Find the differential equation and velocity

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SUMMARY

The discussion centers on solving a differential equation related to motion, specifically finding the velocity at point C using kinetic energy principles. The participant confirms that the work done from point A to C is derived from the difference in potential energy between these points. There was a clarification regarding the translation of "R" from circumference to radius, which is crucial for accurate calculations. Overall, the analysis presented is deemed correct and mathematically sound.

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  • Differential equations
  • Kinetic energy principles
  • Potential energy concepts
  • Mathematical translation of physics problems
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  • Study the application of differential equations in physics problems
  • Learn about the relationship between potential and kinetic energy
  • Explore motion simulation coding techniques
  • Investigate common pitfalls in translating physics concepts into mathematical language
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Students in physics or engineering, educators teaching mechanics, and anyone interested in the mathematical modeling of motion dynamics.

Alexiy
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Homework Statement


probs_Untitled.jpg


Homework Equations


3. The Attempt at a Solution [/B]
rijes_Untitled.jpg
Hello guys,I posted images since its easier to write equations.Please can someone help me check this, if this is correct so far, then i should be able to find the velocity at C, using kinetic energy?
 
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Looks good to me.
 
Chestermiller said:
Looks good to me.
velocity_Untitled.jpg


Edit: Work done from A to C is the difference of the potential energy between these two points, am i wrong?
 
Last edited:
By the way in the problems text i translated R as circumference, but its actually a radius R.
 
In my judgment, you did all this correctly. I think you should have more confidence in your ability. Your analysis was very nice, perceptive, and mathematically talented.

Chet
 
Chestermiller said:
In my judgment, you did all this correctly. I think you should have more confidence in your ability. Your analysis was very nice, perceptive, and mathematically talented.

Chet
Thank you very much Chet, I can't help it,I always had some difficulties to translate "physics thoughts" into math language so maybe I am overly cautious, sometimes i even waste time writing code for motion simulations to make sure something behaves like its supposed to, but it seems I'm getting the hang of it.Thanks again for your support.
 

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