F = ma


The Attempt at a Solution


What we want is for m2 to be at rest relative to m1 because this implies m2 will not be sliding across the surface of m2 and this immediately implies m3 must be at rest in the vertical direction (in the lab frame and frame of m1 because there will be no pseudo forces in the vertical direction on m3) because if m3 was not at rest vertically then m2 would be slipping along m1 while m1 was moving which is a contradiction if we assume m2 is at rest with respect to m1 while m1 is moving. Boosting to a frame co - moving with m1 we have that in this frame, [itex]m_{2}a_{2} = F_{apparent} = T - m_{2}a = 0[/itex] where [itex]a = \frac{F}{m_{1} + m_{2} + m_{3}}[/itex] is the acceleration of the entire apparatus (and consequently m2 since they all move together under F). As noted above, this immediately implies [itex]m_{3}a_{3} = T - m_{3}g = 0[/itex] so combining this together we have that [itex]m_{3}g = m_{2}a[/itex] so [itex]F = (m_{1} + m_{2} + m_{3})(\frac{m3}{m2})g[/itex]. If I take m1 = m2 = m3 = m then F = 3mg as stated in the ans. clue. I also checked the limiting cases m3 = 0 which gives F = 0 as it should because if there is no m3 then m2 will be at rest even in the lab frame so we don't need any force on m1. If m2 = 0 then F = infinity which makes sense since if m2 = 0, m3 will go into free fall and the only way to stop it from going into free fall using a horizontal force would be an infinite one that accelerates it in the horizontal direction so fast that it doesn't get a chance to fall (this is unphysical of course). Is the solution right? Thanks!
 
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I analyzed it from the stationary frame where all masses share a common acceleration and got the same results.
I dislike working with pseudo forces because it encourages engineers to believe centrifugal forces are real.
 

FAQ: Pedagogical Machine: Solving Homework Equations

1. What is a Pedagogical Machine?

A Pedagogical Machine is a computer program or software that is specifically designed to assist students in solving homework equations. It incorporates various interactive features to engage students in the learning process and helps them understand concepts more effectively.

2. How does a Pedagogical Machine work?

A Pedagogical Machine uses algorithms and programming techniques to provide step-by-step guidance for solving homework equations. It also includes visual aids, such as graphs and diagrams, to help students visualize and understand the problem better.

3. Can a Pedagogical Machine solve all types of equations?

No, a Pedagogical Machine may not be able to solve all types of equations as it is designed to cater to a specific set of equations or topics. However, it can provide general guidance and support for a wide range of equations and problems.

4. Is a Pedagogical Machine a substitute for a teacher?

No, a Pedagogical Machine is not a substitute for a teacher. It is meant to supplement classroom learning and provide additional support for students. A teacher's guidance and feedback are still essential for a student's overall understanding and progress.

5. Is a Pedagogical Machine effective in improving student performance?

Research has shown that Pedagogical Machines can be effective in improving student performance, particularly in subjects like math and science. However, the effectiveness may vary depending on the individual student's learning style and engagement with the program.

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