Centripetal Force: Speed Change w/ Doubled Radius & Force

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Homework Help Overview

The problem involves centripetal force, specifically examining how changes in force and radius affect the speed of an object in circular motion. The original poster presents a scenario where both the centripetal force and the radius are doubled, leading to multiple-choice options regarding the speed change.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss substituting values into the centripetal force equation to analyze the impact on speed. There are questions about the cancellation of terms and the interpretation of the problem's wording. Some participants express confusion about the correct answer and seek clarification on calculations.

Discussion Status

The discussion is active, with participants sharing their calculations and questioning the assumptions behind the problem. Some have expressed disagreement with the proposed answer, while others are attempting to clarify their reasoning and calculations.

Contextual Notes

There is a noted concern regarding the wording of the question, particularly the description of centripetal force. Participants are also navigating potential misunderstandings related to the relationship between force, radius, and speed in the context of the problem.

brake4country
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Homework Statement


The centripetal force acting on an object is doubled. The radius is also doubled. The speed of the object:

(a) increases by a factor of 4
(b) increases by a factor of 2
(c) decreases by a factor of 2
(d) The change in the object's speed depends on its mass

Homework Equations


F = mv2/r

The Attempt at a Solution


So if I substitute 2's in for F and r in the above equation, my 2's cancel but the correct answer is a. ?
 
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Do a numerical example...
 
brake4country said:
The centripetal force acting on an object is doubled.
So if I substitute 2's in for F and r in the above equation, my 2's cancel but the correct answer is a. ?
Not happy with the wording of the question. Centripetal force does not act. It is the force required to be supplied by forces which do act in order to produce a certain motion.
Anyway, I don't get how the 2's would cancel. (Not that I necessarily agree with the supposed answer.). Please post detailed working.
 
I am sorry; an erroneous math calculation. By substituting 2 for both the force and the radius, I get 4 which is (a). Thank you!
 
Can you still show your calculation ? It doesn't fit at all.
 
brake4country said:
I am sorry; an erroneous math calculation. By substituting 2 for both the force and the radius, I get 4 which is (a). Thank you!
As I hinted, I disagree with that answer. Looks like BvU disagrees with it too.
 
Sorry everyone! That's what happens when you don't read the answer choices correctly! Okay here is the original question: the centripetal force acting on an object is doubled. The radius of the object's motion is also doubled. The speed of the object is:
(A) increases by a factor of
(B) increases by a factor of 2
(C) decreases by a factor of 2
(D) the change in the object's speed depends on its mass.

Fc = mv2/r. If I plug in 2 for F and r, I get 2 = mv2/2 = 4 = mv2. Therefore, the correct answer is (B) increases by a factor of 2! Thanks everyone!
 

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