Changing factor of centripetal acceleration

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Homework Help Overview

The problem involves a particle moving in a circular path and examines how the centripetal acceleration changes when the particle's speed increases from v to 19v. The context is centered around the concept of centripetal acceleration in circular motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss calculating centripetal acceleration at two different speeds and comparing the results. Some suggest substituting the new speed into the centripetal acceleration formula to find the change. Others express confusion regarding the terminology used in the problem statement.

Discussion Status

The discussion has evolved with participants providing insights and clarifications. Some have noted the simplicity of the problem while others have pointed out potential sources of confusion in the question's wording. There is a sense of progress as one participant indicates understanding after engaging with the responses.

Contextual Notes

There is mention of a possible confusion arising from the use of the term "v" in both the problem statement and the relevant equation, which may have contributed to initial misunderstandings.

dandy9
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Homework Statement


A particle moves in a circular path of radius r with speed v. It then increases its speed to 19v while traveling along the same circular path. By what factor has the centripetal acceleration of the particle changed?



Homework Equations


ac=v^2/r


The Attempt at a Solution


Tried solving for v in terms of a and r to no avail.
 
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What's the centripetal acceleration when the speed is v? When the speed is 19v? Compare.
 
If the initial centripetal acceleration is v^2/r, then try substituting 'v' with '19v', to get the new centripetal acceleration, then compare the 2 values.
 
dandy9 said:
Tried solving for v in terms of a and r to no avail.

This question is so ridiculously simple that it creates a thinking-trap! It is tempting to think "It can't be that easy... must do some difficult equation solving ... etc."
It is good to know that things are not always complicated. Sometimes the answer is right in front of you :smile:

The question asks about centripetal acceleration.
You already have a "relevant equation" giving an expression for centripetal acceleration.
 
If you can see the obvious answer now, that's fine.

If you still can't see the answer I will point out one little criticism of the original question, or at least the way it is entered in message #1. This is a possible source of confusion:

The question contains a term "v" and another term "19v". The relevant equation as quoted above also contains a term "v".
It would be better if the relevant equation was written as acc=(velocity)^2 / r

Then it becomes more natural to recognize that you can insert any value into the (velocity) part of the equation.
The (velocity) term in the equation is initially equal to "v" and then it changes to be equal to "19v".
 
Wow, a lot of replies.
Thanks a lot everyone. I understand it now! (And I was able to tell my friends who were also stumped on this question.)
Thanks again!
 

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