Tension in a string (Kleppner 2.23)

In summary, the problem involves a piece of string of length l and mass M that is fastened into a circular loop and set spinning with uniform angular velocity ω. To find the tension in the string, a force diagram is suggested for a small piece of the loop subtending a small angle Δθ. Using the equation F=ma and solving for tension, the answer is found to be Mω^2l/4π^2. The limits for the tension are integrated from 0 to 2π, and the solution can be found in Kleppner's book in problem 2.23.
  • #1
decerto
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Homework Statement


A piece of string of length I and mass M is fastened into a circular loop and set spinning about the center of a circle with uniform angular velocity ω. Find the tension in the string. Suggestion: Draw a force diagram for a small piece of the loop subtending a small angle Δθ

Homework Equations



F=ma

The Attempt at a Solution



http://imgur.com/nAObr
http://imgur.com/kLLEH

No idea if its the right track, but it seemed a similar problem to one of the examples given. The answer is Mω^(2)l/4pi^(2), What I have in my integral so I think I've done it wrong because If I integrate from 0 to 2pi(the whole string) it will cancel out one of the 2pi's
Also I have no idea what I would even use as limits for the tension.

Its from kleppners book 2.23 also btw

edit* solved it, I was off with the forces causing the circular motion. You need to take the componenets of the two tensions acting inwards and set it equal to the ma I had
 
Last edited:
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  • #2
for the small piece of string. Doing that you can solve for tension and then integrate it from 0 to 2pi
 

1. What is tension in a string?

Tension in a string is the amount of force applied to the string in order to keep it taut and prevent it from breaking or becoming slack.

2. How is tension calculated in a string?

Tension in a string can be calculated using the equation T = F * L, where T is the tension, F is the force applied to the string, and L is the length of the string.

3. What factors affect tension in a string?

The tension in a string is affected by the force applied to the string, the length of the string, and the properties of the material the string is made of (such as elasticity and density).

4. How does tension affect the speed of a wave traveling through a string?

Tension in a string has a direct relationship with the speed of a wave traveling through the string. As tension increases, the speed of the wave also increases.

5. What is the significance of tension in everyday life?

Tension in strings is important in various everyday activities, such as playing musical instruments, construction, and sports. It helps to keep structures stable and allows for the transmission of energy through the string.

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