Centripetal Force String Tension

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Homework Help Overview

The problem involves two masses tied to strings of different lengths, L and 2L, being swung in unison. The main question is which string will break first as the masses are swung faster. The discussion centers around the concepts of tension, centripetal force, and the effects of string length on these forces.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between tension and string length, questioning how the radius affects centripetal force. There are discussions about using different formulas for tension and centripetal force, including Tension = mv^2/r and Fc = mω^2r. Some participants express confusion about the variables involved, particularly the meaning of ω.

Discussion Status

The discussion is active, with participants providing insights and clarifications about the equations and concepts involved. There is an ongoing exploration of how the string length impacts the forces acting on the masses, and participants are encouraged to consider the implications of angular speed and tangential speed in their reasoning.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is a focus on understanding rather than simply arriving at a solution.

scrambledeggs
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Homework Statement



Two masses M of the same amount are tied to two stings of length L and 2L. If both masses are swung in unison faster and faster, which string will break first?


Homework Equations



The formula I've been using is Tension = mv^2/r.

The Attempt at a Solution



My understanding is that when the string breaks, tension will be 0. If I plug that into the formula the radius/length of the string will not matter. What am I doing wrong here?
 
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Welcome to PF!

But you are looking for the tension in the string just before it breaks.
 
scrambledeggs said:

Homework Statement



Two masses M of the same amount are tied to two stings of length L and 2L. If both masses are swung in unison faster and faster, which string will break first?


Homework Equations



The formula I've been using is Tension = mv^2/r.

The Attempt at a Solution



My understanding is that when the string breaks, tension will be 0. If I plug that into the formula the radius/length of the string will not matter. What am I doing wrong here?
Since the two masses have the same rotational speed, to compare the forces you may wish to use: Fc = mω^2r

AM
 
scrambledeggs said:

Homework Statement



Two masses M of the same amount are tied to two stings of length L and 2L. If both masses are swung in unison faster and faster, which string will break first?


Homework Equations



The formula I've been using is Tension = mv^2/r.

The Attempt at a Solution



My understanding is that when the string breaks, tension will be 0. If I plug that into the formula the radius/length of the string will not matter. What am I doing wrong here?

So what variable in this equation changes due to the string length change and how does it affect your force?
 
Andrew Mason said:
Since the two masses have the same rotational speed, to compare the forces you may wish to use: Fc = mω^2r

AM

What is the value ω stand for? I don't think I'm familiar with that equation.

kinematics said:
So what variable in this equation changes due to the string length change and how does it affect your force?

Because the radius is the only thing that changes in the equation, this is what I'm thinking:

Fc = mv2/r

and

Fc = mv2/2r
2Fc = mv2/r

Therefore the longer the string the larger the centripetal force/tension. Am I correct or completely off?
 
scrambledeggs said:
What is the value ω stand for? I don't think I'm familiar with that equation.
ω is the angular speed in radians per second. There are 2π radians in a circle so if the number of rotations per second is f the angular speed is 2πf. Since T = 1/f you can express ω = 2π/T. Tangential speed v = ωr so mv2/r = mω2r = m4π2r/T2

Can you see how to use this to compare the centripetal force on each of these two rotating masses?
Because the radius is the only thing that changes in the equation, this is what I'm thinking:

Fc = mv2/r

and

Fc = mv2/2r
2Fc = mv2/r

Therefore the longer the string the larger the centripetal force/tension. Am I correct or completely off?

You have provided an excellent example of why getting the right answer is not very important when you are a student.

Are the tangential speeds the same for each rotating mass? Can you compare the tangential speeds? (hint: Can you see why using ω makes this a lot easier?)

AM
 

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