What Is the Difference Between Tension Ratios of 3 and 9?

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SUMMARY

The discussion clarifies the relationship between tension ratios of 3 and 9 in circular motion, emphasizing the importance of understanding the equations v=2πr/t and F=mv²/r. It establishes that tension does not increase linearly with ratios but rather depends on the velocity (v) while mass (m) and radius (r) remain constant. The key takeaway is that analyzing the equations reveals the dependency of force on velocity, rather than requiring numerical values for calculation.

PREREQUISITES
  • Understanding of circular motion dynamics
  • Familiarity with the equations of motion: v=2πr/t and F=mv²/r
  • Basic knowledge of physics concepts such as mass and force
  • Ability to interpret relationships between variables in equations
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  • Explore the derivation of the equations v=2πr/t and F=mv²/r
  • Investigate the concept of centripetal force in circular motion
  • Learn about the effects of varying velocity on tension in different scenarios
  • Study practical applications of tension ratios in engineering and physics
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Students studying physics, educators teaching circular motion concepts, and anyone interested in the mathematical relationships governing forces in motion.

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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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An equation which links the 'swinging' speed to the force requred to keep it moving in a circle would certainly help.
 
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.
 
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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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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