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

[Jujubee37]

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!

 

[rsk]

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

 

[Jujubee37]

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.

 

[rsk]

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...

Spoiler

you go from F = mv²/r to F = m(3v)²/r

 

[Jujubee37]

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...

Spoiler

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.