Elliptic path, normal and tangential acceleration

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Homework Help Overview

The discussion revolves around the motion of a point mass in a plane described by parametric equations involving trigonometric functions. Participants are tasked with calculating the speed and the normal and tangential components of acceleration at any time t, within the context of special relativity.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the derivation of velocity and acceleration components, with some questioning the correctness of the calculations. There are attempts to express the tangential and normal components of acceleration in terms of the velocity and acceleration vectors.

Discussion Status

Several participants have pointed out potential errors in the calculations, particularly regarding the magnitude of the velocity and the components of acceleration. There is ongoing exploration of different methods to derive the components, with some guidance provided on using vector relationships.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information available for solving the problem. There are discussions about the implications of specific cases, such as when the parameters a and b are equal, leading to circular motion.

  • #31
@ehild Still no canceling out... I really don't see it. :/ (I wrote only the top line in the attached file because it's so long)
 

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  • #32
JulienB said:
@ehild Still no canceling out... I really don't see it. :/ (I wrote only the top line in the attached file because it's so long)
You forgot to square sin and cos in v^2
 
Last edited:
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  • #33
@JulienB
##(\vec v)^2=w^2(a^2\sin^2(wt)+b^2\cos^2(wt))##
##(\vec a)^2=w^4(a^2\cos^2(wt)+b^2\sin^2(wt))##
What is their product?
 
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  • #34
@ehild aaaah it worked out now! I get the same result as with the other method! Thanks a lot, that was crazy! ;)

Julien.
 
  • #35
JulienB said:
@ehild aaaah it worked out now! I get the same result as with the other method! Thanks a lot, that was crazy! ;)

Julien.
Well done. I must sleep now but tomorrow I show you how the formula you used is connected to vector products.
 
  • #36
@ehild Thanks a lot! I must sleep too otherwise I would post the correct calculation again. I'll do it tomorrow.
 

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