What Is the Minimum Frequency for a Mass in Vertical Circular Motion?

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Homework Help Overview

The problem involves a mass attached to a rope being spun in a vertical circle, specifically focusing on determining the minimum frequency required for the mass to maintain its circular motion without falling. The subject area includes concepts from dynamics and circular motion.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster expresses confusion about how to approach the problem after attempting to manipulate equations without success. Some participants question the definition of the forces involved, particularly the centripetal force and minimum tension. Others suggest considering the physical implications of insufficient frequency on the motion of the mass.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the forces at play and the conditions necessary for maintaining circular motion. Some guidance has been provided regarding the role of tension and weight in achieving the required centripetal force, but no consensus has been reached on a specific solution approach.

Contextual Notes

Participants are discussing the minimum frequency in the context of vertical circular motion, with emphasis on the conditions at the top of the circle where tension may reach zero. There is an acknowledgment of the need to consider the forces acting on the mass and the implications of insufficient frequency.

ninetyfour
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Homework Statement



A 0.2kg mass attached to a rope 1.6m long is being spun in a vertical plane. Find the minimum frequency.

Homework Equations



F = 4(pi^2)(r)(f^2)(m)
Ft min = Fc - mg

- minimum frequency occurs at minimum tension


The Attempt at a Solution



I had this question on a test and spend like 45 minutes on it. I have no idea what to do, and I am curious as to what I should have done. I tried inserting numbers and re arranging formulas and substituting here and there and nothing seemed to work.

HELP? D:
 
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ninetyfour said:


F = 4(pi^2)(r)(f^2)(m)
Ft min = Fc - mg

- minimum frequency occurs at minimum tension



What kind of force is F in your first equation?
How much is the minimum tension?

ehild
 
F = 4(pi^2)(r)(f^2)(m)

That F is centripetal force. It can also be written as:

F = m(v^2) / r
 
Thinking physically, if the frequency is not high enough what happens? The mass will not make it to the top of the circle, right? It will execute free-fall motion (i.e., a parabola) until the string catches it again. So the key is to consider the top of the circle.

What are the forces acting? Weight and tension. These combine together to provide the centripetal force maintaining the circular motion. The smallest the tension can be is zero. So we want to find the frequency in which the weight alone is able to provide the sufficient centripetal force.

I think you can probably take it from here...
 

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