Vertical Circle Motion: Acceleration at Top vs. Bottom

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Homework Help Overview

The problem involves a ball of mass m swinging in a vertical circle, with a focus on comparing the centripetal acceleration at the top and bottom of the circle. The original poster seeks to understand the relationship between tensions at different points in the motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to analyze the forces acting on the ball at both the top and bottom of the circle, questioning whether the tensions at these points are the same. Some participants suggest using conservation of energy to relate the velocities at the top and bottom, while others confirm the approach and encourage further exploration.

Discussion Status

The discussion has progressed with participants providing guidance on using conservation of energy principles. There is an acknowledgment of the calculations leading to a specific value for centripetal acceleration, but no consensus on the interpretation of the results has been reached.

Contextual Notes

The original poster's inquiry is framed within the constraints of a homework assignment, which may limit the depth of exploration into the concepts involved.

ethex
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Homework Statement


A ball of mass m is suspended from a rope of length R. The ball is set into freely swinging circular motion a vertical plane. The centripetal acceleration of the ball at the top of the circle is 13g. What is the centripetal acceleration of the ball at the bottom of the circle.


Homework Equations





The Attempt at a Solution



At the top,

T + mg = mv^2/R


At the bottom, T - mg = mv^2/R

My question is does Ttop and Tbtm the same?

Hint for this question?
 
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Using conservation of energy principle helps you get v(top) in terms of v(bottom) and you may deduce whether the tensions are equal.
 
Ui + Ki = Uf + Kf

0 + 0.5mVbtm^2 = 2mgR + 0.5mVtop^2

Right?
 
Yes. Continue.
 
I got 17g!
 
Now you know what the answer to your question.
 
Yes! thank you.!
 

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