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

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The discussion centers on understanding the difference between tension ratios of 3 and 9 in a circular motion context. Participants clarify that the relevant equations are v=2πr/t and F=mv²/r, emphasizing that mass (m) and radius (r) remain constant while velocity (v) changes. This relationship indicates that tension ratios can be understood without specific numerical values. The explanation helps one participant successfully solve their problem. Overall, the focus is on the mathematical relationships governing tension in circular 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
 
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.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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