Question

What happens when v is increasing (i) slightly, (ii) infinite large ?
equation below:

Answer 1

\(\Large{v= \sqrt{tan \theta g l sin \theta}}\)

Answer 2

v=speed
l=length of a string
g=acceleration due to gravity

Answer 3

Your question does not make sense, but I'll try to answer it anyway.
When v is increasing, the string will swing up higher, so theta increases as well.

Answer 4

i know that it doesn't make sense, that's why I ask.
i'm thinking that it is referring to the relationships between the speed, v, with the other variables but i'm not sure

Answer 5

I'm not even thinking about the physical meaning, just the relationship that's expressed by math.
\(v=\sqrt{\tan(\theta)gl\cos(\theta)}\)
\(g\) and \(l\) are constant.
\(v=\sqrt{\tan(\theta)\cos(\theta)}\sqrt{gl}=\sqrt{\dfrac{\sin\theta}{\cancel{\cos\theta}}\cancel{\cos(\theta)}}\sqrt{gl}=\sqrt{\sin(\theta)}\sqrt{gl}\)
So,
\(v= \sqrt{\sin(\theta)}\sqrt{g\ l\ }\)
Right?
If v gets slightly bigger, \(g\) and \(l\) can get slightly bigger. Or, the \(\theta\rightarrow\dfrac\pi 2\).
If it goes to \(\infty\), then you know it can't be \(\theta\)... So....

Do you see what I mean?

Answer 6

Let me know if you have any questions on this!

Answer 7

why did you use cos theta?The equation uses sin theta.

Answer 8

Haha, thanks! Because I made a mistake!

Answer 9

@AntiNode

Answer 10

but is the relationship still be the same or not? O.o

Answer 11

So, just don't simplify I guess!
Notice that as \(\theta\rightarrow \dfrac\pi2\), \(tan\theta\rightarrow\infty\).

Answer 12

But the \(g\) and \(l\) can still be changing the same.
No normal situation will have \(l\) or \(g\) go to \(\infty\), and I don't think that \(\theta\rightarrow\dfrac\pi2\)\(\implies v\rightarrow\infty\) in the swinging example... But, that's what the math looks like to me.

Answer 13

i'm just wondering. is there a difference when the speed is increasing "SLIGHTLY" or "INFINITELY LARGE" ? because it looks same to me. Both cases are increasing so what's the difference?

Answer 14

@agent0smith please?

Answer 15

Is this the actual question? Post a screenshot of it.

Answer 16

As v increases the angle increases. As v approaches infinity, the angle approaches 90 degrees.

Answer 17

@theEric that's what happens. You can try it with an object on a string - as you swing faster, the angle comes closer to being horizontal.

Answer 18

only for letter c

Answer 19

Then yeah, what i said above. If v increases then sin and tan theta must also increase, since g and l are constants

Answer 20

oh okay....
thanks...!
one more thing...
is there a difference when the speed is increasing "SLIGHTLY" or "INFINITELY LARGE" ? because the question asked it separately..

Answer 21

oh nvm :)
thanks!

Answer 22

I think they're just asking what happens if the speed increases a little - the angle increases

infinitely large - angle approaches 90 degrees

note the the first answer doesn't necessarily lead you to the second, that's why they ask both.