Exploring Tension Ratios: 3 vs. 9

In summary, the conversation discusses the use of equations to determine the force required to keep an object moving in a circle. The equations v=2pir/t and f=mv^2/r are mentioned and it is explained that in the given problem, only the velocity changes while mass and radius remain constant. This information helps the individual solve the problem successfully.
  • #1
Jujubee37
22
4
Homework Statement
a ball is tied onto a string and is swung around in a circle. If the swinging speed is tripled, what would happen to the tension force in the string?
Relevant Equations
I am actually not sure if an equation would come in play here. Is this an equation problem or kind of just an application type problem.
I was thinking it would 3 or 9 times the tension rather than 1/3 or 1/9 but that is just a guess. an explanation would help very much!
 
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  • #2
An equation which links the 'swinging' speed to the force requred to keep it moving in a circle would certainly help.
 
  • #3
rsk said:
An equation which links the 'swinging' speed to the force requred to keep it moving in a circle would certainly help.
Yes okay thanks. I have two formulas for that. v=2pir/t and f=mv^2/r. If I used those equations how would I apply those to the problem because I was not given numbers to plug in.
 
  • #4
You don't need numbers, just look at what those equations tell you about the relation.

In the equation you've written there, F depends on m, v and r. In the question you've been given, m and r do not change, only v does. So...

you go from F = mv²/r to F = m(3v)²/r
 
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  • #5
rsk said:
You don't need numbers, just look at what those equations tell you about the relation.

In the equation you've written there, F depends on m, v and r. In the question you've been given, m and r do not change, only v does. So...

you go from F = mv²/r to F = m(3v)²/r
ohhh okay that explained a lot. Thank you I got the problem right.
 
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1. What is the purpose of exploring tension ratios?

The purpose of exploring tension ratios is to understand the relationship between two different levels of tension and how it affects a system or object. By studying tension ratios, scientists can gain insight into the behavior and properties of materials, structures, and systems.

2. How do you determine the tension ratio of 3 vs. 9?

The tension ratio is determined by dividing the higher tension value by the lower tension value. So for a tension ratio of 3 vs. 9, the ratio would be 9/3 = 3. This means that the higher tension is three times greater than the lower tension.

3. What are some examples of tension ratios in real-world applications?

Tension ratios can be seen in various real-world applications, such as bridge construction, cable-stayed structures, and suspension systems. In these cases, the tension ratio is an important factor in determining the stability and strength of the structure.

4. How does a tension ratio of 3 vs. 9 affect the behavior of a material?

A tension ratio of 3 vs. 9 can have different effects on different materials. In general, a higher tension ratio means that the material is under more stress and may be more prone to deformation or failure. However, some materials may exhibit different behaviors, such as strain hardening, under different tension ratios.

5. What are the potential implications of studying tension ratios?

The study of tension ratios can have various implications, such as improving the design and construction of structures, developing new materials with specific tension ratio properties, and understanding the mechanics of tension in biological systems. This research can also lead to advancements in industries such as aerospace, civil engineering, and biomechanics.

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