Math Help - Mechanic conical pendulum taut string

1. Mechanic conical pendulum taut string

I get that if one fixed string tauts, that means the string has a tension, so the condition is T>0. (Correct me plz if its wrong)

But what if we have 2 strings (like in the image) and the question asks for the least value of w in order that strings are taut?
Whats the condition for two strings to taut..? Do both T1 and T2 have to be equal? What happens if one force is bigger than the other?

2. Re: Mechanic conical pendulum taut string

You need the bob to have angular velocity $\omega$ such that the centripetal force keeps the bob at distance P from the center.

If this is done exactly T2=0 and it will be "just taut".

You can work your force equations to find out what value of $\omega$ keeps your bob at distance P from the center.

Remember $a_c = \omega^2 r$ where $a_c$ is the centripetal acceleration, $\omega$ is the angular velocity, and $r$ is the radius of the circular motion.

3. Re: Mechanic conical pendulum taut string

Originally Posted by romsek
You need the bob to have angular velocity $\omega$ such that the centripetal force keeps the bob at distance P from the center.

If this is done exactly T2=0 and it will be "just taut".

You can work your force equations to find out what value of $\omega$ keeps your bob at distance P from the center.

Remember $a_c = \omega^2 r$ where $a_c$ is the centripetal acceleration, $\omega$ is the angular velocity, and $r$ is the radius of the circular motion.
What do u mean by 'just' taut?

So the condition for two strings are taut is only T2=0 regardless T1?
But if 'taut' means having a tension, why is T2=0.. So confusinnnnngg

What happens if one tension is bigger than the other (T1>T2 or T2<T1)?

When does the string break?

Sorry for so many Qs

4. Re: Mechanic conical pendulum taut string

Originally Posted by gahyunkk
What do u mean by 'just' taut?
Just taut means that the tension on it is 0 but it is at full extension. If the angular velocity were any greater then T2>0. If it were any less the second string would be loose.

So the condition for two strings are taut is only T2=0 regardless T1?
no. obviously not. T1 is always > 0 because the bob is hanging from it. Even if $\omega=0$ there would still be tension in string 1 because of this. The tension in string 2 is 0 up until $\omega$ increases to the point that the radius of motion of the bob is P. When the radius is exactly P the tension on string 2 is still 0 but it is now at full extension.

But if 'taut' means having a tension, why is T2=0.. So confusinnnnngg
that's why I said "just taut". Taut means full extension. If you ignore the weight of the string you can have the string at full extension and yet have 0 tension on it.

What happens if one tension is bigger than the other (T1>T2 or T2<T1)?
T1 > T2 always because the bob hangs from it. Draw your force diagram.

When does the string break?
without info about the strength of the string etc. there's no answer to this. Clearly as $\omega$ increases the tension in both strings will increase. Eventually that tension will be greater than the breaking point of the string. If T1 and T2 are identical strings string 1 will always break first.

5. Re: Mechanic conical pendulum taut string

Originally Posted by romsek
Just taut means that the tension on it is 0 but it is at full extension. If the angular velocity were any greater then T2>0. If it were any less the second string would be loose.

no. obviously not. T1 is always > 0 because the bob is hanging from it. Even if $\omega=0$ there would still be tension in string 1 because of this. The tension in string 2 is 0 up until $\omega$ increases to the point that the radius of motion of the bob is P. When the radius is exactly P the tension on string 2 is still 0 but it is now at full extension.

that's why I said "just taut". Taut means full extension. If you ignore the weight of the string you can have the string at full extension and yet have 0 tension on it.

T1 > T2 always because the bob hangs from it. Draw your force diagram.

without info about the strength of the string etc. there's no answer to this. Clearly as $\omega$ increases the tension in both strings will increase. Eventually that tension will be greater than the breaking point of the string. If T1 and T2 are identical strings string 1 will always break first.
Thank you ! It makes sense now. So T1string is taut but T2string is loose at first (and T2=0 here?), but when angular velocity increases and reaches the point where r=P, then T2 is still 0 but both of the strings are taut?
And then if angular velocity futher increases, T2>0 (what's happening for the strings this case when T2 is increasing? Is the position of P going up..?)
So the least value of omega for just taut is when T2=0, and the condition for both are taut will be T2>=0?

Is my understanding correct?

6. Re: Mechanic conical pendulum taut string

Originally Posted by gahyunkk
Thank you ! It makes sense now. So T1string is taut but T2string is loose at first (and T2=0 here?), but when angular velocity increases and reaches the point where r=P, then T2 is still 0 but both of the strings are taut?
yes

And then if angular velocity futher increases, T2>0 (what's happening for the strings this case when T2 is increasing? Is the position of P going up..?)
no. the bob is constrained by the strings. It will remain moving in a circle with radius P but the tension on the strings will increase.

So the least value of omega for just taut is when T2=0, and the condition for both are taut will be T2>=0?

Is my understanding correct?
there's no difference between "just taut" and "taut". They are both taut. "just taut" means the tension happens to be 0. So the $\omega$ where the radius of the circle of motion is P is where both strings become taut.

7. Re: Mechanic conical pendulum taut string

Oh okok so i can say T2>=0 for whenever both strings are taut

8. Re: Mechanic conical pendulum taut string

No. Tension on a string is always positive so T2 >= 0 doesn't say anything.

If the radius of motion = P both strings are taut.

9. Re: Mechanic conical pendulum taut string

Then when im solving the question least value of w in order that strings are taut, is it only T2=0?

10. Re: Mechanic conical pendulum taut string

Originally Posted by gahyunkk
Then when im solving the question least value of w in order that strings are taut, is it only T2=0?
I've explained this about 3 times now. The tension in string 2 will be 0 up until the radius of motion becomes P. At the precise angular velocity that accomplishes this the tension in string 2 will still be 0. At an infinitesimally larger angular velocity T2 now becomes > 0.

Oops..ok..
Thank you!!