Circular Motion Problem 2: Help with Solving | Physics Forum

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Homework Help Overview

The discussion revolves around a circular motion problem involving acceleration and integration. Participants are exploring the relationship between tangential and normal acceleration under specific conditions.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Some participants suggest using different forms of acceleration, specifically a=vdv/ds instead of a=dv/dt. There are discussions about integrating with proper limits and checking the correctness of the approach taken. Questions arise regarding the handling of limits during integration and the implications of deceleration in the context of the problem.

Discussion Status

Participants have provided various approaches and some guidance on integration techniques. There is acknowledgment of different methods leading to answers, but also a recognition of potential errors in reasoning and assumptions. The conversation reflects a mix of validation and inquiry into the correctness of the methods used.

Contextual Notes

There are mentions of specific conditions such as the particle's deceleration and the importance of limits in integration. Some participants note that the original problem statement includes specific constraints that may affect the integration process.

thunderhadron
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Hi friend the problem is as follows:



Attempt:





Please friends help me in this.
Thank you all in advance
 
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Instead of using a=dv/dt use a=vdv/ds.

The given condition is |aT|=|aN|

i.e -vdv/ds=v2/R .

Integrate with proper limits and you will get the answer.
 
Tanya Sharma said:
Instead of using a=dv/dt use a=vdv/ds.

The given condition is |aT|=|aN|

i.e -vdv/ds=v2/R .

Integrate with proper limits and you will get the answer.

Thank you very much tanya. I got the answer.

But Was I doing it in wrong manner?
 
You got the answer with your approach or the one i asked you to do ?
 
Tanya Sharma said:
You got the answer with your approach or the one i asked you to do ?

By your approach.
 
thunderhadron said:
Thank you very much tanya. I got the answer.

But Was I doing it in wrong manner?

The particle was decelerating, so your first equation should have been a=-v2/R. The other error was, that when you integrated v with respect time, you forgot the lower limit of integration. So your result is dimensionally incorrect. Tanya's solution is very elegant and simple, but yours is also all right if you do it properly. :smile:

ehild
 
ehild said:
The other error was, that when you integrated v with respect time, you forgot the lower limit of integration. :smile:

ehild

The lower limit of time should be zero. The question states that.
 
thunderhadron said:
The lower limit of time should be zero. The question states that.

Yes, but you have ln(R-volt), it is not zero at t=0.
 
  • #10
After integration when you put t=0,the term doesn't vanish.You have erroneously assumed it to be 0.
 
  • #11
Thank you very much friends. I got the answer. Problem has been cleared.
 

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